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Eiichiro FUJISAKI, Tatsuaki OKAMOTO, "Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 1, pp. 81-92, January 1999, doi: .
Abstract: This paper proposes a bit-commitment scheme, BC(), and an efficient statistical zero-knowledge (in short, SZK) protocol in which, for any given multi-variable polynomial, f(X1,,Xt), and any given modulus, n, a prover, P, gives (I1,,It) to a verifier,ν, and can convince ν that P knows (x1,,xt) which satisfies f(x1,,xt) 0 (mod n) and Ii = BC(xi), (i = 1,,t). The proposed protocol is O(|n|) times more efficient than the corresponding previous ones. The (knowledge) soundness of our protocol holds under a computational assumption, the intractability of a modified RSA problem (see Def. 3.2), while the (statistical) zero-knowledgeness of the protocol needs no computational assumption. The protocol can be employed to construct various practical cryptographic protocols, such as fair exchange, untraceable electronic cash and verifiable secret sharing protocols.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_1_81/_p
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@ARTICLE{e82-a_1_81,
author={Eiichiro FUJISAKI, Tatsuaki OKAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations},
year={1999},
volume={E82-A},
number={1},
pages={81-92},
abstract={This paper proposes a bit-commitment scheme, BC(), and an efficient statistical zero-knowledge (in short, SZK) protocol in which, for any given multi-variable polynomial, f(X1,,Xt), and any given modulus, n, a prover, P, gives (I1,,It) to a verifier,ν, and can convince ν that P knows (x1,,xt) which satisfies f(x1,,xt) 0 (mod n) and Ii = BC(xi), (i = 1,,t). The proposed protocol is O(|n|) times more efficient than the corresponding previous ones. The (knowledge) soundness of our protocol holds under a computational assumption, the intractability of a modified RSA problem (see Def. 3.2), while the (statistical) zero-knowledgeness of the protocol needs no computational assumption. The protocol can be employed to construct various practical cryptographic protocols, such as fair exchange, untraceable electronic cash and verifiable secret sharing protocols.},
keywords={},
doi={},
ISSN={},
month={January},}
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TY - JOUR
TI - Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 81
EP - 92
AU - Eiichiro FUJISAKI
AU - Tatsuaki OKAMOTO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 1999
AB - This paper proposes a bit-commitment scheme, BC(), and an efficient statistical zero-knowledge (in short, SZK) protocol in which, for any given multi-variable polynomial, f(X1,,Xt), and any given modulus, n, a prover, P, gives (I1,,It) to a verifier,ν, and can convince ν that P knows (x1,,xt) which satisfies f(x1,,xt) 0 (mod n) and Ii = BC(xi), (i = 1,,t). The proposed protocol is O(|n|) times more efficient than the corresponding previous ones. The (knowledge) soundness of our protocol holds under a computational assumption, the intractability of a modified RSA problem (see Def. 3.2), while the (statistical) zero-knowledgeness of the protocol needs no computational assumption. The protocol can be employed to construct various practical cryptographic protocols, such as fair exchange, untraceable electronic cash and verifiable secret sharing protocols.
ER -