Abstract
This paper presents a zero-knowledge interactive protocol that demonstrates that two factors, a and b, of a composite number n (= ab) are actually known by the prover, without revelation of the factors themselves and where a and b are not necessarily primes. The security of this protocol is based on the difficulty of computing a discrete logarithm modulo a large prime. As an extension of this, a protocol that can demonstrate that two or more factors are known by the prover is shown and applied to a weighted membership protocol with hierarchical classes within a group.
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Shizuya, H., Koyama, K., Itoh, T. (1990). Demonstrating possession without revealing factors and its application. In: Seberry, J., Pieprzyk, J. (eds) Advances in Cryptology — AUSCRYPT '90. AUSCRYPT 1990. Lecture Notes in Computer Science, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030368
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DOI: https://doi.org/10.1007/BFb0030368
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