Provably Secure Integration Cryptosystem on Non-Commutative Group

TL;DR

This paper proves the security of a braid group cryptosystem against CPA and introduces a new braid group cryptosystem secure against CCA2, using random oracle models and the CCS assumption.

Contribution

It provides the first proof of security for Ko's braid group cryptosystem against CPA and proposes a novel CCA2-secure cryptosystem based on braid groups.

Findings

Ko's cryptosystem is CPA-secure but vulnerable to active attacks.

A new braid group cryptosystem is secure against CCA2.

Security proofs are based on the random oracle model and CCS assumption.

Abstract

Braid group is a very important non-commutative group. It is also an important tool of quantum field theory, and has good topological properties. This paper focuses on the provable security research of cryptosystem over braid group, which consists of two aspects: One, we proved that the Ko's cryptosystem based on braid group is secure against chosen-plaintext-attack(CPA) which proposed in CRYPTO2000, while it dose not resist active attack. The other is to propose a new public key cryptosystem over braid group which is secure against adaptive chosen-ciphertext-attack(CCA2). Our proofs are based on random oracle models, under the computational conjugacy search assumption( the CCS assumption ). This kind of results have never been seen before.