Toward Separating Integer Factoring from Discrete Logarithm mod p

  • Authors:

  • Shuji Isobe;Wataru Kumagai;Masahiro Mambo;Hiroki Shizuya

  • Affiliations:

  • The authors are with the Department of Computer and Mathematical Sciences, the Graduate School of Information Sciences, Tohoku University, Sendai-shi, 980-8576 Japan. E-mail: iso@ise.he.tohoku.ac. ...;The authors are with the Department of Computer and Mathematical Sciences, the Graduate School of Information Sciences, Tohoku University, Sendai-shi, 980-8576 Japan. E-mail: iso@ise.he.tohoku.ac. ...;The author is with the Department of Computer Science, the Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba-shi, 305-8573 Japan.,;The authors are with the Department of Computer and Mathematical Sciences, the Graduate School of Information Sciences, Tohoku University, Sendai-shi, 980-8576 Japan. E-mail: iso@ise.he.tohoku.ac. ...

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2007

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Abstract

This paper studies the reduction among cyptographic functions. Our main result is that the prime factoring function IF does not reduce to the certified discrete logarithm function modulo a prime nor its variant with respect to some special reducibility, i.e. the range injection reducibility, under the assumption that the Heath-Brown conjecture is true and IF â聢聣 PF. Since there is no known direct relationship between these functions, this is the first result that could separate these functions. Our approach is based on the notion of the preimage functions.