Provably Secure Integration Cryptosystem on Non-Commutative Group
This work addresses security vulnerabilities in non-commutative group-based cryptography, providing provable defenses for cryptosystems used in quantum-resistant applications, though it is incremental as it builds on existing methods.
The paper tackled the security of cryptosystems over braid groups by proving that Ko's cryptosystem is secure against chosen-plaintext attacks but not active attacks, and proposed a new public key cryptosystem secure against adaptive chosen-ciphertext attacks, with proofs based on random oracle models and the computational conjugacy search assumption.
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.