How to construct random functions
Journal of the ACM (JACM)
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
Improved security bounds for pseudorandom permutations
Proceedings of the 4th ACM conference on Computer and communications security
The Security of Cipher Block Chaining
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
LFSR-based Hashing and Authentication
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
MDx-MAC and Building Fast MACs from Hash Functions
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
XOR MACs: New Methods for Message Authentication Using Finite Pseudorandom Functions
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
On Fast and Provably Secure Message Authentication Based on Universal Hashing
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
A Concrete Security Treatment of Symmetric Encryption
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
L-collision Attacks against Randomized MACs
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Indistinguishability of Random Systems
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Increasing the Lifetime of a Key: A Comparative Analysis of the Security of Re-keying Techniques
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
On the Security of Randomized CBC-MAC Beyond the Birthday Paradox Limit: A New Construction
FSE '02 Revised Papers from the 9th International Workshop on Fast Software Encryption
How to thwart birthday attacks against MACs via small randomness
FSE'10 Proceedings of the 17th international conference on Fast software encryption
Domain extension for MACs beyond the birthday barrier
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
A new variant of PMAC: beyond the birthday bound
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Benes and butterfly schemes revisited
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
Hardness preserving reductions via cuckoo hashing
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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Many cryptographic solutions based on pseudorandom functions (for common problems like encryption, message-authentication or challenge-response protocols) have the following feature: There is a stateful (counter based) version of the scheme that has high security, but if, to avoid the use of state, we substitute a random value for the counter, the security of the scheme drops below the birthday bound. In some situations the use of counters or other forms of state is impractical or unsafe. Can we get security beyond the birthday bound without using counters? This paper presents a paradigm for strengthening pseudorandom function usages to this end, the idea of which is roughly to use the XOR of the values of a pseudorandom function on a small number of distinct random points in place of its value on a single point. We establish two general security properties of our construction, "pseudorandomness" and "integrity", with security beyond the birthday bound. These can be applied to derive encryption schemes, and MAC schemes (based on universal hash functions), that have security well beyond the birthday bound, without the use of state and at moderate computational cost.