Undeniable-Signature-Scheme-on-Modular-Lattice

Overview

This project presents an undeniable signature scheme based on modular lattices to enhance security and align with proposed post-quantum cryptographic standards. The GPV (Gentry, Peikert, and Vaikuntanathan) signature scheme serves as the base, with modifications to adapt it to modular lattices.

Reasons for Modification

1. Enhanced Security: Shifting to modular lattices for improved security.
2. Standardization Alignment: Aligning with proposed cryptographic standards.
3. Research Development: Embracing algorithmic advances suited for modular lattices.

Implementation Plan

Developed new key generation, signing, and verification functions tailored for modular lattices.

Key Algorithms

KeyGen Algorithm

Generates signing and verification keys.

• Input: Security parameter n.
• Output: Signing key (sk) and verification key (pk).

Sign Algorithm

Creates a signature for a given plaintext message.

• Input: Message (m) and signing key (sk).
• Output: Returns 1 for a valid signature; otherwise, 0.

Confirmation Protocol

Interactive communication between Signer (S) and Verifier (V).

• Returns 1 for a valid signature; otherwise, 0.

Disavowal Protocol

Interactive communication between Signer (S) and Verifier (V).

• Returns 1 for an invalid signature; otherwise, 0.

Experimental Setup

Utilized two cryptographically secure collision-resistant hash functions:

Two variants for the modular hash function:

• Hash_com: To hash a random seed
• Hash_com_message: To hash a message concatenated with a random seed

Key Generation

Executes MLTrapGen algorithm to obtain a pair (A, T).

• Outputs public key (PK) and secret key (SK).

Signature Generation

Produces a signature σ on the message m.

• Outputs the signature σ for the message m.

Verification

2. Confirmation/Disavowal Protocol: This protocol operates between the signer and verifier
   • If all verifications pass successfully, the verifier outputs 1; otherwise, it outputs 0.