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Collision-free hashing from lattice problems. (English) Zbl 1343.94055
Goldreich, Oded (ed.), Studies in complexity and cryptography. Miscellanea on the interplay between randomness and computation. In collaboration with Lidor Avigad, Mihir Bellare, Zvika Brakerski, Shafi Goldwasser, Shai Halevi, Tali Kaufman, Leonid Levin, Noam Nisan, Dana Ron, Madhu Sudan, Luca Trevisan, Salil Vadhan, Avi Wigderson, David Zuckerman. Berlin: Springer (ISBN 978-3-642-22669-4/pbk). Lecture Notes in Computer Science 6650, 30-39 (2011).
Summary: M. Ajtai [in: Proceedings of the 28th annual ACM symposium on the theory of computing, STOC ’96. New York, NY: ACM. 99–108 (1996; Zbl 0921.11071)] described a construction of one-way functions whose security is equivalent to the difficulty of some well known approximation problems in lattices. We show that essentially the same construction can also be used to obtain collision-free hashing. This paper contains a self-contained proof sketch of Ajtai’s result.
For the entire collection see [Zbl 1220.68005].

MSC:
94A60 Cryptography
11H06 Lattices and convex bodies (number-theoretic aspects)
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