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Several cryptographic applications of Σ-protocol

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Abstract

Σ-protocol has been proved to be a very powerful cryptographic tool and widely used in numerous important cryptographic applications. In this paper, the authors make use of Σ-protocol as a main tool to resolve the following difficult problems 1–3 and to construct three efficient cryptographic protocols 4–6:

  1. 1)

    How to construct a protocol for proving a secret integer to be a Blum integer with form PQ, where P, Q are two different primes and both ≡ 3(mod 4);

  2. 2)

    How to construct a protocol for proving a secret polynomial with exact degree t − 1 in a (t, n)-threshold secret sharing scheme;

  3. 3)

    How to construct witness indistinguishable and witness hiding protocol not from zero-knowledge proof;

  4. 4)

    A publicly verifiable secret sharing scheme with information-theoretic security;

  5. 5)

    A delegateable signature scheme under the existence of one-way permutations;

  6. 6)

    Non-interactive universal designated verifier signature schemes.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Chunming Tang

  2. State Key Laboratory of Information Security, Institute of Software Science, Beijing, 100190, China

    Chunming Tang

  3. School of Mathematics and Computational Sciences, Sun Yat-Sen University, Guangzhou, 510275, China

    Zheng-an Yao

Authors
  1. Chunming Tang
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  2. Zheng-an Yao
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Corresponding author

Correspondence to Chunming Tang.

Additional information

This work was supported by the Foundation of the National Natural Science of China under Grant Nos. 90604034 (Key Project), 10726012, 10871222, 10531040, and 10471156.

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Tang, C., Yao, Za. Several cryptographic applications of Σ-protocol. J Syst Sci Complex 22, 260–279 (2009). https://doi.org/10.1007/s11424-009-9162-x

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  • DOI: https://doi.org/10.1007/s11424-009-9162-x

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