## Efficient Cryptographic Schemes Provably as Secure as Subset Sum (1993)

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Venue: | Journal of Cryptology |

Citations: | 78 - 8 self |

### BibTeX

@ARTICLE{Impagliazzo93efficientcryptographic,

author = {Russell Impagliazzo and Moni Naor},

title = {Efficient Cryptographic Schemes Provably as Secure as Subset Sum},

journal = {Journal of Cryptology},

year = {1993},

volume = {9},

pages = {236--241}

}

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### Abstract

We show very efficient constructions for a pseudo-random generator and for a universal one-way hash function based on the intractability of the subset sum problem for certain dimensions. (Pseudo-random generators can be used for private key encryption and universal one-way hash functions for signature schemes). The increase in efficiency in our construction is due to the fact that many bits can be generated/hashed with one application of the assumed one-way function. All our construction can be implemented in NC using an optimal number of processors. Part of this work done while both authors were at UC Berkeley and part when the second author was at the IBM Almaden Research Center. Research supported by NSF grant CCR 88 - 13632. A preliminary version of this paper appeared in Proc. of the 30th Symp. on Foundations of Computer Science, 1989. 1 Introduction Many cryptosystems are based on the intractability of such number theoretic problems such as factoring and discrete logarit...