Chinese Remainder Theorem

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Ali Aydin Selcuk - One of the best experts on this subject based on the ideXlab platform.

  • Sharing DSS by the Chinese Remainder Theorem
    Journal of Computational and Applied Mathematics, 2014
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    In this paper, we propose a new threshold scheme for the Digital Signature Standard (DSS) using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth-Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on CRT.

  • Sharing DSS by the Chinese Remainder Theorem
    2012
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    In this paper, we propose a new threshold scheme for the Digital Signature  Standard (DSS) using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth-Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on the CRT.

  • Secret Sharing Extensions based on the Chinese Remainder Theorem.
    2010
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure from an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop joint random secret sharing (JRSS) and proactive SSS protocols, which, to the best of our knowledge, are the first secure protocols of their kind based on the CRT.

  • robust threshold schemes based on the Chinese Remainder Theorem
    International Conference on Progress in Cryptology, 2008
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing.

  • AFRICACRYPT - Robust threshold schemes based on the Chinese Remainder Theorem
    Progress in Cryptology – AFRICACRYPT 2008, 1
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing.

Kamer Kaya - One of the best experts on this subject based on the ideXlab platform.

  • Multilevel Threshold Secret Sharing based on the Chinese Remainder Theorem
    2019
    Co-Authors: Oguzhan Ersoy, Kamer Kaya, Kerem Kaskaloglu
    Abstract:

    In multilevel secret sharing, a secret is shared among a set of hierarchically organized participants in a way that the members of the superior compartments are more powerful and can replace the participants of an inferior one to form an authorized coalition during secret reconstruction. In this work, we first show that the only existing multilevel threshold secret sharing scheme based on the Chinese Remainder Theorem (CRT) is not secure and fails to work with certain natural threshold settings on compartments. As the main contribution, we propose a secure CRTbased scheme that works for all threshold settings. In the proposed scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the anchor sequence. Based on this novel idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem.

  • Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem.
    arXiv: Cryptography and Security, 2016
    Co-Authors: Oguzhan Ersoy, Kamer Kaya, Kerem Kaskaloglu
    Abstract:

    A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the anchor sequence. Based on this idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we discuss how the proposed schemes can be used for multilevel threshold function sharing by employing it in a threshold RSA cryptosystem as an example.

  • Sharing DSS by the Chinese Remainder Theorem
    Journal of Computational and Applied Mathematics, 2014
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    In this paper, we propose a new threshold scheme for the Digital Signature Standard (DSS) using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth-Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on CRT.

  • Sharing DSS by the Chinese Remainder Theorem
    2012
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    In this paper, we propose a new threshold scheme for the Digital Signature  Standard (DSS) using Asmuth-Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth-Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on the CRT.

  • Secret Sharing Extensions based on the Chinese Remainder Theorem.
    2010
    Co-Authors: Kamer Kaya, Ali Aydin Selcuk
    Abstract:

    In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure from an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop joint random secret sharing (JRSS) and proactive SSS protocols, which, to the best of our knowledge, are the first secure protocols of their kind based on the CRT.

Werner Schindler - One of the best experts on this subject based on the ideXlab platform.

  • A timing attack against RSA with the Chinese Remainder Theorem
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2000
    Co-Authors: Werner Schindler
    Abstract:

    We introduce a new type of timing attack which enables the factorization of an RSA-modulus if the exponentiation with the secret exponent uses the Chinese Remainder Theorem and Montgomery’s algorithm. Its standard variant assumes that both exponentiations are carried out with a simple square and multiply algorithm. However, although its effciency decreases, our attack can also be adapted to more advanced exponentiation algorithms. The previously known timing attacks do not work if the Chinese Remainder Theorem is used.

  • CHES - A Timing Attack against RSA with the Chinese Remainder Theorem
    Cryptographic Hardware and Embedded Systems — CHES 2000, 2000
    Co-Authors: Werner Schindler
    Abstract:

    We introduce a new type of timing attack which enables the factorization of an RSA-modulus if the exponentiation with the secret exponent uses the Chinese Remainder Theorem and Montgomery's algorithm. Its standard variant assumes that both exponentiations are carried out with a simple square and multiply algorithm. However, although its efficiency decreases, our attack can also be adapted to more advanced exponentiation algorithms. The previously known timing attacks do not work if the Chinese Remainder Theorem is used.

Sorin Iftene - One of the best experts on this subject based on the ideXlab platform.

  • Compartmented Threshold RSA Based on the Chinese Remainder Theorem.
    2008
    Co-Authors: Sorin Iftene, Stefan Ciobaca, Manuela Grindei
    Abstract:

    In this paper we combine the compartmented secret sharing schemes based on the Chinese Remainder Theorem with the RSA scheme in order to obtain, as a novelty, a dedicated solution for compartmented threshold decryption or compartmented threshold digital signature generation. AMS Subject Classification: 94A60, 94A62, 11A07

  • SYNASC - Weighted Threshold RSA Based on the Chinese Remainder Theorem
    Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2007), 2007
    Co-Authors: Sorin Iftene, Manuela Grindei
    Abstract:

    In this paper we combine the weighted threshold secret sharing schemes based on the Chinese Remainder Theorem with the RSA scheme [25] in order to obtain, as a novelty, weighted threshold decryption or weighted threshold digital signature generation.

  • General Secret Sharing Based on the Chinese Remainder Theorem with Applications in E-Voting
    Electronic Notes in Theoretical Computer Science, 2007
    Co-Authors: Sorin Iftene
    Abstract:

    Threshold secret sharing based on the Chinese Remainder Theorem has been considered by Mignotte [Mignotte, M., How to share a secret, in: T. Beth, editor, Cryptography-Proceedings of the Workshop on Cryptography, Burg Feuerstein, 1982, Lecture Notes in Computer Science 149 (1983), pp. 371-375] and Asmuth and Bloom [Asmuth, C.A. and J. Bloom, A modular approach to key safeguarding, IEEE Transactions on Information Theory IT-29 (1983), pp. 208-210]. In this paper we demonstrate that the Chinese Remainder Theorem can be used for realizing more general access structures, as the compartmented or the weighted threshold ones. We also prove that there exist some non-weighted threshold access structures whose realizations require the general variant of the Chinese Remainder Theorem, i.e., the variant in which the modules are not necessarily pairwise coprime. As an application of the proposed secret sharing schemes, we present a multi-authority e-voting schemes in which, as a novelty, the tallying authorities may have non-equal weights.

I Hartimo - One of the best experts on this subject based on the ideXlab platform.

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