Breaking RSA may not be equivalent to factoring

Extended abstract
  • Dan Boneh
  • Ramarathnam Venkatesan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1403)


We provide evidence that breaking low-exponent RSA cannot be equivalent to factoring integers. We show that an algebraic reduction from factoring to breaking low-exponent RSA can be converted into an efficient factoring algorithm. Thus, in effect an oracle for breaking RSA does not help in factoring integers. Our result suggests an explanation for the lack of progress in proving that breaking rsa is equivalent to factoring. We emphasize that our results do not expose any specific weakness in the rsa system.


RSA Factoring Straight line programs Algebraic circuits 


  1. 1.
    D. Boneh, R. Lipton, “Black box fields and their application to cryptography”, Proc. of Crypto '96, pp. 283–297.Google Scholar
  2. 2.
    D. Coppersmith, “Finding a small root of a univariate modular equation”, Proc. of Eurocrypt '96, pp. 155–165.Google Scholar
  3. 3.
    W. Diffie, M. Hellman, “New directions in cryptography”, IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644–654, 1976.zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    J. Hastad, “Solving simultaneous modular equations of low degree”, SIAM Journal of Computing, vol. 17, pp 336–341, 1988.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Lang, “Algebra”, Addison-Wesley, 1993.Google Scholar
  6. 6.
    A. Lenstra, H.W. Lenstra, “Algorithms in Number Theory”, Handbook of Theoretical Computer Science (Volume A: Algorithms and Complexity), Elsevier and MIT Press, Ch. 12, pp. 673–715, 1990.Google Scholar
  7. 7.
    H. W. Lenstra, “Factoring integers with elliptic curves”, Annals of Math., Vol. 126, pp. 649–673, 1987.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    U. Maurer, “Towards proving the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms”, Proc. of Crypto '94, pp. 271–281.Google Scholar
  9. 9.
    U. Maurer, S. Wolf, “Diffie-Hellman oracles”, Proc. of Crypto '96, pp. 268–282.Google Scholar
  10. 10.
    R. Rivest, A. Shamir, L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems”, Communications of the ACM, vol. 21, pp. 120–126, 1978.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Dan Boneh
    • 1
  • Ramarathnam Venkatesan
    • 2
  1. 1.Computer Science Dept.Stanford UniversityUSA
  2. 2.Microsoft ResearchUSA

Personalised recommendations