A ring signature scheme over braid groups

Satyam Omar

Rahul Kundnani

Abstract We propose BRCE (Braid-Ring Convolutional Encryption), a novel quantum-resilient group ring-based encryption scheme built over the non-abelian structure of braid groups and their integral group rings. The encryption mechanism applies convolution-based masking with randomized braid elements to achieve semantic obfuscation without relying on periodic structures. Our design embeds high-entropy messages into non-commutative algebraic carriers , resulting in ciphertexts that resist both classical and quantum algebraic attacks. We provide a provable security reduction from the Conjugacy Search Problem (CSP) in braid groups and show that the scheme satisfies IND-CPA and IND-CCA security notions under reasonable pseudorandomness assumptions. We anchor security in a new hardness assump-tion—the Group Ring Convolution Inversion Problem (GRCIP)—tailored to non-abelian group rings. Further, we demonstrate that the structure resists reductions to the Hidden Subgroup Problem (HSP), positioning BRCE as a competitive post-quantum candidate rooted in topological and algebraic hardness. MSC 2020: 94A60, 20F36, 68Q12, 11T71

Kunal Dey, Mansi Goyal, Aditi Kar Gangopadhyay +1 more

Xiufeng Zhao

Three types of traditional hard problem could be resolved by Shor,Boneh and Lipton's quantum algorithms in po-lynomial time.By the braid group constructed a lot of mathematics difficulties were not an effective solution under the conditions of the quantum computer.It seemed that braid group was a kind of considerable considerable cryptography platform in the future.This paper proposed a new proxy blind signature scheme based on conjugate search problem and the p-th root finding problem,and the exchangeable of the group operation between the elements in the left subgroup and the right subgroup of a braid group.Through program analysis shows that the new scheme is effective and feasible.

Zihao Xiong, Aihan Yin

Chi Qiu, Shibin Zhang, Yan Zuo Chang +2 more