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On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators
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  • Published: March 2003

On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators

  • Goldreich1 &
  • Rosen2 

Journal of Cryptology volume 16, pages 71–93 (2003)Cite this article

  • 317 Accesses

  • 20 Citations

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Abstract. Assuming the intractability of factoring, we show that the output of the exponentiation modulo a composite function f N,g (x)=gx mod N (where N=P⋅ Q ) is pseudorandom, even when its input is restricted to being half the size (i.e. x<

$\sqrt N$

). This result is equivalent to the simultaneous hardness of the upper half of the bits of f N,g , proven by Hastad, Schrift and Shamir. Yet, we provide a different proof that is significantly simpler than the original one. In addition, we suggest a pseudorandom generator that is more efficient than all previously known factoring-based pseudorandom generators.

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Authors and Affiliations

  1. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel oded@wisdom.weizmann.ac.il, , , , , , IL

    Goldreich

  2. Check Point Software Technologies Ltd., 3A Jabotinsky St., Diamond Tower, Ramat Gan, Israel vrosen@checkpoint.com, , , , , , IL

    Rosen

Authors
  1. Goldreich
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  2. Rosen
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Goldreich, ., Rosen, . On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators . J. Cryptology 16, 71–93 (2003). https://doi.org/10.1007/s00145-002-0038-7

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  • Received: 10 September 2002

  • Revised: 06 December 2002

  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00145-002-0038-7

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  • Key words. Modular exponentiation, Discrete logarithm, Hard-core predicates, Simultaneous security, Pseudorandom generator, Factoring assumption.
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