Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes
 Tatsuaki Okamoto
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Abstract
This paper presents a threemove interactive identification scheme and proves it to be as secure as the discrete logarithm problem. This provably secure scheme is almost as efficient as the Schnorr identification scheme, while the Schnorr scheme is not provably secure. This paper also presents another practical identification scheme which is proven to be as secure as the factoring problem and is almost as efficient as the GuillouQuisquater identification scheme: the GuillouQuisquater scheme is not provably secure. We also propose practical digital signature schemes based on these identification schemes. The signature schemes are almost as efficient as the Schnorr and GuillouQuisquater signature schemes, while the security assumptions of our signature schemes are weaker than those of the Schnorr and GuillouQuisquater. signature schemes. This paper also gives a theoretically generalized result: a threemove identification scheme can be constructed which is as secure as the randomselfreducible problem. Moreover, this paper proposes a variant which is proven to be as secure as the difficulty of solving both the discrete logarithm problem and the specific factoring problem simultaneously. Some other variants such as an identitybased variant and an elliptic curve variant are also proposed.
 Title
 Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes
 Book Title
 Advances in Cryptology — CRYPTO’ 92
 Book Subtitle
 12th Annual International Cryptology Conference Santa Barbara, California, USA August 16–20, 1992 Proceedings
 Book Part
 Session I:
 Pages
 pp 3153
 Copyright
 1993
 DOI
 10.1007/3540480714_3
 Print ISBN
 9783540573401
 Online ISBN
 9783540480716
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 740
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
 Topics
 Industry Sectors
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 Editors

 Ernest F. Brickell ^{(3)}
 Editor Affiliations

 3. Department 1423, Sandia National Laboratories
 Authors

 Tatsuaki Okamoto ^{(4)}
 Author Affiliations

 4. NTT Laboratories, Nippon Telegraph and Telephone Corporation, 12356, Take, Yokosukashi, Kanagawaken, 23803, Japan
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