Module `0x1::sigma_protocol_fiat_shamir`

Enum DomainSeparator
Struct FiatShamirInputs
Constants
Function new_domain_separator
Function fiat_shamir

use 0x1::aptos_hash;
use 0x1::error;
use 0x1::option;
use 0x1::ristretto255;
use 0x1::sigma_protocol_statement;
use 0x1::string;
use 0x1::type_info;
use 0x1::vector;

Enum `DomainSeparator`

A domain separator prevents replay attacks in $\Sigma$ protocols and consists of 5 things.

The contract address (defense in depth: binds the proof to a specific deployed contract)
The chain ID (defense in depth: binds the proof to a specific Aptos network)
A protocol identifier, which is typically split up into two things:

A higher-level protocol: “Confidential Assets v1 on Aptos”
A lower-level relation identifier (e.g., “PedEq”, “Schnorr”, “DLEQ”, etc.)

Statement (i.e., the public statement in the NP relation being proved)

This is captured implicitly in our prove and verify functions ==> it is not part of this struct.

Session identifier

Chosen by user
specifies the “context” in which this proof is valid
e.g., “Alice (0x1) is paying Bob (0x2) at time t
together with the protocol identifier, prevents replay attacks across the same protocol or different protocols

Note: The session identifier can be tricky, since in some settings the “session” accumulates implicitly in the statement being proven. For confidential assets, it does not AFAICT: the “session” is represented at least by the confidential balances of the users & their addresses.

enum DomainSeparator has copy, drop

Variants

Fields

contract_address: address
chain_id: u8
protocol_id: vector<u8>
session_id: vector<u8>

Struct `FiatShamirInputs`

Unfortunately, we cannot directly use the Statement struct here because its vector<RistrettoPoint> will not serialize correctly via bcs::to_bytes, since a RistrettoPoint stores a Move VM “handle” rather than an actual point.

struct FiatShamirInputs has drop

Fields

dst: sigma_protocol_fiat_shamir::DomainSeparator
type_name: string::String: The fully-qualified type name of the phantom marker type P in Statement<P>. E.g., "0x7::sigma_protocol_registration::Registration". This binds the Fiat-Shamir challenge to the specific protocol type for defense in depth.
k: u64
stmt_X: vector<ristretto255::CompressedRistretto>
stmt_x: vector<ristretto255::Scalar>
proof_A: vector<ristretto255::CompressedRistretto>

Constants

One of our internal invariants was broken. There is likely a logical error in the code.

const E_INTERNAL_INVARIANT_FAILED: u64 = 2;

The length of the A field in Proof should NOT be zero

const E_PROOF_COMMITMENT_EMPTY: u64 = 1;

Function `new_domain_separator`

public(friend) fun new_domain_separator(contract_address: address, chain_id: u8, protocol_id: vector<u8>, session_id: vector<u8>): sigma_protocol_fiat_shamir::DomainSeparator

Implementation

public(friend) fun new_domain_separator(contract_address: address, chain_id: u8, protocol_id: vector<u8>, session_id: vector<u8>): DomainSeparator {
    DomainSeparator::V1 {
        contract_address,
        chain_id,
        protocol_id,
        session_id
    }
}

Function `fiat_shamir`

Returns the Sigma protocol challenge $e$ and $1,\beta,\beta^2,\ldots, \beta^{m-1}$

public(friend) fun fiat_shamir<P>(dst: sigma_protocol_fiat_shamir::DomainSeparator, stmt: &sigma_protocol_statement::Statement<P>, compressed_A: &vector<ristretto255::CompressedRistretto>, k: u64): (ristretto255::Scalar, vector<ristretto255::Scalar>)

Implementation

public(friend) fun fiat_shamir<P>(
    dst: DomainSeparator,
    stmt: &Statement<P>,
    compressed_A: &vector<CompressedRistretto>,
    k: u64): (Scalar, vector<Scalar>)
{
    let m = compressed_A.length();
    assert!(m != 0, error::invalid_argument(E_PROOF_COMMITMENT_EMPTY));

    // We will hash an application-specific domain separator and the (full) public statement,
    // which will include any public parameters like group generators $G$, $H$.

    // Note: A hardcodes $m$, the statement hardcodes $n_1$ and $n_2$, and $k$ is specified manually!
    let fs_inputs = FiatShamirInputs {
        dst,
        type_name: type_info::type_name<P>(),
        k,
        stmt_X: *stmt.get_compressed_points(),
        stmt_x: *stmt.get_scalars(),
        proof_A: *compressed_A
    };

    let seed = sha2_512_value(&fs_inputs);

    // Note:A more principled `Merlin` / `spongefish`-like approach would have been preferred, but... more code.
    //
    // e = SHA2-512(SHA2-512(fs_inputs.to_bcs_bytes()) || 0x00)
    seed.push_back(0u8);
    assert!(*seed.last() == 0, error::internal(E_INTERNAL_INVARIANT_FAILED));
    let e_hash = sha2_512(seed);

    // beta = SHA2-512(SHA2-512(fs_inputs.to_bcs_bytes()) || 0x01)
    *seed.last_mut() += 1;
    assert!(*seed.last() == 1, error::internal(E_INTERNAL_INVARIANT_FAILED));
    let beta_hash = sha2_512(seed);

    let e = new_scalar_uniform_from_64_bytes(e_hash).extract();
    let beta = new_scalar_uniform_from_64_bytes(beta_hash).extract();

    let betas = vector[];
    let prev_beta = scalar_one();
    betas.push_back(prev_beta);
    for (_i in 1..m) {
        prev_beta = prev_beta.scalar_mul(&beta);
        betas.push_back(prev_beta);
    };

    // This will only fail when our logic above for generating the `\beta_i`'s is broken
    assert!(betas.length() == m, error::internal(E_INTERNAL_INVARIANT_FAILED));

    (e, betas)
}

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Module 0x1::sigma_protocol_fiat_shamir

Enum DomainSeparator

Struct FiatShamirInputs