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A protocol compiler is described, that transforms any prov-ably secure authenticated 2-party key establishment into a provably secure authenticated group key establishment with 2 more rounds of communication. The compiler introduces neither idealizing assumptions nor high-entropy secrets, e. g., for signing. In particular, applying the compiler to a… (More)

We examine the popular proof models for group key establishment of Bresson et al. [BCPQ01,BCP01] and point out missing security properties that are present in some models for two-party key establishment. These properties are actually of more importance in group key establishments due to the possibility of malicious insiders. We show that established group… (More)

Boneh and Venkatesan have recently proposed a polynomial time algorithm for recovering a " hidden " element α of a finite field IFp of p elements from rather short strings of the most significant bits of the remainder modulo p of αt for several values of t selected uniformly at random from IF * p. We use some recent bounds of exponential sums to generalize… (More)

Boneh and Venkatesan have recently proposed a polynomial time algorithm for recovering a " hidden " element α of a finite field Fp of p elements from rather short strings of the most significant bits of the remainder modulo p of αt for several values of t selected uniformly at random from F * p. Unfortunately the applications to the computational security… (More)

A provably secure password-authenticated protocol for group key establishment in the common reference string (CRS) model is presented. Our construction assumes the participating users to share a common password and combines smooth hashing as introduced by Cramer and Shoup with a construction of Burmester and Desmedt. Our protocol is constant-round. Namely,… (More)

We generalize and extend results obtained by Boneh and Venkatesan in 1996 and by González Vasco and Shparlinski in 2000 on the hardness of computing bits of the Diffie-Hellman key, given the public values. Specifically, while these results could only exclude (essentially) error-free predictions, we here exclude any non-negligible advantage , though for… (More)