Ring and semigroup security Sample Clauses

Ring and semigroup security. ‌ The primary question is whether an adversary seeing the two deliveries d and e can also compute the key abc. In other words, can abc be computed from d, b and e? A secondary question is whether an adversary can deduce a from d, which could be an additional problem for Xxxxx if she re-uses a, in the key over an authenticated (but public) channel. 5In some applications, only one of the parties of authenticated, perhaps with post- agreement authentication being used for the party whose delivery was not authenticated. agreement, or otherwise. These questions can be re-stated as computational problems for a semigroup or a ring. The basic security of key agreement requires that a hard computational problem in the underlying semigroup, the wedge problem of computing abc from [ab, b, bc]. If the wedge problem is easy, then the associative key agree- ment scheme is insecure. The division problem must also be hard. For example, if a = d/b, then Xxxxx’s secret a can be computed from d and b, neither of which are secret. An adversary who also sees e can compute Xxxxx’s key f = ae. If Xxxxx uses the secret a for other purposes, then the division problem can be more important than the wedge problem. In Diffie–Xxxxxxx key agreement, the underlying semigroup has division problem equivalent to the discrete logarithm problem, and has a wedge prob- lem equivalent to the well-known Diffie–Xxxxxxx problem.