On the Security of the Cha-Ko-Lee-Han-Cheon Braid Group Public Key Cryptosystem

At the CRYPTO 2000 conference the seminal KLCHKP (Ko-Lee-CheonHan-Kang-Park) braid group public-key cryptosystem was published see [2]. An updated version of the KLCHKP cryptosystem which is the CKLHC (ChaKo-Lee-Han-Cheon) braid group cryptosystem was introduced at ASIACRYPT 2001 conference [10] the claim of the authors was the updated cryptosystem is based on the DH-DP (Diffie-Hellman Decomposition Problem). We show that the KLCHKP and CKLHC cryptosystems are based on the MSCSP and it has been assumed for several years the security of these cryptosystems are based on the DH-CP and DH-DP respectively, we also show the related cryptosystems may be based on the MSCSP and hence give a new way to break the KLCHKP and CKLHC cryptosystems and the related cryptosystems for some parameters. It has been shown there is a linear algebraic attack on the KLCHKP and CKLHC cryptosystems but our attack is more practical.