A way of making trapdoor one-way functions trapdoor no-way

Eikoh Chida, Motoji Ohmori, Hiroki Shizuya

Research output: Contribution to journalArticlepeer-review


SUMMARY A trapdoor one-way function is an extended version of a zero-way permutation. A zero-way permutation was first introduced by Niemi-Renvall in Asiacrypt'94 [7]. In this paper we define the class of functions called no-way functions. This is an extended version of a zero-way permutation. Intuitively, a function f is no-way if, without trapdoor, both computing / and computing f-1 are hard. Li-Chida-Shizuya [6] defined the notion of a no-way function, which is a provable-security version of a zero-way permutation. They also gave an example of a no-way function such that computing f and f-1 is proven to be as hard as breaking the Diffie-Hellman key exchange scheme. We redefine the notion of a trapdoor no-way function more preciously, classify no-way functions by the property of the trapdoor: common, separated and semi-separated trapdoor no-way, give a method for constructing trapdoor no-way functions from trapdoor one-way functions, and also give an example of trapdoor no-way functions.

Original languageEnglish
Pages (from-to)151-156
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number1
Publication statusPublished - 2001 Jan


  • No-way function
  • One-way function
  • Trapdoor


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