mirror of https://github.com/zcash/zips.git
address comment, update spec ref, add paper ref
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Conrado Gouvea
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@ -135,7 +135,7 @@ written.
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<tr> <td><span class="reserved">309</span></td> <td class="left"><a class="reserved" href="zips/zip-0309.rst">Blind Off-chain Lightweight Transactions (BOLT)</a></td> <td>Reserved</td>
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<tr> <td>310</td> <td class="left"><a href="zips/zip-0310.rst">Security Properties of Sapling Viewing Keys</a></td> <td>Draft</td>
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<tr> <td>311</td> <td class="left"><a href="zips/zip-0311.rst">Zcash Payment Disclosures</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">312</span></td> <td class="left"><a class="reserved" href="zips/zip-0312.rst">Shielded Multisignatures using FROST</a></td> <td>Reserved</td>
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<tr> <td>312</td> <td class="left"><a href="zips/zip-0312.rst">FROST for Spend Authorization Multisignatures</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">314</span></td> <td class="left"><a class="reserved" href="zips/zip-0314.rst">Privacy upgrades to the Zcash light client protocol</a></td> <td>Reserved</td>
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<tr> <td>315</td> <td class="left"><a href="zips/zip-0315.rst">Best Practices for Wallet Implementations</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">318</span></td> <td class="left"><a class="reserved" href="zips/zip-0318.rst">Associated Payload Encryption</a></td> <td>Reserved</td>
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@ -267,7 +267,7 @@ Index of ZIPs
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<tr> <td><span class="reserved">309</span></td> <td class="left"><a class="reserved" href="zips/zip-0309.rst">Blind Off-chain Lightweight Transactions (BOLT)</a></td> <td>Reserved</td>
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<tr> <td>310</td> <td class="left"><a href="zips/zip-0310.rst">Security Properties of Sapling Viewing Keys</a></td> <td>Draft</td>
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<tr> <td>311</td> <td class="left"><a href="zips/zip-0311.rst">Zcash Payment Disclosures</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">312</span></td> <td class="left"><a class="reserved" href="zips/zip-0312.rst">Shielded Multisignatures using FROST</a></td> <td>Reserved</td>
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<tr> <td>312</td> <td class="left"><a href="zips/zip-0312.rst">FROST for Spend Authorization Multisignatures</a></td> <td>Draft</td>
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<tr> <td><strike>313</strike></td> <td class="left"><strike><a href="zips/zip-0313.rst">Reduce Conventional Transaction Fee to 1000 zatoshis</a></strike></td> <td>Obsolete</td>
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<tr> <td><span class="reserved">314</span></td> <td class="left"><a class="reserved" href="zips/zip-0314.rst">Privacy upgrades to the Zcash light client protocol</a></td> <td>Reserved</td>
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<tr> <td>315</td> <td class="left"><a href="zips/zip-0315.rst">Best Practices for Wallet Implementations</a></td> <td>Draft</td>
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@ -100,7 +100,7 @@
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<tr> <td><span class="reserved">309</span></td> <td class="left"><a class="reserved" href="zip-0309">Blind Off-chain Lightweight Transactions (BOLT)</a></td> <td>Reserved</td>
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<tr> <td>310</td> <td class="left"><a href="zip-0310">Security Properties of Sapling Viewing Keys</a></td> <td>Draft</td>
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<tr> <td>311</td> <td class="left"><a href="zip-0311">Zcash Payment Disclosures</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">312</span></td> <td class="left"><a class="reserved" href="zip-0312">Shielded Multisignatures using FROST</a></td> <td>Reserved</td>
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<tr> <td>312</td> <td class="left"><a href="zip-0312">FROST for Spend Authorization Multisignatures</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">314</span></td> <td class="left"><a class="reserved" href="zip-0314">Privacy upgrades to the Zcash light client protocol</a></td> <td>Reserved</td>
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<tr> <td>315</td> <td class="left"><a href="zip-0315">Best Practices for Wallet Implementations</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">318</span></td> <td class="left"><a class="reserved" href="zip-0318">Associated Payload Encryption</a></td> <td>Reserved</td>
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@ -213,7 +213,7 @@
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<tr> <td><span class="reserved">309</span></td> <td class="left"><a class="reserved" href="zip-0309">Blind Off-chain Lightweight Transactions (BOLT)</a></td> <td>Reserved</td>
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<tr> <td>310</td> <td class="left"><a href="zip-0310">Security Properties of Sapling Viewing Keys</a></td> <td>Draft</td>
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<tr> <td>311</td> <td class="left"><a href="zip-0311">Zcash Payment Disclosures</a></td> <td>Draft</td>
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<tr> <td><span class="reserved">312</span></td> <td class="left"><a class="reserved" href="zip-0312">Shielded Multisignatures using FROST</a></td> <td>Reserved</td>
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<tr> <td>312</td> <td class="left"><a href="zip-0312">FROST for Spend Authorization Multisignatures</a></td> <td>Draft</td>
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<tr> <td><strike>313</strike></td> <td class="left"><strike><a href="zip-0313">Reduce Conventional Transaction Fee to 1000 zatoshis</a></strike></td> <td>Obsolete</td>
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<tr> <td><span class="reserved">314</span></td> <td class="left"><a class="reserved" href="zip-0314">Privacy upgrades to the Zcash light client protocol</a></td> <td>Reserved</td>
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<tr> <td>315</td> <td class="left"><a href="zip-0315">Best Practices for Wallet Implementations</a></td> <td>Draft</td>
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@ -19,7 +19,7 @@ License: MIT
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Discussions-To: <<a href="https://github.com/zcash/zips/issues/382">https://github.com/zcash/zips/issues/382</a>>
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Pull-Request: <<a href="https://github.com/zcash/zips/pull/662">https://github.com/zcash/zips/pull/662</a>></pre>
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<section id="terminology"><h2><span class="section-heading">Terminology</span><span class="section-anchor"> <a rel="bookmark" href="#terminology"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
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<p>{Edit this to reflect the key words that are actually used.} The key words "MUST", "MUST NOT", "SHOULD", and "MAY" in this document are to be interpreted as described in RFC 2119. <a id="id1" class="footnote_reference" href="#rfc2119">2</a></p>
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<p>{Edit this to reflect the key words that are actually used.} The key words "MUST", "MUST NOT", "SHOULD", and "MAY" in this document are to be interpreted as described in RFC 2119. <a id="footnote-reference-1" class="footnote_reference" href="#rfc2119">2</a></p>
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<p>The terms below are to be interpreted as follows:</p>
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<dl>
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<dt>Unlinkability</dt>
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@ -27,17 +27,17 @@ Pull-Request: <<a href="https://github.com/zcash/zips/pull/662">https://githu
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</dl>
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</section>
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<section id="abstract"><h2><span class="section-heading">Abstract</span><span class="section-anchor"> <a rel="bookmark" href="#abstract"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
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<p>This proposal adapts FROST <a id="id2" class="footnote_reference" href="#frost">3</a>, a threshold signature scheme, to make it unlinkable, which is a requirement for its use in the Zcash protocol. The adapted scheme generates signatures compatible with spend authorization signatures in the Zcash protocol, for the Sapling and Orchard shielded pools.</p>
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<p>This proposal adapts FROST <a id="footnote-reference-2" class="footnote_reference" href="#frost">3</a>, a threshold signature scheme, to make it unlinkable, which is a requirement for its use in the Zcash protocol. The adapted scheme generates signatures compatible with spend authorization signatures in the Sapling and Orchard shielded protocols as deployed in Zcash.</p>
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</section>
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<section id="motivation"><h2><span class="section-heading">Motivation</span><span class="section-anchor"> <a rel="bookmark" href="#motivation"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
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<p>In the Zcash protocol, Spend Authorization Signatures are employed to authorize a transaction. The ability to generate these signatures with the user's private key is what effectively allows the user to spend funds.</p>
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<p>This is a security-critical step, since anyone who obtains access to the private key will be able to spend the user's funds. For this reason, one interesting possibility is to require multiple parties to allow the transaction to go through. This can be accomplished with threshold signatures, where the private key is split between parties (or generated already split using a distributed protocol) in a way that a threshold (e.g. 2 out of 3) of them must sign the transaction in order to create the final signature. This enables scenarios such as users and third-party services sharing custody of a wallet, or a group of people managing shared funds, for example.</p>
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<p>FROST is one of such threshold signature protocols. However, it can't be used as-is since the Zcash protocol also requires re-randomizing public and private keys to ensure unlinkability between transactions. This ZIP specifies a variant of FROST with re-randomization support.</p>
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<p>FROST is one of such threshold signature protocols. However, it can't be used as-is since the Zcash protocol also requires re-randomizing public and private keys to ensure unlinkability between transactions. This ZIP specifies a variant of FROST with re-randomization support. This variant is named "Re-Randomized FROST" and has been described in <a id="footnote-reference-3" class="footnote_reference" href="#frost-rerandomized">4</a>.</p>
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</section>
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<section id="requirements"><h2><span class="section-heading">Requirements</span><span class="section-anchor"> <a rel="bookmark" href="#requirements"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
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<ul>
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<li>All signatures generated by following this ZIP must be verified successfully as Sapling or Orchard spend authorization signatures using the appropriate validating key.</li>
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<li>The signatures generated by following this ZIP should meet the security criteria for Signature with Re-Randomizable Keys as specified in the Zcash protocol <a id="id3" class="footnote_reference" href="#protocol-concretereddsa">11</a>.</li>
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<li>The signatures generated by following this ZIP should meet the security criteria for Signature with Re-Randomizable Keys as specified in the Zcash protocol <a id="footnote-reference-4" class="footnote_reference" href="#protocol-concretereddsa">12</a>.</li>
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<li>The threat model described below must be taken into account.</li>
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</ul>
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<section id="threat-model"><h3><span class="section-heading">Threat Model</span><span class="section-anchor"> <a rel="bookmark" href="#threat-model"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h3>
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@ -50,7 +50,7 @@ Pull-Request: <<a href="https://github.com/zcash/zips/pull/662">https://githu
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<p>When employing re-randomizable FROST as specified in this ZIP, the goal is to split the spend authorization private key
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<span class="math">\(\mathsf{ask}\)</span>
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among multiple possible signers. This means that the proof generation will still be performed by a single participant, likely the one that created the transaction in the first place. Note that this user already controls the privacy of the transaction since they are responsible for creating the proof.</p>
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<p>This fits well into the "Coordinator" role from the FROST specification <a id="id4" class="footnote_reference" href="#frost-protocol">4</a>. The Coordinator is responsible for sending the message to be signed to all participants, and to aggregate the signature shares.</p>
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<p>This fits well into the "Coordinator" role from the FROST specification <a id="footnote-reference-5" class="footnote_reference" href="#frost-protocol">5</a>. The Coordinator is responsible for sending the message to be signed to all participants, and to aggregate the signature shares.</p>
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<p>With those considerations in mind, the threat model considered in this ZIP is:</p>
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<ul>
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<li>The Coordinator is trusted with the privacy of the transaction (which includes the unlinkability property). A rogue Coordinator will be able to break unlinkability and privacy, but should not be able to create signed transactions without the approval of <code>MIN_PARTICIPANTS</code> participants, as specified in FROST.</li>
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@ -60,38 +60,38 @@ Pull-Request: <<a href="https://github.com/zcash/zips/pull/662">https://githu
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</section>
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<section id="non-requirements"><h2><span class="section-heading">Non-requirements</span><span class="section-anchor"> <a rel="bookmark" href="#non-requirements"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
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<ul>
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<li>This ZIP does not support removing the Coordinator role, as described in <a id="id5" class="footnote_reference" href="#frost-removingcoordinator">5</a>.</li>
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<li>This ZIP does not support removing the Coordinator role, as described in <a id="footnote-reference-6" class="footnote_reference" href="#frost-removingcoordinator">6</a>.</li>
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<li>This ZIP does not prevent key share holders from linking the signing operation to a transaction in the blockchain.</li>
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<li>Like the FROST specification <a id="id6" class="footnote_reference" href="#frost">3</a>, this ZIP does not specify a key generation procedure; but refer to that specification for guidelines.</li>
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<li>Like the FROST specification <a id="footnote-reference-7" class="footnote_reference" href="#frost">3</a>, this ZIP does not specify a key generation procedure; but refer to that specification for guidelines.</li>
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<li>Network privacy is not in scope for this ZIP, and must be obtained with other tools if desired.</li>
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</ul>
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</section>
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<section id="specification"><h2><span class="section-heading">Specification</span><span class="section-anchor"> <a rel="bookmark" href="#specification"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
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<p>Algorithms in this section are specified using Python pseudo-code, in the same fashion as the FROST specification <a id="id7" class="footnote_reference" href="#frost">3</a>.</p>
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<p>The types Scalar, Element, and G are defined in <a id="id8" class="footnote_reference" href="#frost-primeordergroup">6</a>, as well as the notation for elliptic-curve arithmetic, which uses the additive notation. Note that this notation differs from that used in the Zcash Protocol Specification. For example, <code>G.ScalarMult(P, k)</code> is used for scalar multiplication, where the protocol spec would use
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<p>Algorithms in this section are specified using Python pseudo-code, in the same fashion as the FROST specification <a id="footnote-reference-8" class="footnote_reference" href="#frost">3</a>.</p>
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<p>The types Scalar, Element, and G are defined in <a id="footnote-reference-9" class="footnote_reference" href="#frost-primeordergroup">7</a>, as well as the notation for elliptic-curve arithmetic, which uses the additive notation. Note that this notation differs from that used in the Zcash Protocol Specification. For example, <code>G.ScalarMult(P, k)</code> is used for scalar multiplication, where the protocol spec would use
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<span class="math">\([k] P\)</span>
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with the group implied by
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<span class="math">\(P\)</span>
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.</p>
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<p>An additional per-ciphersuite hash function is used, denote <code>HR(m)</code>, which receives an arbitrary-sized byte string and returns a Scalar. It is defined concretely in the Ciphersuites section.</p>
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<section id="key-generation"><h3><span class="section-heading">Key Generation</span><span class="section-anchor"> <a rel="bookmark" href="#key-generation"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h3>
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<p>While key generation is out of scope for this ZIP and the FROST spec <a id="footnote-reference-10" class="footnote_reference" href="#frost">3</a>, it needs to be consistent with FROST, see <a id="footnote-reference-11" class="footnote_reference" href="#frost-tdkg">9</a> for guidance. The spend authorization private key
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<span class="math">\(\mathsf{ask}\)</span>
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<a id="footnote-reference-12" class="footnote_reference" href="#protocol-spendauthsig">14</a> is the particular key that must be used in the context of this ZIP. Note that the
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<span class="math">\(\mathsf{ask}\)</span>
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is usually derived from the spending key
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<span class="math">\(\mathsf{sk}\)</span>
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, though that is not required. Not doing so allows using distributed key generation, since the key it generates is unpredictable. Note however that not deriving
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<span class="math">\(\mathsf{ask}\)</span>
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from
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<span class="math">\(\mathsf{sk}\)</span>
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prevents using seed phrases to recover the original secret (which may be something desirable in the context of FROST).</p>
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</section>
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<section id="re-randomizable-frost"><h3><span class="section-heading">Re-randomizable FROST</span><span class="section-anchor"> <a rel="bookmark" href="#re-randomizable-frost"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h3>
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<p>To add re-randomization to FROST, follow the specification <a id="id9" class="footnote_reference" href="#frost">3</a> with the following modifications.</p>
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<section id="key-generation"><h4><span class="section-heading">Key Generation</span><span class="section-anchor"> <a rel="bookmark" href="#key-generation"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h4>
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<p>While key generation is out of scope for this ZIP and the FROST spec <a id="id10" class="footnote_reference" href="#frost">3</a>, it needs to be consistent with FROST, see <a id="id11" class="footnote_reference" href="#frost-tdkg">8</a> for guidance. The spend authorization private key
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<span class="math">\(\mathsf{ask}\)</span>
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<a id="id12" class="footnote_reference" href="#protocol-spendauthsig">13</a> is the particular key that must be used in the context of this ZIP. Note that the
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<span class="math">\(\mathsf{ask}\)</span>
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is usually derived from the spending key
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<span class="math">\(\mathsf{sk}\)</span>
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, though that is not required. Not doing so allows using distributed key generation, since the key it generates is unpredictable. Note however that not deriving
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<span class="math">\(\mathsf{ask}\)</span>
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from
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<span class="math">\(\mathsf{sk}\)</span>
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prevents using seed phrases to recover the original secret (which may be something desirable in the context of FROST).</p>
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</section>
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<p>To add re-randomization to FROST, follow the specification <a id="footnote-reference-13" class="footnote_reference" href="#frost">3</a> with the following modifications.</p>
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<section id="randomizer-generation"><h4><span class="section-heading">Randomizer Generation</span><span class="section-anchor"> <a rel="bookmark" href="#randomizer-generation"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h4>
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<p>A new helper function is defined, which generates a randomizer. The <cite>encode_signing_package</cite> is defined as the byte serialization of the <cite>msg</cite>, <cite>commitment_list</cite> values as described in <a id="id13" class="footnote_reference" href="#frost-serialization">10</a>. Implementations MAY choose another encoding as long as all values (the message, and the identifier, binding nonce and hiding nonce for each participant) are unambiguously encoded.</p>
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<p>The function <cite>random_bytes(n)</cite> is defined in <a id="id14" class="footnote_reference" href="#frost">3</a> and it returns a buffer with <cite>n</cite> bytes sampled uniformly at random. The constant <cite>Ns</cite> is also specified in <a id="id15" class="footnote_reference" href="#frost">3</a> and is the size of a serialized scalar.</p>
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<p>A new helper function is defined, which generates a randomizer. The <cite>encode_signing_package</cite> is defined as the byte serialization of the <cite>msg</cite>, <cite>commitment_list</cite> values as described in <a id="footnote-reference-14" class="footnote_reference" href="#frost-serialization">11</a>. Implementations MAY choose another encoding as long as all values (the message, and the identifier, binding nonce and hiding nonce for each participant) are unambiguously encoded.</p>
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<p>The function <cite>random_bytes(n)</cite> is defined in <a id="footnote-reference-15" class="footnote_reference" href="#frost">3</a> and it returns a buffer with <cite>n</cite> bytes sampled uniformly at random. The constant <cite>Ns</cite> is also specified in <a id="footnote-reference-16" class="footnote_reference" href="#frost">3</a> and is the size of a serialized scalar.</p>
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<pre>randomizer_generate():
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Inputs:
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return HR(randomizer_input)</pre>
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</section>
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<section id="round-one-commitment"><h4><span class="section-heading">Round One - Commitment</span><span class="section-anchor"> <a rel="bookmark" href="#round-one-commitment"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h4>
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<p>Roune One is exactly the same as specified <a id="id16" class="footnote_reference" href="#frost">3</a>. But for context, it involves these steps:</p>
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<p>Roune One is exactly the same as specified <a id="footnote-reference-17" class="footnote_reference" href="#frost">3</a>. But for context, it involves these steps:</p>
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<ul>
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<li>Each signer generates nonces and their corresponding public commitments. A nonce is a pair of Scalar values, and a commitment is a pair of Element values.</li>
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<li>The nonces are stored locally by the signer and kept private for use in the second round.</li>
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@ -143,37 +143,37 @@ def randomizer_generate(msg, commitment_list):
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</section>
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<section id="ciphersuites"><h3><span class="section-heading">Ciphersuites</span><span class="section-anchor"> <a rel="bookmark" href="#ciphersuites"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h3>
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<section id="frost-jubjub-blake2b-512"><h4><span class="section-heading">FROST(Jubjub, BLAKE2b-512)</span><span class="section-anchor"> <a rel="bookmark" href="#frost-jubjub-blake2b-512"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h4>
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<p>This ciphersuite uses Jubjub for the Group and BLAKE2b-512 for the Hash function <code>H</code> meant to produce signatures indistinguishable from RedJubjub Sapling Spend Authorization Signatures as specified in <a id="id17" class="footnote_reference" href="#protocol-concretespendauthsig">12</a>.</p>
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<p>This ciphersuite uses Jubjub for the Group and BLAKE2b-512 for the Hash function <code>H</code> meant to produce signatures indistinguishable from RedJubjub Sapling Spend Authorization Signatures as specified in <a id="footnote-reference-18" class="footnote_reference" href="#protocol-concretespendauthsig">13</a>.</p>
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<ul>
|
||||
<li>Group: Jubjub <a id="id18" class="footnote_reference" href="#protocol-jubjub">14</a> with base point
|
||||
<li>Group: Jubjub <a id="footnote-reference-19" class="footnote_reference" href="#protocol-jubjub">15</a> with base point
|
||||
<span class="math">\(\mathcal{G}^{\mathsf{Sapling}}\)</span>
|
||||
as defined in <a id="id19" class="footnote_reference" href="#protocol-concretespendauthsig">12</a>.
|
||||
as defined in <a id="footnote-reference-20" class="footnote_reference" href="#protocol-concretespendauthsig">13</a>.
|
||||
<ul>
|
||||
<li>Order:
|
||||
<span class="math">\(r_\mathbb{J}\)</span>
|
||||
as defined in <a id="id20" class="footnote_reference" href="#protocol-jubjub">14</a>.</li>
|
||||
<li>Identity: as defined in <a id="id21" class="footnote_reference" href="#protocol-jubjub">14</a>.</li>
|
||||
as defined in <a id="footnote-reference-21" class="footnote_reference" href="#protocol-jubjub">15</a>.</li>
|
||||
<li>Identity: as defined in <a id="footnote-reference-22" class="footnote_reference" href="#protocol-jubjub">15</a>.</li>
|
||||
<li>RandomScalar(): Implemented by returning a uniformly random Scalar in the range [0, <code>G.Order()</code> - 1]. Refer to {{frost-randomscalar}} for implementation guidance.</li>
|
||||
<li>SerializeElement(P): Implemented as
|
||||
<span class="math">\(\mathsf{repr}_\mathbb{J}(P)\)</span>
|
||||
as defined in <a id="id22" class="footnote_reference" href="#protocol-jubjub">14</a></li>
|
||||
as defined in <a id="footnote-reference-23" class="footnote_reference" href="#protocol-jubjub">15</a></li>
|
||||
<li>DeserializeElement(P): Implemented as
|
||||
<span class="math">\(\mathsf{abst}_\mathbb{J}(P)\)</span>
|
||||
as defined in <a id="id23" class="footnote_reference" href="#protocol-jubjub">14</a>, returning an error if
|
||||
as defined in <a id="footnote-reference-24" class="footnote_reference" href="#protocol-jubjub">15</a>, returning an error if
|
||||
<span class="math">\(\bot\)</span>
|
||||
is returned. Additionally, this function validates that the resulting element is not the group identity element, returning an error if the check fails.</li>
|
||||
<li>SerializeScalar: Implemented by outputting the little-endian 32-byte encoding of the Scalar value.</li>
|
||||
<li>DeserializeScalar: Implemented by attempting to deserialize a Scalar from a little-endian 32-byte string. This function can fail if the input does not represent a Scalar in the range [0, <code>G.Order()</code> - 1].</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li>Hash (<code>H</code>): BLAKE2b-512 <a id="id24" class="footnote_reference" href="#blake">1</a> (BLAKE2b with 512-bit output and 16-byte personalization string), and Nh = 64.
|
||||
<li>Hash (<code>H</code>): BLAKE2b-512 <a id="footnote-reference-25" class="footnote_reference" href="#blake">1</a> (BLAKE2b with 512-bit output and 16-byte personalization string), and Nh = 64.
|
||||
<ul>
|
||||
<li>H1(m): Implemented by computing BLAKE2b-512("FROST_RedJubjubR", m), interpreting the 64 bytes as a little-endian integer, and reducing the resulting integer modulo <code>G.Order()</code>.</li>
|
||||
<li>H2(m): Implemented by computing BLAKE2b-512("Zcash_RedJubjubH", m), interpreting the 64 bytes as a little-endian integer, and reducing the resulting integer modulo <code>G.Order()</code>. (This is equivalent to
|
||||
<span class="math">\(\mathsf{H}^\circledast(m)\)</span>
|
||||
, as defined by the
|
||||
<span class="math">\(\mathsf{RedJubjub}\)</span>
|
||||
scheme instantiated in <a id="id25" class="footnote_reference" href="#protocol-concretereddsa">11</a>.)</li>
|
||||
scheme instantiated in <a id="footnote-reference-26" class="footnote_reference" href="#protocol-concretereddsa">12</a>.)</li>
|
||||
<li>H3(m): Implemented by computing BLAKE2b-512("FROST_RedJubjubN", m), interpreting the 64 bytes as a little-endian integer, and reducing the resulting integer modulo <code>G.Order()</code>.</li>
|
||||
<li>H4(m): Implemented by computing BLAKE2b-512("FROST_RedJubjubM", m).</li>
|
||||
<li>H5(m): Implemented by computing BLAKE2b-512("FROST_RedJubjubC", m).</li>
|
||||
|
|
@ -181,40 +181,40 @@ def randomizer_generate(msg, commitment_list):
|
|||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
<p>Signature verification is as specified in <a id="id26" class="footnote_reference" href="#protocol-concretespendauthsig">12</a> for RedJubjub.</p>
|
||||
<p>Signature verification is as specified in <a id="footnote-reference-27" class="footnote_reference" href="#protocol-concretespendauthsig">13</a> for RedJubjub.</p>
|
||||
</section>
|
||||
<section id="frost-pallas-blake2b-512"><h4><span class="section-heading">FROST(Pallas, BLAKE2b-512)</span><span class="section-anchor"> <a rel="bookmark" href="#frost-pallas-blake2b-512"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h4>
|
||||
<p>This ciphersuite uses Pallas for the Group and BLAKE2b-512 for the Hash function <code>H</code> meant to produce signatures indistinguishable from RedPallas Orchard Spend Authorization Signatures as specified in <a id="id27" class="footnote_reference" href="#protocol-concretespendauthsig">12</a>.</p>
|
||||
<p>This ciphersuite uses Pallas for the Group and BLAKE2b-512 for the Hash function <code>H</code> meant to produce signatures indistinguishable from RedPallas Orchard Spend Authorization Signatures as specified in <a id="footnote-reference-28" class="footnote_reference" href="#protocol-concretespendauthsig">13</a>.</p>
|
||||
<ul>
|
||||
<li>Group: Pallas <a id="id28" class="footnote_reference" href="#protocol-pallasandvesta">15</a> with base point
|
||||
<li>Group: Pallas <a id="footnote-reference-29" class="footnote_reference" href="#protocol-pallasandvesta">16</a> with base point
|
||||
<span class="math">\(\mathcal{G}^{\mathsf{Orchard}}\)</span>
|
||||
as defined in <a id="id29" class="footnote_reference" href="#protocol-concretespendauthsig">12</a>.
|
||||
as defined in <a id="footnote-reference-30" class="footnote_reference" href="#protocol-concretespendauthsig">13</a>.
|
||||
<ul>
|
||||
<li>Order:
|
||||
<span class="math">\(r_\mathbb{P}\)</span>
|
||||
as defined in <a id="id30" class="footnote_reference" href="#protocol-pallasandvesta">15</a>.</li>
|
||||
<li>Identity: as defined in <a id="id31" class="footnote_reference" href="#protocol-pallasandvesta">15</a>.</li>
|
||||
as defined in <a id="footnote-reference-31" class="footnote_reference" href="#protocol-pallasandvesta">16</a>.</li>
|
||||
<li>Identity: as defined in <a id="footnote-reference-32" class="footnote_reference" href="#protocol-pallasandvesta">16</a>.</li>
|
||||
<li>RandomScalar(): Implemented by returning a uniformly random Scalar in the range [0, <code>G.Order()</code> - 1]. Refer to {{frost-randomscalar}} for implementation guidance.</li>
|
||||
<li>SerializeElement(P): Implemented as
|
||||
<span class="math">\(\mathsf{repr}_\mathbb{P}(P)\)</span>
|
||||
as defined in <a id="id32" class="footnote_reference" href="#protocol-pallasandvesta">15</a>.</li>
|
||||
as defined in <a id="footnote-reference-33" class="footnote_reference" href="#protocol-pallasandvesta">16</a>.</li>
|
||||
<li>DeserializeElement(P): Implemented as
|
||||
<span class="math">\(\mathsf{abst}_\mathbb{P}(P)\)</span>
|
||||
as defined in <a id="id33" class="footnote_reference" href="#protocol-pallasandvesta">15</a>, failing if
|
||||
as defined in <a id="footnote-reference-34" class="footnote_reference" href="#protocol-pallasandvesta">16</a>, failing if
|
||||
<span class="math">\(\bot\)</span>
|
||||
is returned. Additionally, this function validates that the resulting element is not the group identity element, returning an error if the check fails.</li>
|
||||
<li>SerializeScalar: Implemented by outputting the little-endian 32-byte encoding of the Scalar value.</li>
|
||||
<li>DeserializeScalar: Implemented by attempting to deserialize a Scalar from a little-endian 32-byte string. This function can fail if the input does not represent a Scalar in the range [0, <code>G.Order()</code> - 1].</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li>Hash (<code>H</code>): BLAKE2b-512 <a id="id34" class="footnote_reference" href="#blake">1</a> (BLAKE2b with 512-bit output and 16-byte personalization string), and Nh = 64.
|
||||
<li>Hash (<code>H</code>): BLAKE2b-512 <a id="footnote-reference-35" class="footnote_reference" href="#blake">1</a> (BLAKE2b with 512-bit output and 16-byte personalization string), and Nh = 64.
|
||||
<ul>
|
||||
<li>H1(m): Implemented by computing BLAKE2b-512("FROST_RedPallasR", m), interpreting the 64 bytes as a little-endian integer, and reducing the resulting integer modulo <code>G.Order()</code>.</li>
|
||||
<li>H2(m): Implemented by computing BLAKE2b-512("Zcash_RedPallasH", m), interpreting the 64 bytes as a little-endian integer, and reducing the resulting integer modulo <code>G.Order()</code>. (This is equivalent to
|
||||
<span class="math">\(\mathsf{H}^\circledast(m)\)</span>
|
||||
, as defined by the
|
||||
<span class="math">\(\mathsf{RedPallas}\)</span>
|
||||
scheme instantiated in <a id="id35" class="footnote_reference" href="#protocol-concretereddsa">11</a>.)</li>
|
||||
scheme instantiated in <a id="footnote-reference-36" class="footnote_reference" href="#protocol-concretereddsa">12</a>.)</li>
|
||||
<li>H3(m): Implemented by computing BLAKE2b-512("FROST_RedPallasN", m), interpreting the 64 bytes as a little-endian integer, and reducing the resulting integer modulo <code>G.Order()</code>.</li>
|
||||
<li>H4(m): Implemented by computing BLAKE2b-512("FROST_RedPallasM", m).</li>
|
||||
<li>H5(m): Implemented by computing BLAKE2b-512("FROST_RedPallasC", m).</li>
|
||||
|
|
@ -222,14 +222,14 @@ def randomizer_generate(msg, commitment_list):
|
|||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
<p>Signature verification is as specified in <a id="id36" class="footnote_reference" href="#protocol-concretespendauthsig">12</a> for RedPallas.</p>
|
||||
<p>Signature verification is as specified in <a id="footnote-reference-37" class="footnote_reference" href="#protocol-concretespendauthsig">13</a> for RedPallas.</p>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
<section id="rationale"><h2><span class="section-heading">Rationale</span><span class="section-anchor"> <a rel="bookmark" href="#rationale"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
|
||||
<p>FROST is a threshold Schnorr signature scheme, and Zcash Spend Authorization are also Schnorr signatures, which allows the usage of FROST with Zcash. However, since there is no widespread standard for Schnorr signatures, it must be ensured that the signatures generated by the FROST variant specified in this ZIP can be verified successfully by a Zcash implementation following its specification. In practice this entails making sure that the generated signature can be verified by the
|
||||
<span class="math">\(\mathsf{RedDSA.Validate}\)</span>
|
||||
function specified in <a id="id37" class="footnote_reference" href="#protocol-concretereddsa">11</a>:</p>
|
||||
function specified in <a id="footnote-reference-38" class="footnote_reference" href="#protocol-concretereddsa">12</a>:</p>
|
||||
<ul>
|
||||
<li>The FROST signature, when split into R and S in the first step of
|
||||
<span class="math">\(\mathsf{RedDSA.Validate}\)</span>
|
||||
|
|
@ -244,7 +244,7 @@ def randomizer_generate(msg, commitment_list):
|
|||
<li>Note that <code>r</code> (and thus <code>R</code>) will not be generated as specified in RedDSA.Sign. This is not an issue however, since with Schnorr signatures it does not matter for the verifier how the <code>r</code> value was chosen, it just needs to be generated uniformly at random, which is true for FROST.</li>
|
||||
<li>The above will ensure that the verification equation in
|
||||
<span class="math">\(\mathsf{RedDSA.Validate}\)</span>
|
||||
will pass, since FROST ensures the exact same equation will be valid as described in <a id="id38" class="footnote_reference" href="#frost-primeorderverify">7</a>.</li>
|
||||
will pass, since FROST ensures the exact same equation will be valid as described in <a id="footnote-reference-39" class="footnote_reference" href="#frost-primeorderverify">8</a>.</li>
|
||||
</ul>
|
||||
<p>The second step is adding the re-randomization functionality so that each FROST signing generates a re-randomized signature:</p>
|
||||
<ul>
|
||||
|
|
@ -256,8 +256,8 @@ def randomizer_generate(msg, commitment_list):
|
|||
, which refers to the randomizer as
|
||||
<span class="math">\(\alpha\)</span>
|
||||
) and <code>sum(lambda_i * c * (sk_i + randomizer))</code>. The latter can be rewritten as <code>c * (sum(lambda_i * sk_i) + randomizer *
|
||||
sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Shamir secret sharing mechanism used by FROST, and since <code>sum(lambda_i) == 1</code> <a id="id39" class="footnote_reference" href="#sum-lambda-proof">17</a>, we arrive at <code>c * (sk + randomizer)</code> as required.</li>
|
||||
<li>The re-randomization procedure must be exactly the same as in <a id="id40" class="footnote_reference" href="#protocol-concretereddsa">11</a> to ensure that re-randomized keys are uniformly distributed and signatures are unlinkable. This is also true; observe that <code>randomizer_generate</code> generates randomizer uniformly at random as required by
|
||||
sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Shamir secret sharing mechanism used by FROST, and since <code>sum(lambda_i) == 1</code> <a id="footnote-reference-40" class="footnote_reference" href="#sum-lambda-proof">18</a>, we arrive at <code>c * (sk + randomizer)</code> as required.</li>
|
||||
<li>The re-randomization procedure must be exactly the same as in <a id="footnote-reference-41" class="footnote_reference" href="#protocol-concretereddsa">12</a> to ensure that re-randomized keys are uniformly distributed and signatures are unlinkable. This is also true; observe that <code>randomizer_generate</code> generates randomizer uniformly at random as required by
|
||||
<span class="math">\(\mathsf{RedDSA.GenRandom}\)</span>
|
||||
; and signature generation is compatible with
|
||||
<span class="math">\(\mathsf{RedDSA.RandomizedPrivate}\)</span>
|
||||
|
|
@ -269,9 +269,10 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<span class="math">\(\mathsf{RedDSA.Validate}\)</span>
|
||||
as explained in the previous item.</li>
|
||||
</ul>
|
||||
<p>The security of Re-Randomized FROST with respect to the security assumptions of regular FROST is shown in <a id="footnote-reference-42" class="footnote_reference" href="#frost-rerandomized">4</a>.</p>
|
||||
</section>
|
||||
<section id="reference-implementation"><h2><span class="section-heading">Reference implementation</span><span class="section-anchor"> <a rel="bookmark" href="#reference-implementation"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
|
||||
<p>The <cite>reddsa</cite> crate <a id="id41" class="footnote_reference" href="#crate-reddsa">16</a> contains a re-randomized FROST implementation of both ciphersuites.</p>
|
||||
<p>The <cite>reddsa</cite> crate <a id="footnote-reference-43" class="footnote_reference" href="#crate-reddsa">17</a> contains a re-randomized FROST implementation of both ciphersuites.</p>
|
||||
</section>
|
||||
<section id="references"><h2><span class="section-heading">References</span><span class="section-anchor"> <a rel="bookmark" href="#references"><img width="24" height="24" class="section-anchor" src="assets/images/section-anchor.png" alt=""></a></span></h2>
|
||||
<table id="blake" class="footnote">
|
||||
|
|
@ -294,62 +295,70 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<tbody>
|
||||
<tr>
|
||||
<th>3</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST</a></td>
|
||||
<td><a href="https://www.rfc-editor.org/rfc/rfc9591.html">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-rerandomized" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>4</th>
|
||||
<td><a href="https://eprint.iacr.org/2024/436">Re-Randomized FROST</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-protocol" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>4</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-two-round-frost-signing-pro">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Section 5: Two-Round FROST Signing Protocol</a></td>
|
||||
<th>5</th>
|
||||
<td><a href="https://www.rfc-editor.org/rfc/rfc9591.html#name-two-round-frost-signing-pro">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Section 5: Two-Round FROST Signing Protocol</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-removingcoordinator" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>5</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-removing-the-coordinator-ro">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Section 7.3: Removing the Coordinator Role</a></td>
|
||||
<th>6</th>
|
||||
<td><a href="https://www.rfc-editor.org/rfc/rfc9591.html#name-removing-the-coordinator-ro">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Section 7.3: Removing the Coordinator Role</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-primeordergroup" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>6</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-prime-order-group">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Section 3.1: Prime-Order Group</a></td>
|
||||
<th>7</th>
|
||||
<td><a href="https://www.rfc-editor.org/rfc/rfc9591.html#name-prime-order-group">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Section 3.1: Prime-Order Group</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-primeorderverify" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>7</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#name-schnorr-signature-generatio">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Appendix B: Schnorr Signature Generation and Verification for Prime-Order Groups</a></td>
|
||||
<th>8</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#name-schnorr-signature-generatio">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Appendix B: Schnorr Signature Generation and Verification for Prime-Order Groups</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-tdkg" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>8</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-trusted-dealer-key-generati">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Appendix B: Trusted Dealer Key Generation</a></td>
|
||||
<th>9</th>
|
||||
<td><a href="https://www.rfc-editor.org/rfc/rfc9591.html#name-trusted-dealer-key-generati">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Appendix B: Trusted Dealer Key Generation</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-randomscalar" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>9</th>
|
||||
<td><a href="https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-random-scalar-generation">Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Appendix C: Random Scalar Generation</a></td>
|
||||
<th>10</th>
|
||||
<td><a href="https://www.rfc-editor.org/rfc/rfc9591.html#name-random-scalar-generation">RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Appendix C: Random Scalar Generation</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<table id="frost-serialization" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>10</th>
|
||||
<th>11</th>
|
||||
<td><a href="https://frost.zfnd.org/user/serialization.html">The ZF FROST Book, Serialization Format</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -357,7 +366,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="protocol-concretereddsa" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>11</th>
|
||||
<th>12</th>
|
||||
<td><a href="protocol/protocol.pdf#concretereddsa">Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 5.4.7: RedDSA, RedJubjub, and RedPallas</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -365,7 +374,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="protocol-concretespendauthsig" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>12</th>
|
||||
<th>13</th>
|
||||
<td><a href="protocol/protocol.pdf#concretespendauthsig">Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 5.4.7.1: Spend Authorization Signature (Sapling and Orchard)</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -373,7 +382,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="protocol-spendauthsig" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>13</th>
|
||||
<th>14</th>
|
||||
<td><a href="protocol/protocol.pdf#spendauthsig">Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 4.15: Spend Authorization Signature (Sapling and Orchard)</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -381,7 +390,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="protocol-jubjub" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>14</th>
|
||||
<th>15</th>
|
||||
<td><a href="protocol/protocol.pdf#jubjub">Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 5.4.9.3: Jubjub</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -389,7 +398,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="protocol-pallasandvesta" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>15</th>
|
||||
<th>16</th>
|
||||
<td><a href="protocol/protocol.pdf#pallasandvesta">Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 5.4.9.6: Pallas and Vesta</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -397,7 +406,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="crate-reddsa" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>16</th>
|
||||
<th>17</th>
|
||||
<td><a href="https://github.com/ZcashFoundation/reddsa">reddsa</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
@ -405,7 +414,7 @@ sum(lambda_i)</code>. Since <code>sum(lambda_i * sk_i) == sk</code> per the Sham
|
|||
<table id="sum-lambda-proof" class="footnote">
|
||||
<tbody>
|
||||
<tr>
|
||||
<th>17</th>
|
||||
<th>18</th>
|
||||
<td><a href="https://math.stackexchange.com/questions/1325292/prove-that-the-sum-of-the-lagrange-interpolation-coefficients-is-equal-to-1/1325342#1325342">Prove that the sum of the Lagrange (interpolation) coefficients is equal to 1</a></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
|
|
|||
|
|
@ -59,7 +59,8 @@ people managing shared funds, for example.
|
|||
FROST is one of such threshold signature protocols. However, it can't be used
|
||||
as-is since the Zcash protocol also requires re-randomizing public and private
|
||||
keys to ensure unlinkability between transactions. This ZIP specifies a variant
|
||||
of FROST with re-randomization support.
|
||||
of FROST with re-randomization support. This variant is named "Re-Randomized
|
||||
FROST" and has been described in [#frost-rerandomized]_.
|
||||
|
||||
|
||||
Requirements
|
||||
|
|
@ -137,15 +138,8 @@ receives an arbitrary-sized byte string and returns a Scalar. It is defined
|
|||
concretely in the Ciphersuites section.
|
||||
|
||||
|
||||
Re-randomizable FROST
|
||||
---------------------
|
||||
|
||||
To add re-randomization to FROST, follow the specification [#FROST]_ with the
|
||||
following modifications.
|
||||
|
||||
|
||||
Key Generation
|
||||
''''''''''''''
|
||||
--------------
|
||||
|
||||
While key generation is out of scope for this ZIP and the FROST spec [#FROST]_,
|
||||
it needs to be consistent with FROST, see [#frost-tdkg]_ for guidance. The spend
|
||||
|
|
@ -159,6 +153,13 @@ using seed phrases to recover the original secret (which may be something
|
|||
desirable in the context of FROST).
|
||||
|
||||
|
||||
Re-randomizable FROST
|
||||
---------------------
|
||||
|
||||
To add re-randomization to FROST, follow the specification [#FROST]_ with the
|
||||
following modifications.
|
||||
|
||||
|
||||
Randomizer Generation
|
||||
'''''''''''''''''''''
|
||||
|
||||
|
|
@ -252,9 +253,6 @@ to the ``randomizer`` as following:
|
|||
- ``group_public_key = group_public_key + G.ScalarBaseMult(randomizer)``
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
Ciphersuites
|
||||
------------
|
||||
|
||||
|
|
@ -421,6 +419,9 @@ signing generates a re-randomized signature:
|
|||
:math:`\mathsf{RedDSA.RandomizedPublic}`, :math:`\mathsf{RedDSA.Sign}` and
|
||||
:math:`\mathsf{RedDSA.Validate}` as explained in the previous item.
|
||||
|
||||
The security of Re-Randomized FROST with respect to the security assumptions of
|
||||
regular FROST is shown in [#frost-rerandomized]_.
|
||||
|
||||
|
||||
Reference implementation
|
||||
========================
|
||||
|
|
@ -434,13 +435,14 @@ References
|
|||
|
||||
.. [#BLAKE] `BLAKE2: simpler, smaller, fast as MD5 <https://blake2.net/#sp>`_
|
||||
.. [#RFC2119] `RFC 2119: Key words for use in RFCs to Indicate Requirement Levels <https://www.rfc-editor.org/rfc/rfc2119.html>`_
|
||||
.. [#FROST] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html>`_
|
||||
.. [#frost-protocol] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Section 5: Two-Round FROST Signing Protocol <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-two-round-frost-signing-pro>`_
|
||||
.. [#frost-removingcoordinator] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Section 7.3: Removing the Coordinator Role <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-removing-the-coordinator-ro>`_
|
||||
.. [#frost-primeordergroup] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Section 3.1: Prime-Order Group <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-prime-order-group>`_
|
||||
.. [#frost-primeorderverify] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Appendix B: Schnorr Signature Generation and Verification for Prime-Order Groups <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#name-schnorr-signature-generatio>`_
|
||||
.. [#frost-tdkg] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Appendix B: Trusted Dealer Key Generation <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-trusted-dealer-key-generati>`_
|
||||
.. [#frost-randomscalar] `Draft RFC: Two-Round Threshold Schnorr Signatures with FROST. Appendix C: Random Scalar Generation <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-14.html#name-random-scalar-generation>`_
|
||||
.. [#FROST] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures <https://www.rfc-editor.org/rfc/rfc9591.html>`_
|
||||
.. [#frost-rerandomized] `Re-Randomized FROST <https://eprint.iacr.org/2024/436>`_
|
||||
.. [#frost-protocol] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Section 5: Two-Round FROST Signing Protocol <https://www.rfc-editor.org/rfc/rfc9591.html#name-two-round-frost-signing-pro>`_
|
||||
.. [#frost-removingcoordinator] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Section 7.3: Removing the Coordinator Role <https://www.rfc-editor.org/rfc/rfc9591.html#name-removing-the-coordinator-ro>`_
|
||||
.. [#frost-primeordergroup] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Section 3.1: Prime-Order Group <https://www.rfc-editor.org/rfc/rfc9591.html#name-prime-order-group>`_
|
||||
.. [#frost-primeorderverify] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Appendix B: Schnorr Signature Generation and Verification for Prime-Order Groups <https://www.ietf.org/archive/id/draft-irtf-cfrg-frost-11.html#name-schnorr-signature-generatio>`_
|
||||
.. [#frost-tdkg] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Appendix B: Trusted Dealer Key Generation <https://www.rfc-editor.org/rfc/rfc9591.html#name-trusted-dealer-key-generati>`_
|
||||
.. [#frost-randomscalar] `RFC 9591: The Flexible Round-Optimized Schnorr Threshold (FROST) Protocol for Two-Round Schnorr Signatures. Appendix C: Random Scalar Generation <https://www.rfc-editor.org/rfc/rfc9591.html#name-random-scalar-generation>`_
|
||||
.. [#frost-serialization] `The ZF FROST Book, Serialization Format <https://frost.zfnd.org/user/serialization.html>`_
|
||||
.. [#protocol-concretereddsa] `Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 5.4.7: RedDSA, RedJubjub, and RedPallas <protocol/protocol.pdf#concretereddsa>`_
|
||||
.. [#protocol-concretespendauthsig] `Zcash Protocol Specification, Version 2022.3.4 [NU5]. Section 5.4.7.1: Spend Authorization Signature (Sapling and Orchard) <protocol/protocol.pdf#concretespendauthsig>`_
|
||||
|
|
|
|||
Loading…
Reference in New Issue