Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations (Special Section on Cryptography and Information Security)

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概要

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• 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(X_1, .., X_t), and any given modulus, n, a prover. P, gives (l_1, .., l_t) to a verifier, ν, and can convince ν that P knows (x_1, .., x_t) which satisfies f(x_1, .., x_t)≡O (mod n) and I_i=BC(x_i), (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.

• 一般社団法人電子情報通信学会の論文
• 1999-01-25

著者

• Okamoto T

  Ntt Corp. Yokosuka‐shi Jpn

• Okamoto Tatsuaki

  Ntt Laboratories

• FUJISAKI Eiichiro

  NTT Laboratories

関連論文

• Security and Performance Evaluation of ESIGN and RSA on IC Cards by Using Byte-Unit Modular Algorithms(Fundamental Theories for Communications)
• One-Time Zero-Knowledge Authentications and Their Applications to Untraceable Electronic Cash (Special Section on Cryptography and Information Security)
• Provable Security of Practical Public-Key Encryption Systems
• How to Enhance the Security of Public-Key Encryption at Minimum Cost(Special Section on Cryptography and Information Security)
• Multi-Signature Schemes Secure against Active Insider Attacks (Special Section on Cryptography and Information Security)
• Security of the Extended Fiat-Shamir Schemes (Special Section on Cryptography and Information Security)
• Practical Escrow Cash Schemes (Special Section on Cryptography and Information Security)
• A Note on Computationally Sound Proof in Group of Unknown Order (コンピュータセキュリティ研究報告)
• Threshold Key-Recovery Systems for RSA (Special Section on Cryptography and Information Security)
• Statistical Zero-Knowledge Protocols to Prove Modular Polynomial Relations (Special Section on Cryptography and Information Security)
• A Note on Computationally Sound Proof in Group of Unknown Order

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