Demonstrating possession without revealing factors and its application

Hiroki Shizuya, Kenji Koyama, Toshiya Itoh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationAdvances in Cryptology — AUSCRYPT 1990, International Conference on Cryptology, Proceedings
EditorsJennifer Seberry, Josef Pieprzyk
PublisherSpringer Verlag
Number of pages21
ISBN (Print)9783540530008
Publication statusPublished - 1990
Event1st International Conference on Cryptology, AUSCRYPT 1990 - Sydney, Australia
Duration: 1990 Jan 81990 Jan 11

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume453 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference1st International Conference on Cryptology, AUSCRYPT 1990


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