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Version: 3.7.0

Pairings in ICICLE

Pairings are a fundamental cryptographic primitive that enable a wide range of advanced cryptographic protocols, including zero-knowledge proofs, identity-based encryption, and more. ICICLE provides efficient implementations of cryptographic pairings optimized for various hardware backends.

What are Pairings?​

A cryptographic pairing is a bilinear map e: G1 × G2 → GT, where:

  • G1 and G2 are elliptic curve groups
  • GT is a multiplicative subgroup of a field extension
  • The map preserves the bilinear property: e(aP, bQ) = e(P,Q)^(ab)

This bilinear property makes pairings particularly useful for constructing complex cryptographic protocols.

Pairing Implementation in ICICLE​

ICICLE implements pairings through a templated interface that supports different pairing configurations. The main pairing function is defined in pairing.h:

template <typename PairingConfig>
eIcicleError pairing(
  const typename PairingConfig::G1Affine& p,
  const typename PairingConfig::G2Affine& q,
  typename PairingConfig::TargetField* output);

Key Components​

  1. PairingConfig: A configuration type that defines:

    • Field definitions
    • Implementation details
    • Group types (G1, G2)
    • Target field type (GT)

  2. Input Points: The pairing takes two input points:

    • p: An affine point in G1
    • q: An affine point in G2

  3. Output: The result is stored in the target field (GT)

Supported Pairing Types​

Currently, ICICLE supports the following pairing-friendly curves:

  • bn254
  • bls12-381
  • bls12-377

The specific implementations can be found in the models/ directory.

Usage Example​

Here's a basic example of how to use pairings in ICICLE:

#include "icicle/pairing/pairing.h"
#include "icicle/pairing/models/bn254.h"

// Initialize points
Bn254::G1Affine p = ...;
Bn254::G2Affine q = ...;
Bn254::TargetField result;

// Compute pairing
eIcicleError err = icicle::pairing<Bn254>(p, q, result);

Further Reading​

For specific implementation details and advanced usage, refer to the API documentation in the source code.