Discrete Applied Mathematics
UMAC: Fast and Secure Message Authentication
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
SQUARE HASH: Fast Message Authenication via Optimized Universal Hash Functions
CRYPTO '99 Proceedings of the 19th 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
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
MMH: Software Message Authentication in the Gbit/Second Rates
FSE '97 Proceedings of the 4th International Workshop on Fast Software Encryption
Universal Hash Functions from Exponential Sums over Finite Fields and Galois Rings
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
New hash functions for message authentication
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Square hash with a small key size
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
New Applications of Differential Bounds of the SDS Structure
ISC '08 Proceedings of the 11th international conference on Information Security
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In this paper, we propose a generalization of the SQUARE hash function family to the function sum hash, which is based on functions with low maximal differential over arbitrary Abelian groups. These new variants allow the designer to construct SQUARE-like hash functions on different platforms for efficient and secure message authentication. A variant using functions with low algebraic degree over a finite field is also proposed which enables the user to use a shorter key. For more versatility, we also propose a trade-off between the hash key length and security bound. Finally, we show that we can use an SPN structure in the function sum hash to construct a provably secure MAC with performance which is several times faster than the traditional CBC-MAC. Moreover, there are implementation advantages like parallelizability to increase the speed further and re-use of cipher components which help save on implementation resources.