How to construct random functions
Journal of the ACM (JACM)
A digital signature scheme secure against adaptive chosen-message attacks
SIAM Journal on Computing - Special issue on cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
From Fixed-Length to Arbitrary-Length RSA Padding Schemes
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Short Signatures from the Weil Pairing
Journal of Cryptology
On the algebraic complexity of set equality and inclusion
Information Processing Letters
The exact security of digital signatures-how to sign with RSA and Rabin
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
From fixed-length to arbitrary-length RSA encoding schemes revisited
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
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A multi-set (ms ) is a set where an element can occur more than once. ms hash functions (mshf s) map ms s of arbitrary cardinality to fixed-length strings. This paper introduces a new rsa -based mshf . The new function is efficient and produces small hashes. We prove that the proposed mshf is collision-resistant under the assumption of unforgeability of deterministic rsa signatures. In many practical applications, programmers need to compare two (unordered) sets of integers. A trivial solution consists in sorting both sets ($\mathcal{O}(n \log n)$) and comparing them linearly. We show how ms hash functions can be turned into a quasi-linear-time, quasi-constant-space integer set equality test. An interesting advantage of the proposed algorithm is its ability to compare ms s without sorting them. This can prove useful when comparing very large files which are read-only or otherwise hard to sort (e.g. on tapes, distributed across web-sites etc).