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 non-interactive. 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.
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Poupard, G., Stern, J. (2000). Short Proofs of Knowledge for Factoring. In: Imai, H., Zheng, Y. (eds) Public Key Cryptography. PKC 2000. Lecture Notes in Computer Science, vol 1751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46588-1_11
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DOI: https://doi.org/10.1007/978-3-540-46588-1_11
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