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Low exponent attack against elliptic curve RSA

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Advances in Cryptology — ASIACRYPT'94 (ASIACRYPT 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 917))

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Abstract

Hastad showed that low exponent RSA is not secure if the same message is encrypted to several receivers. This is true even if time-stamp is used for each receiver. For example, let e=3. Then if the number of receivers =7, the eavesdropper can find the plaintext from the seven ciphertexts of each receiver.

This paper shows that elliptic curve RSA is not secure in the same scenario. It is shown that the KMOV scheme and Demytko's scheme are not secure if e=5, n≥21024 and the number of receivers =428. In Demytko's scheme, e can take the value of 2. In this case, this system is not secure if the number of receiver =11 for n≥2175.

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References

  1. J.Hastad: On using RSA with low exponent in a public key network. Proc. of Crypto'85, pp.403–408 (1985)

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  2. K.Koyama, U.M.Maurer, T.Okamoto and S.A.Vanstone: New public-key schemes based on elliptic curves over the ring Z n . Proc. of Crypto'91 (1991)

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  3. N.Demytko: A new elliptic curve based analogue of RSA. Proc. of Eurocrypt'93, pp.39–48, May 24 (1993)

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  4. D.M.Bressoud: Factorization and primality testing. Springer-Verlag (1989)

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  5. K.Kurosawa and S.Tsujii: Low exponent attack against elliptic curve RSA. Technical Report of IEICE, ISEC94-2, pp.11–17 (1994)

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  6. H.Kuwakado and K.Koyama: On the security of RSA-type schemes over cubic curves against the Hastad attack. Technical report of IEICE, ISEC94-10, pp.23–30 (1994)

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Faculty of Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, 152, Tokyo, Japan

    Kaoru Kurosawa & Koji Okada

  2. Department of Information Systems Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, 112, Tokyo, Japan

    Shigeo Tsujii

Authors
  1. Kaoru Kurosawa
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  2. Koji Okada
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  3. Shigeo Tsujii
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Editor information

Josef Pieprzyk Reihanah Safavi-Naini

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© 1995 Springer-Verlag Berlin Heidelberg

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Kurosawa, K., Okada, K., Tsujii, S. (1995). Low exponent attack against elliptic curve RSA. In: Pieprzyk, J., Safavi-Naini, R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000449

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  • DOI: https://doi.org/10.1007/BFb0000449

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59339-3

  • Online ISBN: 978-3-540-49236-8

  • eBook Packages: Springer Book Archive

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