On the Security of Two Public Key Cryptosystems Using Non-Abelian Groups

The security of two public key encryption schemes relying on the hardness of different computational problems in non-abelian groups is investigated. First, an attack on a conceptual public key scheme based on Grigorchuk groups is presented: We show that from the public data one can easily derive an ‘equivalent’ secret key that allows the decryption of arbitrary messages encrypted under the public key. Hereafter, a security problem in another conceptual public key scheme based on non-abelian groups is pointed out: We show that in the present form the BMW scheme is vulnerable to an attack, which can recover large parts of the private subgroup chain from the public key.