Annual International Cryptology Conference

CRYPTO 1995: Advances in Cryptology — CRYPT0’ 95 pp 424-437

Quantum Cryptanalysis of Hidden Linear Functions

Extended Abstract
  • Dan Boneh
  • Richard J. Lipton
Conference paper

DOI: 10.1007/3-540-44750-4_34

Volume 963 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Boneh D., Lipton R.J. (1995) Quantum Cryptanalysis of Hidden Linear Functions. In: Coppersmith D. (eds) Advances in Cryptology — CRYPT0’ 95. CRYPTO 1995. Lecture Notes in Computer Science, vol 963. Springer, Berlin, Heidelberg


Recently there has been a great deal of interest in the power of “Quantum Computers” [4, 15, 18]. The driving force is the recent beautiful result of Shor that shows that discrete log and factoring are solvable in random quantum polynomial time [15]. We use a method similar to Shor’s to obtain a general theorem about quantum polynomial time. We show that any cryptosystem based on what we refer to as a ‘hidden linear form’ can be broken in quantum polynomial time. Our results imply that the discrete log problem is doable in quantum polynomial time over any group including Galois fields and elliptic curves. Finally, we introduce the notion of ‘junk bits’ which are helpful when performing classical computations that are not injective.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Dan Boneh
    • 1
  • Richard J. Lipton
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityPrinceton