Authentication theory/coding theory
Proceedings of CRYPTO 84 on Advances in cryptology
On families of hash functions via geometric codes and concatenation
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Universal hashing and authentication codes
Designs, Codes and Cryptography
LFSR-based Hashing and Authentication
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Bucket Hashing and its Application to Fast Message Authentication
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
On the covering radius of cyclic linear codes and arithmetic codes
Discrete Applied Mathematics
New hash functions for message authentication
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
On the cardinality of systematic authentication codes via error-correcting codes
IEEE Transactions on Information Theory
An upper bound for Weil exponential sums over Galois rings and applications
IEEE Transactions on Information Theory
The Hidden Number Problem in Extension Fields and Its Applications
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
SQUARE HASH: Fast Message Authenication via Optimized Universal Hash Functions
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Almost Independent and Weakly Biased Arrays: Efficient Constructions and Cryptologic Applications
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Universal Hashing and Multiple Authentication
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Optimal authentication codes from difference balanced functions
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
New constructions of universal hash functions based on function sums
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
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In this paper new families of strongly universal hash functions, or equivalently, authentication codes, are proposed. Their parameters are derived from bounds on exponential sums over finite fields and Galois rings. This is the first time hash families based upon such exponential sums have been considered. Their performance improves the previously best known constructions and they can be made general in their choice of parameters. Furthermore, the constructions are suitable both for hardware and software implementations. The latter is an aspect that is significant and has been considered in several recent papers.