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    Senior Research Fellow / David.Pointcheval@ens.fr

    ENS, Paris, France

    The Composite Discrete Logarithm and Secure Authentication

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    For the two last decades, electronic authentication has been an important topic. The first applications were digital signatures to mimic handwritten signatures for digital documents. Then, Chaum wanted to create an electronic version of money, with similar properties, namely bank certification and users anonymity. Therefore, he proposed the concept of blind signatures. For all those problems, and furthermore for online authentication, zero-knowledge proofs of knowledge became a very powerful tool. Nevertheless, high computational load is often the drawback of a high security level. More recently, witness-indistinguishability has been found to be a better property that can conjugate security together with efficiency. This paper studies the discrete logarithm problem with a composite modulus and namely its witness-indistinguishability. Then we offer new authentications more secure than factorization and furthermore very efficient from the prover point of view. Moreover, we significantly improve the reduction cost in the security proofs of Giraults variants of the Schnorr schemes which validates practical sizes for security parameters. Finally, thanks to the witness-indistinguishability of the basic protocol, we can derive a blind signature scheme with security related to factorization.

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    Description

    Title : The Composite Discrete Logarithm and Secure Authentication
    Author(s) : David Pointcheval
    Abstract : For the two last decades, electronic authentication has been an important topic. The first applications were digital signatures to mimic handwritten signatures for digital documents. Then, Chaum wanted to create an electronic version of money, with similar properties, namely bank certification and users anonymity. Therefore, he proposed the concept of blind signatures. For all those problems, and furthermore for online authentication, zero-knowledge proofs of knowledge became a very powerful tool. Nevertheless, high computational load is often the drawback of a high security level. More recently, witness-indistinguishability has been found to be a better property that can conjugate security together with efficiency. This paper studies the discrete logarithm problem with a composite modulus and namely its witness-indistinguishability. Then we offer new authentications more secure than factorization and furthermore very efficient from the prover point of view. Moreover, we significantly improve the reduction cost in the security proofs of Giraults variants of the Schnorr schemes which validates practical sizes for security parameters. Finally, thanks to the witness-indistinguishability of the basic protocol, we can derive a blind signature scheme with security related to factorization.
    Subject : unspecified
    Area : Other
    Language : English
    Year : 2000

    Affiliations ENS, Paris, France
    Conference_title : Public Key Cryptography — PKC 2000
    Volume : 1751
    Publisher : Springer Berlin / Heidelberg
    Pages : 113-128
    Url : http://www.springerlink.com/content/9rtablme5lkj4hml/
    Doi : 10.1007/978-3-540-46588-1_9

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