Secure Sessions from Weak Secrets

Sometimes two parties who share a weak secret k such as a password wish to share a strong secret s such as a session key without revealing information about k to an active attacker. We assume that both parties can generate strong random numbers and forget secrets, and present three protocols for secure strong secret sharing, based on RSA, Diffie-Hellman, and El-Gamal. As well as being simpler and quicker than their predecessors, our protocols also have slightly stronger security properties: in particular, they make no cryptographic use of s and so impose no subtle restrictions upon the use which is made of s by other