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elliptic curve’s …","Variable representing a full-width element of the elliptic …","A signed short element of the given elliptic curve’s …","Variable representing a signed short element of the …","An element of the given elliptic curve’s base field, …","Variable representing an element of the elliptic curve’s …","Fixed points that can be used with short scalar …","The affine short Weierstrass x-coordinate of an elliptic …","Variable representing the affine short Weierstrass …","Performs complete point addition, returning <code>a + b</code>.","Returns <code>self + other</code> using complete addition.","Returns <code>self + other</code> using complete addition.","Performs incomplete point addition, returning <code>a + b</code>.","Returns <code>self + other</code> using incomplete addition. The …","","","","","","","","","","","","","","","","","","","Chip implementations for the ECC gadgets.","","","","","","","","","","","Constrains point <code>a</code> to be equal in value to point <code>b</code>.","Constrains this point to be equal in value to another …","Constrains this point to be equal in value to another …","","","","","","","","","","","","","","","","","","","","","","","","","","","","Extracts the x-coordinate of a point.","Extracts the x-coordinate of a point.","Extracts the x-coordinate of a point.","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Wraps the given point (obtained directly from an …","Wraps the given point (obtained directly from an …","Wraps the given x-coordinate (obtained directly from an …","Wraps the given fixed base (obtained directly from an …","Wraps the given fixed base (obtained directly from an …","Wraps the given fixed base (obtained directly from an …","","","","","","","","","","Returns the inner point.","Returns the inner point.","Returns the inner x-coordinate.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Performs variable-base scalar multiplication, returning …","Returns <code>[by] self</code>.","Returns <code>[by] self</code>.","Returns <code>[by] self</code>.","Returns <code>[by] self</code>.","Performs fixed-base scalar multiplication using a …","Performs fixed-base scalar multiplication using a base …","Performs fixed-base scalar multiplication using a short …","Constructs a new point with the given value.","Constructs a new point with the given value.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Witnesses the given point as a private input to the …","Witnesses the given point as a private input to the …","Type marker representing a base field element being used …","A chip implementing EccInstructions","Configuration for the ECC chip","A curve point represented in affine (x, y) coordinates, or …","A full-width scalar used for fixed-base scalar …","A signed short scalar used for fixed-base scalar …","Returns information about a fixed point that is required …","Type marker representing a full-width scalar for use in …","The number of windows that this scalar kind requires.","A non-identity point represented in affine (x, y) …","A trait representing the kind of scalar used with a …","The kind of scalar that this fixed point can be multiplied …","Type marker representing a signed 64-bit scalar for use in …","","","Advice columns needed by instructions in the ECC chip.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Side effects","Constants required for the ECC chip.","","Reconstructs this chip from the given config.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Returns the argument unchanged.","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the generator for this fixed point.","","","","","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Returns the Lagrange coefficients for this fixed point.","","Lookup range check using 10-bit lookup table","","","","","","","Returns the value of this curve point, if known.","Returns the value of this curve point, if known.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Returns the $u$ values for this fixed point.","","","","","","","","","","","","The cell containing the affine short-Weierstrass …","The cell containing the affine short-Weierstrass …","The cell containing the affine short-Weierstrass …","The cell containing the affine short-Weierstrass …","Returns the $z$ value for this fixed point.","Window size for fixed-base scalar multiplication","$2^{<code>FIXED_BASE_WINDOW_SIZE</code>}$","Number of windows for a full-width scalar","Number of windows for a short signed scalar","For each window, we interpolate the $x$-coordinate. Here, …","For each window, $z$ is a field element such that for each …","Test that Lagrange interpolation coefficients reproduce …","Test that the z-values and u-values satisfy the conditions:","A Poseidon hash function, built around a sponge.","A message word provided by the prover.","A word from the padded input to a Poseidon sponge.","A padding word, that will be fixed in the circuit …","The set of circuit instructions required to use the …","The set of circuit instructions required to use the <code>Sponge</code> …","A Poseidon chip using an $x^5$ S-Box.","Configuration for a <code>Pow5Chip</code>.","A Poseidon sponge.","A word in the Poseidon state.","A word over which the Poseidon permutation operates.","Variable representing the word over which the Poseidon …","Absorbs an element into the sponge.","Adds the given input to the state.","","","","","","","","","","","","","","","","","","","","","","","","Configures this chip for use in a circuit.","Construct a <code>Pow5Chip</code>.","","","","","","","","","","","","","","","","","","","","","","Transitions the sponge into its squeezing state.","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Construct a <code>Word</code> gadget from the inner word.","Extracts sponge output from the given state.","","Hashes the given input.","","","","","","","Initializes a new hasher.","","Returns the initial empty state for the given domain.","","The word contained in this gadget.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","Constructs a new duplex sponge for the given Poseidon …","Applies the Poseidon permutation to the given state.","","Squeezes an element from the sponge.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","The Poseidon algebraic hash function.","The Sinsemilla hash function and commitment scheme.","The absorbing state of the <code>Sponge</code>.","A Poseidon hash function used with constant input length.","A domain in which a Poseidon hash function is being used.","A Poseidon hash function, built around a sponge.","Poseidon-128 using the $x^5$ S-box, with a width of 3 …","Iterator that outputs padding field elements.","A specification for a Poseidon permutation.","The state of the <code>Sponge</code>.","The squeezing state of the <code>Sponge</code>.","","","","","","","","","","","","","Generates <code>(round_constants, mds, mds^-1)</code> corresponding to …","","","","","","","","","","","","","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","The number of full rounds for this specification.","","","Hashes the given input.","","Initializes a new hasher.","","","","","The initial capacity element, encoding this domain.","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","The name of this domain, for debug formatting purposes.","","Returns the padding to be appended to the input.","","The number of partial rounds for this specification.","","","The S-box for this specification.","","","Side-loaded index of the first correct and secure MDS that …","","","","","","","","","","","","","","","","","","","","","","","","The largest integer such that $2^c \\\\leq (r_P - 1) / 2$, …","A domain in which $\\\\mathsf{SinsemillaCommit}$ and …","A domain in which $\\\\mathsf{SinsemillaHashToPoint}$ and …","$\\\\frac{1}{2^K}$","Number of bits of each message piece in …","Returns the Sinsemilla $Q$ constant for this domain.","Returns the Sinsemilla $Q$ constant for this domain.","SWU hash-to-curve personalization for Sinsemilla $Q$ …","Returns the Sinsemilla $R$ constant for this domain.","The precomputed bases for the Sinsemilla hash function.","SWU hash-to-curve personalization for Sinsemilla $S$ …","","","","","","","$\\\\mathsf{SinsemillaCommit}$ from § 5.4.8.4.","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","$\\\\mathsf{SinsemillaHash}$ from § 5.4.1.9.","$\\\\mathsf{SinsemillaHashToPoint}$ from § 5.4.1.9.","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Constructs a new <code>HashDomain</code> with a specific prefix string.","Constructs a new <code>CommitDomain</code> with a specific prefix …","$\\\\mathsf{SinsemillaShortCommit}$ from § 5.4.8.4.","","","","","","","","","","","The size of a SHA-256 block, in 32-bit words.","A word in a <code>Table16</code> message block.","Variable representing a 32-bit word of the input block to …","A gadget that constrains a SHA-256 invocation. It supports …","The output of a SHA-256 circuit invocation.","The set of circuit instructions required to use the <code>Sha256</code> …","Variable representing the SHA-256 internal state.","A chip that implements SHA-256 with a maximum lookup table …","Configuration for a <code>Table16Chip</code>.","","","","","","","","","","","","","","","","","Starting from the given initialized state, processes a …","","","Configures a circuit to include this chip.","Reconstructs this chip from the given config.","","","","","","","","","","","","Converts the given state into a message digest.","","Convenience function to compute hash of the data. It will …","","","","","","Retrieve result and consume hasher instance.","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","","","","","Creates an initial state from the output state of a …","","Places the SHA-256 IV in the circuit, returning the …","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Loads the lookup table required by this chip into the …","","Create a new hasher instance.","","","","","","","","","","","","","","","","","","","Digest data, updating the internal state.","","","","","","A variable in the circuit.","Gadget representing a domain in which …","Trait allowing circuit’s Sinsemilla CommitDomains to be …","CommitDomains used in this instruction.","A type enumerating the fixed points used in <code>CommitDomains</code>.","A domain in which $\\\\mathsf{SinsemillaHashToPoint}$ and …","Trait allowing circuit’s Sinsemilla HashDomains to be …","HashDomains used in this instruction.","A message to be hashed.","A message composed of <code>Self::MessagePiece</code>s.","A message piece with a bitlength of some multiple of <code>K</code>.","A piece in a message containing a number of <code>K</code>-bit words. A …","A point output of <code>Self::hash_to_point</code>.","Returns the <code>Q</code> constant for this domain.","A cumulative sum <code>z</code> is used to decompose a Sinsemilla …","The set of circuit instructions required to use the …","The x-coordinate of a point output of <code>Self::hash_to_point</code>.","","","","","","","","","Chip implementations for the Sinsemilla gadgets.","","","","","$\\\\mathsf{SinsemillaCommit}$ from § 5.4.8.4.","","","","","","","","","","","","","Extracts the x-coordinate of the output of a Sinsemilla …","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Constructs a MessagePiece from a field element.","Constructs a message from a vector of <code>MessagePiece</code>s.","$\\\\mathsf{SinsemillaHash}$ from § 5.4.1.9.","Returns the HashDomain contained in this CommitDomain","Hashes a message to an ECC curve point. This returns both …","$\\\\mathsf{SinsemillaHashToPoint}$ from § 5.4.1.9.","","","","","Returns the inner MessagePiece contained in this gadget.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Gadgets for implementing a Merkle tree with Sinsemilla.","Constructs a new <code>HashDomain</code> for the given domain.","Constructs a new <code>CommitDomain</code> for the given domain.","Returns the fixed point corresponding to the R constant …","$\\\\mathsf{SinsemillaShortCommit}$ from § 5.4.8.4.","","","","","","","","","","","","","","","","","","","Witness a message piece given a field element. Returns a …","A chip that implements 10-bit Sinsemilla using a lookup …","Configuration for the Sinsemilla hash chip","","","","","","","","","","Side-effects","Reconstructs this chip from the given config.","","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Loads the lookup table required by this chip into the …","","Returns the lookup range check config used in this config.","","","","","","","","","","","","","","SWU hash-to-curve personalization for the Merkle CRH …","Instructions to check the validity of a Merkle path of a …","Gadget representing a Merkle path that proves a leaf …","","","Calculates the root of the tree containing the given leaf …","Chip implementing a Merkle hash using Sinsemilla as the …","","","Constructs a <code>MerklePath</code>.","","","","","Returns the argument unchanged.","Compute MerkleCRH for a given <code>layer</code>. The hash that …","","Calls <code>U::from(self)</code>.","","","","","","Chip implementing <code>MerkleInstructions</code>.","Configuration for the <code>MerkleChip</code> implementation.","","","","","","","","","","Configures the <code>MerkleChip</code>.","Constructs a <code>MerkleChip</code> given a <code>MerkleConfig</code>.","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","","","","","","","","","","","","","Trait for utilities used across circuits.","Trait for a variable in the circuit.","Variable in the circuit.","Takes a specified subsequence of the little-endian bit …","Checks that an expression is either 1 or 0.","The cell at which this variable was allocated.","Gadget and chip for a conditional swap utility.","Decomposes an $n$-bit field element $\\\\alpha$ into $W$ …","Decompose a word <code>alpha</code> into <code>window_num_bits</code> bits …","The sequence of bits representing a u64 in little-endian …","The u64 integer represented by an L-bit little-endian …","Load a variable.","Make use of a K-bit lookup table to decompose a field …","Check that an expression is in the small range [0..range), …","If <code>a</code> then <code>b</code>, else <code>c</code>. Returns (a * b) + (1 - a) * c.","The value allocated to this variable.","A chip implementing a conditional swap.","Configuration for the <code>CondSwapChip</code>.","Instructions for a conditional swap gadget.","","","","","","","","","","Configures this chip for use in a circuit.","Constructs a <code>CondSwapChip</code> given a <code>CondSwapConfig</code>.","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","Given an input pair (a,b) and a <code>swap</code> boolean flag, returns …","","","","","","","","","","","","The running sum $[z_0, …, z_W]$. If created in strict …","Configuration that provides methods for running sum …","","","","","","","<code>perm</code> MUST include the advice column <code>z</code>.","Decompose an existing variable alpha that is copied into …","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","","","","","","","","","","Decompose a field element alpha that is witnessed in this …","Configuration that provides methods for a lookup range …","The running sum $[z_0, …, z_W]$. If created in strict …","","","","","","","The <code>running_sum</code> advice column breaks the field element …","Range check on an existing cell that is copied into this …","Short range check on an existing cell that is copied into …","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","","","","","","","","","","Range check on a value that is witnessed in this helper.","Short range check on value that is witnessed in this 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module provides common utilities, traits and …","Traits and structs for implementing circuit components.","Tools for developing circuits.","This module provides an implementation of a variant of …","Contains utilities for performing arithmetic over …","This module contains utilities and traits for dealing with …","The affine version of the curve","The base field over which this elliptic curve is …","The base field over which this elliptic curve is …","CURVE_ID used for hash-to-curve.","The affine coordinates of a point on an elliptic curve.","This trait is the affine counterpart to <code>Curve</code> and is used …","This trait is a common interface for dealing with elements …","The projective form of the curve","Generator of the $t-order$ multiplicative subgroup","This trait represents an element of a field.","This trait is a common interface for dealing with elements …","This represents an element of a group with basic …","Modulus of the field written as a string for display …","Inverse of <code>PrimeField::root_of_unity()</code>","The group is assumed to be of prime order $p$. <code>Scalar</code> is …","The scalar field of this elliptic curve.","The scalar field of this elliptic curve.","A trait that exposes additional operations related to …","Tables used for square root computation.","Inverse of $2$ in the field.","The value $(T-1)/2$ such that $2^S \\\\cdot T = p - 1$ with …","Element of multiplicative order $3$.","Returns the curve constant a.","Returns the curve constant $a$.","Returns the curve constant b.","Returns the curve constant $b$.","Performs a radix-$2$ Fast-Fourier Transformation (FFT) on …","Performs a multi-exponentiation operation.","","","","","","","This computes the inner product of two vectors <code>a</code> and <code>b</code>.","","Gets the coordinates of this point.","Cubes this element.","","","","","","Doubles this element.","","","Apply the curve endomorphism by multiplying the …","This evaluates a provided polynomial (in coefficient form) …","","","Returns the argument unchanged.","Returns the argument unchanged.","Obtains a field element that is congruent to the provided …","Obtains a field element congruent to the integer <code>v</code>.","Obtains a point given $(x, y)$, failing if it is not on the","Obtains a <code>Coordinates</code> value given $(x, y)$, failing if it …","Gets the lower 128 bits of this field element when …","Gets the lower 32 bits of this field element when expressed","Adds <code>rhs</code> to this group element.","Scales this group element by a scalar.","Subtracts <code>rhs</code> from this group element.","Returns the additive identity of the group.","Requests a hasher that accepts messages and returns …","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Computes the multiplicative inverse of this element, …","Returns whether or not this element is on the curve; should","Returns whether or not this element is on the curve; should","Returns true iff this element is zero.","Returns true iff this element is zero.","Return the Jacobian coordinates of this point.","Divides polynomial <code>a</code> in <code>X</code> by <code>X - b</code> with no remainder.","Returns coefficients of an n - 1 degree polynomial given a …","Build tables given parameters for the perfect hash.","Obtains a point given Jacobian coordinates $X : Y : Z$, …","Returns the one element of the field, the multiplicative …","This simple utility function will parallelize an operation …","Exponentiates <code>self</code> by <code>by</code>, where <code>by</code> is a little-endian order","Raise this field element to the power <code>Self::T_MINUS1_OVER2</code>.","Exponentiates <code>self</code> by <code>exp</code>, where <code>exp</code> is a little-endian …","Returns an element chosen uniformly at random using a …","Performs a small multi-exponentiation operation. Uses the …","Returns the square root of the field element, if it is …","Equivalent to <code>Self::sqrt_ratio(self, one())</code>.","Same as sqrt_ratio(u, one()) but more efficient.","Computes:","Computes:","Squares this element.","","","","","","","","Returns the u-coordinate.","Returns the v-coordinate.","","","Returns the x-coordinate.","Returns the y-coordinate.","Returns the zero element of the field, the additive …","An assigned cell.","A pointer to a cell within a circuit.","A chip implements a set of instructions that can be used …","A type that holds the configuration for this chip, and any …","A layout strategy within a circuit. The layouter is …","A type that holds any general chip state that needs to be …","This is a “namespaced” layouter which borrows a …","A region of the circuit in which a <code>Chip</code> can assign cells.","Index of a region in a layouter","Starting row of a region in a layouter","Represents the type of the “root” of this layouter, so …","A simple <code>FloorPlanner</code> that performs minimal optimizations.","A lookup table in the circuit.","Assign an advice column value (witness).","Assigns a constant value to the column <code>advice</code> at <code>offset</code> …","Assign the value of the instance column’s cell at …","Assigns a fixed value to a table cell.","Assign a fixed value.","Assign a region of gates to an absolute row number.","","Assign a table region to an absolute row number.","","","","","","","","","","","","","","","","","","Returns the cell.","","","","","","","","","The chip holds its own configuration.","Constrains a cell to have a constant value.","Constrains two cells to have the same value.","Constrains a <code>Cell</code> to equal an instance column’s row …","","Copies the value to a given advice cell and constrains …","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Evaluates this assigned cell’s value directly, …","Implementations of common circuit floor planners.","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","Returns the argument unchanged.","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","","Returns the argument unchanged.","Returns the argument unchanged.","Gets the “root” of this assignment, bypassing the …","","","","","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Implementations of common circuit layouters.","Provides access to general chip state loaded at the …","Enters into a namespace.","","Exits out of the existing namespace.","","Creates a new (sub)namespace and enters into it.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Returns the value of the <code>AssignedCell</code>.","Returns the field element value of the <code>AssignedCell</code>.","","","","","","","","","The version 1 <code>FloorPlanner</code> provided by <code>halo2</code>.","A single pass of the <code>V1</code> layouter.","","","","","","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","","","","","","","","","","","Concrete column","The virtual column involved in a region. This includes …","Helper trait for implementing a custom <code>Layouter</code>.","The shape of a region. For a region at a certain index, we …","Virtual column representing a (boolean) selector","Helper trait for implementing a custom <code>Layouter</code>.","Assign an advice column value (witness)","","Assigns a constant value to the column <code>advice</code> at <code>offset</code> …","","Assign the value of the instance column’s cell at …","","Assigns a fixed value to a table cell.","Assign a fixed value","","","","","","","","","","","Get a reference to the set of <code>columns</code> used in a <code>RegionShape</code>…","Constrains a cell to have a constant value.","","Constraint two cells to have the same value.","","","","","","","","Enables a selector at the given offset.","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","Create a new <code>RegionShape</code> for a region at <code>region_index</code>.","","Get the <code>region_index</code> of a <code>RegionShape</code>.","Get the <code>row_count</code> of a <code>RegionShape</code>.","","","","","","","","","","","","","A cell used in an active gate was not assigned to.","A struct for collecting and displaying the gates within a …","Graphical renderer for circuit layouts.","A constraint was not satisfied for a particular row.","A constraint was active on an unusable row, and is likely …","The location within the circuit at which a particular …","A location inside a region.","A lookup input did not exist in its corresponding table.","A test prover for debugging circuits.","A location outside of a region.","A permutation did not preserve the original value of a …","The reasons why a particular circuit is not satisfied.","Panics if the circuit being checked by this <code>MockProver</code> is …","","","","","","","","","","","","","Builds a dot graph string representing the given circuit.","Collects the gates from within the circuit.","","Developer tools for investigating the cost of a circuit.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Marks cells involved in equality constraints, in red.","Metadata about circuits.","","","","","Prints the queries in this circuit to a CSV grid.","","Renders the given circuit on the given drawing area.","Runs a synthetic keygen-and-prove operation on the given …","Draws red lines between equality-constrained cells.","Sets the visibility of region labels.","","","","","","","","","","","","","","","","","","","Returns <code>Ok(())</code> if this <code>MockProver</code> is satisfied, or a list …","Sets the view height for this layout, as a number of rows.","Sets the view width for this layout, as a number of …","","","","","","The offset (relative to the start of the region) at which …","The region in which the failure occurred.","The circuit row on which the failure occurred.","The values of the virtual cells used by this constraint.","The column in which this cell should be assigned.","The column in which this permutation is not satisfied.","The polynomial constraint that is not satisfied.","The polynomial constraint that is not satisfied.","The index of the active gate.","The offset (relative to the start of the region) at which …","The location at which this constraint is not satisfied.","The location at which the lookup is not satisfied.","The location at which the permutation is not satisfied.","The index of the lookup that is not satisfied. These …","The offset (relative to the start of the region) at which …","The region in which this cell should be assigned.","Measures a circuit to determine its costs, and explain …","The marginal size of a Halo 2 proof, broken down into its …","The size of a Halo 2 proof, broken down into its …","","","","","","","","","","","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Returns the marginal proof size per instance of this …","Measures a circuit with parameter constant <code>k</code>.","Returns the proof size for the given number of instances …","","","","","","","","","","","","","Metadata about a column within a circuit.","Metadata about a configured constraint within a circuit.","Metadata about a configured gate within a circuit.","Metadata about an assigned region within a circuit.","A “virtual cell” is a PLONK cell that has been queried …","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Returns the argument unchanged.","","","","Returns the argument unchanged.","Returns the argument unchanged.","","Returns the argument unchanged.","","","Returns the argument unchanged.","","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","An advice column","An Advice variant","This is an advice (witness) column queried at a certain …","An enum over the Advice, Fixed, Instance structs","A value assigned to a cell within a circuit.","This trait allows a <code>Circuit</code> to direct some backend to …","A verifier that checks multiple proofs in a batch.","Out of bounds index passed to a backend","This is a trait that circuits provide implementations for …","A column with an index and type","The instance sets up a copy constraint involving a column …","A column type","This is a configuration object that stores things like …","This is a constant polynomial","An individual polynomial constraint.","This is a description of the circuit environment, such as …","The constraint system is not satisfied.","A set of polynomial constraints with a common selector.","This is an error that could occur during proving or …","Low-degree expression representing an identity that must …","A fixed column","A Fixed variant","This is a fixed column queried at a certain relative …","A floor planning strategy for a circuit.","The floor planner used for this circuit. This is an …","An instance column","An Instance variant","This is an instance (external) column queried at a certain …","Instance provided exceeds number of available rows","The provided instances do not match the circuit parameters.","This is a negated polynomial","Circuit synthesis requires global constants, but circuit …","<code>k</code> is too small for the given circuit.","Opening error","The output type of this verification strategy after …","Represents the minimal parameters that determine a …","Minimal representation of a verification key that can be …","This is the product of two polynomials","This is a proving key which allows for the creation of …","A value stored as a fraction to enable batch inversion.","This is a scaled polynomial","A selector, representing a fixed boolean value per row of …","This is a virtual selector","A verifier that checks a single proof at a time.","This is the sum of two polynomials","This is an error that can occur during synthesis of the …","A fixed column of a lookup table.","Transcript error","A value that does not require inversion to evaluate.","Trait representing a strategy for verifying Halo 2 proofs.","This is a verifying key which allows for the verification …","Exposes the “virtual cells” that can be queried while …","The field element zero.","","","","","","","Allocate a new advice column","Assign an advice column value (witness)","Assign a fixed value","Compute the number of blinding factors necessary to …","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Type of this column.","Allocate a new complex selector that can appear anywhere …","The circuit is given an opportunity to describe the exact …","Assign two cells to have the same value","Creates a new gate.","This creates a proof for the provided <code>circuit</code> when given …","Cubes this element.","","Compute the degree of this polynomial","Compute the degree of the constraint system (the maximum …","Returns the denominator, if non-trivial.","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Doubles this element.","","","","","","","","","","","","","","","","","","","","","Enable this selector at the given offset within the given …","Enables this fixed column to be used for global constant …","Enable the ability to enforce equality over cells in this …","Enables a selector at the given row.","Creates a new region and enters into it.","","","","","","","","","Evaluates this assigned value directly, performing an …","Evaluate the polynomial using the provided closures to …","Exits the current region.","Fills a fixed <code>column</code> starting from the given <code>row</code> with …","Finalizes the batch and checks its validity.","Allocate a new fixed column","","","","","","","","","","","","","","","","","","","","","","","","","","Returns the argument unchanged.","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","Returns the argument unchanged.","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Get the underlying <code>EvaluationDomain</code>.","Get the underlying <code>VerifyingKey</code>.","","","","","","","","Hashes a verification key into a transcript.","","","","","","","","","","","","","","","","","","","","","Allocate a new instance column","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","Inverts this assigned value (taking the inverse of zero to …","Is this selector “simple”? Simple selectors can only …","Returns true iff this element is zero.","Generate a <code>ProvingKey</code> from a <code>VerifyingKey</code> and an instance …","Generate a <code>VerifyingKey</code> from an instance of <code>Circuit</code>.","Add a lookup argument for some input expressions and table …","Allocates a new fixed column that can be used in a lookup …","Returns the minimum necessary rows that need to exist in …","","","","","","","","","","","","","Constructs a new single proof verifier.","Constructs a new batch verifier.","Returns the numerator.","","","Obtain a pinned version of this constraint system; a …","Obtains a pinned representation of this verification key …","Exits out of the existing namespace.","Obtains an MSM from the verifier strategy and yields back …","","","Creates a new (sub)namespace and enters into it.","Query an advice column at a relative position","Query an Any column at a relative position","Query a fixed column at a relative position","Queries the cell of an instance column at a particular …","Query an instance column at a relative position","Query a selector at the current position.","Allocate a new (simple) selector. Simple selectors cannot …","Sets the minimum degree required by the circuit, which can …","","Squares this element.","Square this expression.","","","","","","","Given the provided <code>cs</code>, synthesize the given circuit.","Given the provided <code>cs</code>, synthesize the circuit. The …","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","Returns a boolean indicating whether or not the proof is …","","","","","","","","","","","","","","","","","","","","","Constructs a set of constraints that are controlled by the …","Returns a copy of this circuit with no witness values …","","","","","","The current value of <code>k</code> being used.","","","","","","","","","","Column index","Column index","Column index","Query index","Query index","Query index","Rotation of this query","Rotation of this query","Rotation of this query","","The basis over which a polynomial is described.","The polynomial is defined as coefficients","This is an error that could occur during proving or …","This structure contains precomputed constants and other …","The polynomial is defined as coefficients of Lagrange …","The polynomial is defined as coefficients of Lagrange …","OpeningProof is not well-formed","Represents the minimal parameters that determine an …","Represents a univariate polynomial defined over a field …","Describes the relative rotation of a vector. Negative …","Caller needs to re-sample a point","","","","","","","","","","","","","","","","","","","","","","","","","","","","Obtains a polynomial in coefficient form when given a …","This takes us from an n-length coefficient vector into a …","This module contains an implementation of the polynomial …","Returns a constant polynomial in the extended Lagrange …","Returns a constant polynomial in the Lagrange coefficient …","The current location in the evaluation domain","","","","","","","","","","","","","","","","","","","This divides the polynomial (in the extended domain) by …","","","","","","","","","Returns an empty (zero) polynomial in the coefficient basis","Returns an empty (zero) polynomial in the extended …","Returns an empty (zero) polynomial in the Lagrange …","","Get the size of the extended domain","This takes us from the extended evaluation domain and gets …","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Get the generator of the extended domain’s …","Get $\\\\omega$, the generator of the $2^k$ order …","Get $\\\\omega^{-1}$, the inverse of the generator of the …","Gets the quotient polynomial’s degree (as a multiple of …","","","","","","","","","","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Iterate over the values, which are either in coefficient …","Iterate over the values mutably, which are either in …","Computes evaluations (at the point <code>x</code>, where <code>xn = x^n</code>) of …","Obtains a polynomial in Lagrange form when given a vector …","This takes us from an n-length vector into the coefficient …","","This module contains an optimisation of the polynomial …","","This constructs a new evaluation domain object based on …","The next location in the evaluation domain","Gets the size of this polynomial in terms of the number of …","Obtain a pinned version of this evaluation domain; a …","The previous location in the evaluation domain","Rotates the values in a Lagrange basis polynomial by …","Rotate the extended domain polynomial over the original …","Multiplies a value by some power of $\\\\omega$, essentially …","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","","An accumulator instance consisting of an evaluation claim …","Wrapper type around a blinding factor.","A guard returned by the verifier","A multiscalar multiplication in the polynomial commitment …","These are the public parameters for the polynomial …","","","","Add a value to the first entry of <code>g_scalars</code>.","Add another multiexp into this one","Add a vector of scalars to <code>g_scalars</code>. This function will …","Add to <code>u_scalar</code>","Add to <code>w_scalar</code>","Add arbitrary term (the scalar and the point)","","","","","","","","","","","","","","","","","","","This computes a commitment to a polynomial described by …","This commits to a polynomial using its evaluations over …","Computes G = ⟨s, params.g⟩","Create a polynomial commitment opening proof for the …","","","","","","","","","","","","","","","","","Generates an empty multiscalar multiplication struct using …","","Perform multiexp and check that it results in zero","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","The claimed output of the linear-time polycommit opening …","Getter for g generators","","","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","","","","","Create a new, empty MSM using the provided parameters.","Initializes parameters for the curve, given a random …","Reads params from a buffer.","Scale all scalars in the MSM by some scaling factor","","","","","","","","","","","","","","","","","","","","A vector of challenges u_0, …, u_{k - 1} sampled by the …","Lets caller supply the challenges and obtain an MSM with …","Lets caller supply the purported G point and simply appends","Checks to see if the proof represented within <code>transcript</code> …","","","","","","Writes params to a buffer.","A polynomial query at a point","A polynomial query at a point","blinding factor of polynomial","","","","","","","","","Create a multi-opening proof","","","","","","","","","Returns the argument unchanged.","Returns the argument unchanged.","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Create a new verifier query based on a commitment","Create a new verifier query based on a linear combination …","point at which polynomial is queried","coefficients of polynomial","","","","","","","","","Verify a multi-opening proof","","","We will replace BLAKE2b with an algebraic hash function in …","We will replace BLAKE2b with an algebraic hash function in …","A 255-bit challenge.","The scalar representation of a verifier challenge.","<code>EncodedChallenge&lt;C&gt;</code> defines a challenge encoding with a …","The Input type used to derive the challenge encoding. For …","Generic transcript view (from either the prover or verifier…","Transcript view from the perspective of a verifier that …","Transcript view from the perspective of a prover that has …","Cast an encoded challenge as a typed <code>ChallengeScalar</code>.","","","","","","","","","","","","","","","","","Writing the point to the transcript without writing it to …","","","Writing the scalar to the transcript without writing it to …","","","","","","","","","","","","","","","","","Conclude the interaction and return the output buffer …","","","","","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Returns the argument unchanged.","Get a scalar field element from an encoded challenge.","","","Initialize a transcript given an input buffer.","Initialize a transcript given an output buffer.","","","","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Calls <code>U::from(self)</code>.","Get an encoded challenge from a given input challenge.","","Read a curve point from the prover.","","Read a curve scalar from the prover.","","Squeeze an encoded verifier challenge from the transcript.","","","Squeeze a typed challenge (in the scalar field) from the …","","","","","","","","","","","","","","","","","","","","","","Write a curve point to the proof and the transcript.","","Write a scalar to the proof and the 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