N Using RSA with Low Exponent in a Public Key Network

  • Johan Hastad
Conference paper

DOI: 10.1007/3-540-39799-X_29

Part of the Lecture Notes in Computer Science book series (LNCS, volume 218)
Cite this paper as:
Hastad J. (1986) N Using RSA with Low Exponent in a Public Key Network. In: Williams H.C. (eds) Advances in Cryptology — CRYPTO ’85 Proceedings. CRYPTO 1985. Lecture Notes in Computer Science, vol 218. Springer, Berlin, Heidelberg


We consider the problem of solving systems of equations Pi(x) ≡ 0 (mod ni) i = 1...k where Pi are polynomials of degree d and the ni are distinct relatively prime numbers and x < min ni. We prove that if k > d(d+1)/2 we can recover x in polynomial time provided ni > > 2k. This shows that RSA with low exponent is not a good alternative to use as a public key cryptosystem in a large network. It also shows that a protocol by Broder and Dolev [4] is insecure if RSA with low exponent is used.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Johan Hastad
    • 1
  1. 1.MITUSA

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