Short Proofs of Knowledge for Factoring [chapter]

Guillaume Poupard, Jacques Stern
2000 Lecture Notes in Computer Science  
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 e ciency improvement in comparison with the previously known schemes can be compared with the di erence 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
more » ... 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 veri er are enough to reach a high level of security.
doi:10.1007/978-3-540-46588-1_11 fatcat:touuimt47fc65eorvos5culhjm