How to construct random functions
Journal of the ACM (JACM)
Algorithmica
A simple unpredictable pseudo random number generator
SIAM Journal on Computing
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
Computerized patient information system in a psychiatric unit: five-year experience
Journal of Medical Systems
Proceedings of the 4th ACM conference on Computer and communications security
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Improved Online/Offline Signature Schemes
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th 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
Efficient Password-Authenticated Key Exchange Using Human-Memorable Passwords
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Analysis of Key-Exchange Protocols and Their Use for Building Secure Channels
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
The Composite Discrete Logarithm and Secure Authentication
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
How discreet is the discrete log?
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
An Improved Pseudo-Random Generator Based on the Discrete Logarithm Problem
Journal of Cryptology
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
How to generate cryptographically strong sequences of pseudo random bits
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Why and how to establish a private code on a public network
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
RSA/Rabin Bits are 1/2 + 1 Poly (Log N) Secure
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Efficient And Secure Pseudo-Random Number Generation
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
A new paradigm for collision-free hashing: incrementality at reduced cost
EUROCRYPT'97 Proceedings of the 16th 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
Collision free hash functions and public key signature schemes
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
An improved pseudorandom generator based on hardness of factoring
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Finding collisions in the full SHA-1
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Cryptanalysis of the hash functions MD4 and RIPEMD
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
How to break MD5 and other hash functions
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
More efficient DDH pseudorandom generators
Designs, Codes and Cryptography
Efficient pseudorandom generators based on the DDH assumption
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
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Since Diffie-Hellman [12], many secure systems, based on discrete logarithm or Diffie-Hellman assumption in ℤp, were introduced in the literature. In this work, we investigate the possibility to construct efficient primitives from exponentiation techniques over ℤp. Consequently, we propose a new pseudorandom generator, where its security is proven under the decisional Diffie-Hellman assumption. Our generator is the most efficient among all generators from ℤp* that are provably secure under standard assumptions. If an appropriate precomputation is allowed, our generator can produce O(loglogp) bits per modular multiplication. This is the best possible result in the literature (even improved by such a precomputation as well). Interestingly, our generator is the first provably secure under a decisional assumption and might be instructive for discovering potentially more efficient generators in the future. Our second result is a new family of universally collision resistant hash family (CRHF). Our CRHF is provably secure under the discrete log assumption and is more efficient than all previous CRHFs that are provably secure under standard assumptions (especially without a random oracle). This result is important, especially when the unproven hash functions (e.g., MD4, MD5, SHA-1) were broken by Wang et al. [37, 38, 39].