The computational complexity of universal hashing
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
The security of the cipher block chaining message authentication code
Journal of Computer and System Sciences
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
RIPEMD-160: A Strengthened Version of RIPEMD
Proceedings of the Third International Workshop on Fast Software Encryption
Pseudorandom functions revisited: the cascade construction and its concrete security
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Exposure-resilient cryptography
Exposure-resilient cryptography
A computational introduction to number theory and algebra
A computational introduction to number theory and algebra
HMAC is a randomness extractor and applications to TLS
Proceedings of the 2008 ACM symposium on Information, computer and communications security
Hardness of distinguishing the MSB or LSB of secret keys in diffie-hellman schemes
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
New proofs for NMAC and HMAC: security without collision-resistance
CRYPTO'06 Proceedings of the 26th 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
On the security of iterated message authentication codes
IEEE Transactions on Information Theory
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We examine the use of randomness extraction and expansion in key agreement (KA) protocols to generate uniformly random keys in the standard model. Although existing works provide the basic theorems necessary, they lack details or examples of appropriate cryptographic primitives and/or parameter sizes. This has lead to the large amount of min-entropy needed in the (non-uniform) shared secret being overlooked in proposals and efficiency comparisons of KA protocols. We therefore summarize existing work in the area and examine the security levels achieved with the use of various extractors and expanders for particular parameter sizes. The tables presented herein show that the shared secret needs a min-entropy of at least 292 bits (and even more with more realistic assumptions) to achieve an overall security level of 80 bits using the extractors and expanders we consider. The tables may be used to find the min-entropy required for various security levels and assumptions. We also find that when using the short exponent theorems of Gennaro et al., the short exponents may need to be much longer than they suggested.