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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html" class="active"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html" class="active"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html" class="active"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html" class="active"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html" class="active"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html" class="active"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html" class="active"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html" class="active"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<h1><a class="header" href="#elliptic-curve-cryptography" id="elliptic-curve-cryptography">Elliptic Curve Cryptography</a></h1>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html" class="active"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html" class="active"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html" class="active"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html" class="active"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html" class="active"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html" class="active"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html" class="active"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html" class="active"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html" class="active"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html" class="active"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html" class="active">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html" class="active">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html" class="active"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="index.html">Orchard</a></li><li class="chapter-item expanded "><a href="concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="user.html" class="active"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html" class="active"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html" class="active"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html" class="active"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html" class="active"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html" class="active"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html" class="active"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html" class="active"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li></ol></li></ol>
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<ol class="chapter"><li class="chapter-item expanded affix "><a href="../index.html">Orchard</a></li><li class="chapter-item expanded "><a href="../concepts.html"><strong aria-hidden="true">1.</strong> Concepts</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../concepts/preliminaries.html"><strong aria-hidden="true">1.1.</strong> Preliminaries</a></li></ol></li><li class="chapter-item expanded "><a href="../user.html"><strong aria-hidden="true">2.</strong> User Documentation</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../user/keys.html"><strong aria-hidden="true">2.1.</strong> Creating keys and addresses</a></li><li class="chapter-item expanded "><a href="../user/creating-notes.html"><strong aria-hidden="true">2.2.</strong> Creating notes</a></li><li class="chapter-item expanded "><a href="../user/spending-notes.html" class="active"><strong aria-hidden="true">2.3.</strong> Spending notes</a></li><li class="chapter-item expanded "><a href="../user/integration.html"><strong aria-hidden="true">2.4.</strong> Integration into an existing chain</a></li></ol></li><li class="chapter-item expanded "><a href="../design.html"><strong aria-hidden="true">3.</strong> Design</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/keys.html"><strong aria-hidden="true">3.1.</strong> Keys and addresses</a></li><li class="chapter-item expanded "><a href="../design/actions.html"><strong aria-hidden="true">3.2.</strong> Actions</a></li><li class="chapter-item expanded "><a href="../design/commitments.html"><strong aria-hidden="true">3.3.</strong> Commitments</a></li><li class="chapter-item expanded "><a href="../design/commitment-tree.html"><strong aria-hidden="true">3.4.</strong> Commitment tree</a></li><li class="chapter-item expanded "><a href="../design/nullifiers.html"><strong aria-hidden="true">3.5.</strong> Nullifiers</a></li><li class="chapter-item expanded "><a href="../design/signatures.html"><strong aria-hidden="true">3.6.</strong> Signatures</a></li><li class="chapter-item expanded "><a href="../design/circuit.html"><strong aria-hidden="true">3.7.</strong> Circuit</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets.html"><strong aria-hidden="true">3.7.1.</strong> Gadgets</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc.html"><strong aria-hidden="true">3.7.1.1.</strong> Elliptic curve cryptography</a></li><li><ol class="section"><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/complete-add.html"><strong aria-hidden="true">3.7.1.1.1.</strong> Complete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/incomplete-add.html"><strong aria-hidden="true">3.7.1.1.2.</strong> Incomplete addition</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/fixed-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.3.</strong> Fixed-base scalar multiplication</a></li><li class="chapter-item expanded "><a href="../design/circuit/gadgets/ecc/var-base-scalar-mul.html"><strong aria-hidden="true">3.7.1.1.4.</strong> Variable-base scalar multiplication</a></li></ol></li></ol></li></ol></li></ol></li></ol>
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