Isogeny-Based Quantum-Resistant Undeniable Signatures

Abstract

Abstract. We propose an undeniable signature scheme based on elliptic curve isogenies, and prove its security under certain reasonable number-theoretic computational assumptions for which no efficient quantum algorithms are known. Our proposal represents only the second known quantum-resistant undeniable signature scheme, and the first such scheme secure under a number-theoretic complexity assumption.

Efficient Finite Field Multiplication for Isogeny Based Post Quantum Cryptography

“…The authors have described post quantum protocols for zero knowledge proof, key-exchange and public key cryptosystem in their paper [1]. Hash functions [17] and digital signature schemes [16] based on the isogenies have also been proposed.…”

On division polynomial PIT and supersingularity

“…For the second claim we show that (9) holds for any k, and the rest of the proof is the same. Using (8) with (m, n) = (2, p) and (m, n) = (p, 2) we get 2y πP = ψ 2 (π(P )) = ψ 2 (pP ) = 2y pP which implies π(P ) = pP , and hence ψ k (π(P )) = ψ k (pP ) for any k.…”

“…Recent cryptographic initiatives based on supersingular elliptic curves have attracted considerable attention [7,8,3]. In particular, the underlying security assumption in such constructions is the hardness of computing isogenies between two curves.…”

Short Paper: Coercion-Resistant Voting in Linear Time via Fully Homomorphic Encryption

“…Post-Quantum Considerations. For a relaxation of the trustworthiness assumption of R, without assuming secure erasure, quantum-resistant designated verifier proofs [28,20] could replace the classical ones suggested in the original JCJ [21]. To obtain post-quantum security for eligibility verifiability, future research will investigate the use of a quantum-resistant signature scheme that can be evaluated under FHE to preserve ballot anonymity.…”