Abstract
We show that Toeplitz matrices generated by sequences drawn from small biased distributions provide hashing schemes applicable to se- cure message authentication. This work extends our previous results from Crypto'94 [4] where an authentication scheme based on Toeplitz matrices generated by linear feedback shift registers was presented.
Our new results have as special case the LFSR-based construction but ex- tend to a much wider and general family of sequences, including several simple and efficient constructions with close to optimal security. Examples of the new constructions include Toeplitz matrices generated by the Le- gendre symbols of consecutive integers modulo a prime (of size significantly shorter than required by public-key modular arithmetic) as well as other algebraic constructions. The interest of these schemes extends beyond the proposed cryptographic applications to other uses of universal hashing (in- cluding other cryptographic applications).
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Krawczyk, H. (1995). New Hash Functions for Message Authentication. In: Guillou, L.C., Quisquater, JJ. (eds) Advances in Cryptology — EUROCRYPT ’95. EUROCRYPT 1995. Lecture Notes in Computer Science, vol 921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49264-X_24
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DOI: https://doi.org/10.1007/3-540-49264-X_24
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