Toward separating integer factoring from discrete logarithm mod p

Shuji Isobe, Wataru Kumagai, Masahiro Mambo, Hiroki Shizuya

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 ∉ 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.

Original languageEnglish
Pages (from-to)48-53
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 2007 Jan


  • Certified discrete logarithm
  • Integer factoring
  • Preimage functions
  • Range injection reduction
  • The Heath-Brown conjecture


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