## Short Proofs of Knowledge for Factoring (2000)

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Venue: | in PKC 2000, Springer LNCS 1751 |

Citations: | 12 - 4 self |

### BibTeX

@INPROCEEDINGS{Poupard00shortproofs,

author = {Guillaume Poupard and Jacques Stern},

title = {Short Proofs of Knowledge for Factoring},

booktitle = {in PKC 2000, Springer LNCS 1751},

year = {2000},

pages = {147--166},

publisher = {Springer-Verlag}

}

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### Abstract

. The aim of this paper is to design a proof of knowledge for the factorization of an integer n. We propose a statistical zero-knowledge protocol similar to proofs of knowledge of discrete logarithm a la Schnorr. The efficiency improvement in comparison with the previously known schemes can be compared with the difference between the Fiat-Shamir scheme and the Schnorr one. Furthermore, the proof can be made noninteractive. From a practical point of view, the improvement is dramatic: the size of such a non-interactive proof is comparable to the size of the integer n and the computational resources needed can be kept low; three modular exponentiations both for the prover and the verifier are enough to reach a high level of security. This paper appears in the proceedings of PKC2000, LNCS , Springer Verlag, 2000 1 Introduction Zero-knowledge (ZK) proofs have first been proposed in 1985 by Goldwasser, Micali and Rackoff [14]. Those proofs are interactive protocols between a prover who wan...