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A Key Recovery System as Secure as Factoring

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Topics in Cryptology – CT-RSA 2004 (CT-RSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2964))

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Abstract

There has been a lot of recent work in the area of proving in zero-knowledge that an RSA modulus N is in the correct form. For example, protocols have been given that prove that N is the product of: two safe primes, two primes nearly equal in size, etc. Such proof systems are rather remarkable in what they achieve, but may be regarded as being heavyweight protocols due to the computational and messaging overhead they impose. In this paper an efficient zero-knowledge protocol is given that simultaneously proves that N is a Blum integer and that its factorization is recoverable. The proof system requires that the RSA primes p and q be such that p ≡ q ≡ 3 mod 4 and another sematically secure encryption. The solution is therefore amenable for use with systems based on PKCS #1. A proof is given that shows that our algorithm is secure under the integer factorization problem (and can be turned into a non-interactive roof in the random oracle model).

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Author information

Authors and Affiliations

  1. Cigital Labs,  

    Adam Young

  2. Dept. of Computer Science, Columbia University,  

    Moti Yung

Authors
  1. Adam Young
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  2. Moti Yung
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Editor information

Editors and Affiliations

  1. NTT, 3-9-11 Midori-cho, Musashino-shi, 180-8585, Tokyo, Japan

    Tatsuaki Okamoto

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Young, A., Yung, M. (2004). A Key Recovery System as Secure as Factoring. In: Okamoto, T. (eds) Topics in Cryptology – CT-RSA 2004. CT-RSA 2004. Lecture Notes in Computer Science, vol 2964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24660-2_11

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  • DOI: https://doi.org/10.1007/978-3-540-24660-2_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20996-6

  • Online ISBN: 978-3-540-24660-2

  • eBook Packages: Springer Book Archive

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