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A presentation of a group with two generators having unsolvable word problem and an explicit countable presentation of Mihailova subgroup of F 2 × F 2 with finite number of generators are given. Where Mihailova subgroup of F 2 × F 2 enjoys the unsolvable subgroup membership problem. One then can use the presentation to create entities' private keys in a(More)
By introducing extra shields on Shpilrain and Ushakov's Ko-Lee-like protocol based on the decomposition problem of group elements we propose two new key exchange schemes and then a number of public key cryptographic protocols. We show that these protocols are free of known attacks. Particularly, if the entities taking part in our protocols create their(More)
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