Abstract

Abstract. In this paper we introduce very simple deterministic randomness extractors for Diffie-Hellman distributions. More specifically we show that the k most significant bits or the k least significant bits of a random element in a subgroup of Z ⋆ p are indistinguishable from a random bit-string of the same length. This allows us to show that under the Decisional Diffie-Hellman assumption we can deterministically derive a uniformly random bit-string from a Diffie-Hellman exchange in the standard model. Then, we show that it can be used in key exchange or encryption scheme to avoid the leftover hash lemma and universal hash functions. Keywords: Diffie-Hellman transform, randomness extraction, least significant bits, exponential sums. 1

Citations