A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Rounding in lattices and its cryptographic applications
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
An Efficient Discrete Log Pseudo Random Generator
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Extracting randomness from samplable distributions
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A computational introduction to number theory and algebra
A computational introduction to number theory and algebra
On the bit security of the Diffie-Hellman key
Applicable Algebra in Engineering, Communication and Computing
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
On diffie-hellman key agreement with short exponents
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Using hash functions as a hedge against chosen ciphertext attack
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Merkle-Damgård revisited: how to construct a hash function
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
The Twist-AUgmented technique for key exchange
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
HMAC is a randomness extractor and applications to TLS
Proceedings of the 2008 ACM symposium on Information, computer and communications security
Optimal Randomness Extraction from a Diffie-Hellman Element
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
How to Extract and Expand Randomness: A Summary and Explanation of Existing Results
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Efficient pseudorandom generators based on the DDH assumption
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
Efficient simultaneous broadcast
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Strong designated verifier signature in a multi-user setting
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Cryptographic extraction and key derivation: the HKDF scheme
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Pseudorandom functions and permutations provably secure against related-key attacks
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
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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 $\mathbb Z^\star_p$ 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