ECDSA, Schnorr & EdDSA Signatures

All three signature schemes follow a similar pattern with a Cairo struct containing the signature data and hints for efficient verification. Garaga provides tooling in Python/Rust/JavaScript to generate the full expected Cairo struct given signature information.

All signature verification schemes work with all Supported Elliptic Curves in Garaga (except EdDSA which is specific to Ed25519), using the corresponding curve identifier.

Cairo Verification Functions

Verification functions take the public key as a separate parameter:

is_valid_ecdsa_signature_assuming_hash(signature, public_key, curve_id) -> bool
is_valid_schnorr_signature_assuming_hash(signature, public_key, curve_id) -> bool
is_valid_eddsa_signature(signature, Py_twisted) -> bool

Important: The ECDSA and Schnorr verification functions assume that the message hash has been correctly computed by the caller. They verify the signature equation but do not hash the message themselves.

Public Key Handling

The public key is always passed as a separate parameter to the verification function. This allows you to:

Hardcode the public key in your contract if it's known at compile time
Provide the public key dynamically at runtime

When generating calldata with the SDK, use the prepend_public_key parameter:

prepend_public_key=True (default): The public key is included in the serialized calldata, allowing you to deserialize both the signature and public key from the same array
prepend_public_key=False: Only the signature is serialized; you must provide the public key separately (useful when the public key is hardcoded in your contract)

ECDSA Signature Verification

Cairo Structs

use garaga::signatures::ecdsa::{ECDSASignature, ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash};
use garaga::definitions::{G1Point, u384};

/// Core signature data
struct ECDSASignature {
    rx: u384,   // r component (R.x mod n)
    s: u256,    // s component
    v: bool,    // Parity of R.y (false if even, true if odd)
    z: u256,    // Message hash (assumed correctly computed by caller)
}

/// Signature bundled with verification hints
struct ECDSASignatureWithHint {
    signature: ECDSASignature,
    msm_hint: Span<felt252>,
}

Usage Example

use garaga::signatures::ecdsa::{ECDSASignatureWithHint, is_valid_ecdsa_signature_assuming_hash};
use garaga::definitions::{G1Point, u384};

fn verify_ecdsa_signature(
    serialized_signature: Span<felt252>,
    public_key: G1Point,
    curve_id: usize,
) -> bool {
    // Deserialize the signature with hints
    let mut data = serialized_signature;
    let signature_with_hints = Serde::<ECDSASignatureWithHint>::deserialize(ref data).unwrap();

    // Verify the signature
    // curve_id: 0=BN254, 1=BLS12_381, 2=SECP256K1, 3=SECP256R1, 5=GRUMPKIN
    is_valid_ecdsa_signature_assuming_hash(signature_with_hints, public_key, curve_id)
}

Calldata Generation

from garaga.starknet.tests_and_calldata_generators.signatures import ECDSASignature
from garaga.definitions import CurveID

# Create signature object with all required fields
sig = ECDSASignature(
    r=0x...,              # r component of signature
    s=0x...,              # s component of signature
    v=0,                  # 0 if R.y is even, 1 if odd
    px=0x...,             # Public key x-coordinate
    py=0x...,             # Public key y-coordinate
    z=0x...,              # Message hash
    curve_id=CurveID.SECP256K1
)

# Generate calldata with public key included (for dynamic public key)
calldata = sig.serialize_with_hints(prepend_public_key=True)

# Generate calldata without public key (for hardcoded public key in contract)
calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False)

use garaga_rs::calldata::signatures::ecdsa_calldata_builder;
use garaga_rs::definitions::CurveID;

// Generate calldata with public key included
let calldata = ecdsa_calldata_builder(
    r,              // r component
    s,              // s component
    v,              // recovery parameter (0 or 1)
    px,             // public key x
    py,             // public key y
    z,              // message hash
    true,           // prepend_public_key
    CurveID::SECP256K1 as usize,
)?;

// Generate calldata without public key (for hardcoded public key)
let calldata_no_pk = ecdsa_calldata_builder(r, s, v, px, py, z, false, CurveID::SECP256K1 as usize)?;

import { ecdsaCalldataBuilder, CurveId } from 'garaga';

// Generate calldata with public key included
const calldata = ecdsaCalldataBuilder(
    r,              // r component (bigint)
    s,              // s component (bigint)
    v,              // recovery parameter (0 or 1)
    px,             // public key x (bigint)
    py,             // public key y (bigint)
    z,              // message hash (bigint)
    true,           // prependPublickey
    CurveId.SECP256K1
);

// Generate calldata without public key (for hardcoded public key)
const calldataNoKey = ecdsaCalldataBuilder(r, s, v, px, py, z, false, CurveId.SECP256K1);

Schnorr Signature Verification

Cairo Structs

use garaga::signatures::schnorr::{SchnorrSignature, SchnorrSignatureWithHint, is_valid_schnorr_signature_assuming_hash};
use garaga::definitions::{G1Point, u384};

/// Core signature data
struct SchnorrSignature {
    rx: u384,   // x-coordinate of R point
    s: u256,    // s component
    e: u256,    // Challenge hash (assumed correctly computed by caller)
}

/// Signature bundled with verification hints
struct SchnorrSignatureWithHint {
    signature: SchnorrSignature,
    msm_hint: Span<felt252>,
}

BIP340 Requirement: The public key's y-coordinate must be even. The verification function will return false if the public key has an odd y-coordinate.

Usage Example

use garaga::signatures::schnorr::{SchnorrSignatureWithHint, is_valid_schnorr_signature_assuming_hash};
use garaga::definitions::{G1Point, u384};

fn verify_schnorr_signature(
    serialized_signature: Span<felt252>,
    public_key: G1Point,
    curve_id: usize,
) -> bool {
    // Deserialize the signature with hints
    let mut data = serialized_signature;
    let signature_with_hints = Serde::<SchnorrSignatureWithHint>::deserialize(ref data).unwrap();

    // Verify the signature
    // Note: public_key.y must be even (BIP340 requirement)
    is_valid_schnorr_signature_assuming_hash(signature_with_hints, public_key, curve_id)
}

Calldata Generation

from garaga.starknet.tests_and_calldata_generators.signatures import SchnorrSignature
from garaga.definitions import CurveID

# Create signature object (py must be even)
sig = SchnorrSignature(
    rx=0x...,             # x-coordinate of R point
    s=0x...,              # s component
    e=0x...,              # Challenge hash
    px=0x...,             # Public key x-coordinate
    py=0x...,             # Public key y-coordinate (must be even!)
    curve_id=CurveID.BN254
)

# Generate calldata with public key included
calldata = sig.serialize_with_hints(prepend_public_key=True)

# Generate calldata without public key (for hardcoded public key)
calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False)

use garaga_rs::calldata::signatures::schnorr_calldata_builder;
use garaga_rs::definitions::CurveID;

// Generate calldata with public key included
let calldata = schnorr_calldata_builder(
    rx,             // R.x coordinate
    s,              // s component
    e,              // challenge hash
    px,             // public key x
    py,             // public key y (must be even!)
    true,           // prepend_public_key
    CurveID::BN254 as usize,
)?;

// Generate calldata without public key
let calldata_no_pk = schnorr_calldata_builder(rx, s, e, px, py, false, CurveID::BN254 as usize)?;

import { schnorrCalldataBuilder, CurveId } from 'garaga';

// Generate calldata with public key included
const calldata = schnorrCalldataBuilder(
    rx,             // R.x coordinate (bigint)
    s,              // s component (bigint)
    e,              // challenge hash (bigint)
    px,             // public key x (bigint)
    py,             // public key y (bigint, must be even!)
    true,           // prependPublickey
    CurveId.BN254
);

// Generate calldata without public key
const calldataNoKey = schnorrCalldataBuilder(rx, s, e, px, py, false, CurveId.BN254);

EdDSA Signature Verification (Ed25519)

EdDSA signatures use the Ed25519 curve following RFC 8032. The implementation explicitly rejects small-order points to prevent key-compromise and signature-malleability attacks.

Cairo Structs

use garaga::signatures::eddsa_25519::{EdDSASignature, EdDSASignatureWithHint, is_valid_eddsa_signature};

/// Core signature data
struct EdDSASignature {
    Ry_twisted: u256,    // Compressed R point y-coordinate (little-endian)
    s: u256,             // Signature scalar
    msg: Span<u8>,       // Original message bytes
}

/// Signature bundled with verification hints
struct EdDSASignatureWithHint {
    signature: EdDSASignature,
    msm_hint: Span<felt252>,
    sqrt_Rx_hint: u256,  // Hint for R point decompression
    sqrt_Px_hint: u256,  // Hint for public key decompression
}

Note: EdDSA takes the raw message bytes, not a hash. The verification function computes SHA-512(R || A || msg) internally as per RFC 8032.

Usage Example

use garaga::signatures::eddsa_25519::{EdDSASignatureWithHint, is_valid_eddsa_signature};

fn verify_eddsa_signature(
    serialized_signature: Span<felt252>,
    Py_twisted: u256,  // Compressed public key y-coordinate (little-endian)
) -> bool {
    // Deserialize the signature with hints
    let mut data = serialized_signature;
    let signature_with_hints = Serde::<EdDSASignatureWithHint>::deserialize(ref data).unwrap();

    // Verify the signature
    is_valid_eddsa_signature(signature_with_hints, Py_twisted)
}

Calldata Generation

from garaga.starknet.tests_and_calldata_generators.signatures import EdDSA25519Signature

# Create signature object
sig = EdDSA25519Signature(
    Ry_twisted=0x...,     # Compressed R point (little-endian integer)
    s=0x...,              # Signature scalar
    Py_twisted=0x...,     # Compressed public key (little-endian integer)
    msg=b"Hello, World!"  # Raw message bytes
)

# Generate calldata with public key included
calldata = sig.serialize_with_hints(prepend_public_key=True)

# Generate calldata without public key (for hardcoded public key)
calldata_no_pk = sig.serialize_with_hints(prepend_public_key=False)

use garaga_rs::calldata::signatures::eddsa_calldata_builder;

let message = b"Hello, World!".to_vec();

// Generate calldata with public key included
let calldata = eddsa_calldata_builder(
    ry_twisted,     // Compressed R point y-coordinate
    s,              // Signature scalar
    py_twisted,     // Compressed public key y-coordinate
    message.clone(),
    true,           // prepend_public_key
)?;

// Generate calldata without public key
let calldata_no_pk = eddsa_calldata_builder(ry_twisted, s, py_twisted, message, false)?;

import { eddsaCalldataBuilder } from 'garaga';

const message = new TextEncoder().encode("Hello, World!");

// Generate calldata with public key included
const calldata = eddsaCalldataBuilder(
    ry_twisted_le,  // Compressed R point (bigint, little-endian)
    s,              // Signature scalar (bigint)
    py_twisted_le,  // Compressed public key (bigint, little-endian)
    message,        // Uint8Array
    true            // prependPublickey
);

// Generate calldata without public key
const calldataNoKey = eddsaCalldataBuilder(ry_twisted_le, s, py_twisted_le, message, false);

Curve Identifiers

Curve ID

Value

Notes

BN254

BLS12_381

SECP256K1

Bitcoin/Ethereum

SECP256R1

P-256/NIST

ED25519

Only for EdDSA

GRUMPKIN

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EdDSA Signature Verification (Ed25519)

Cairo Structs

Usage Example

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