Feebly secure cryptographic primitives

E. A. Hirsch, O. Melanich, S. I. Nikolenko

Research output: Contribution to journalArticlepeer-review


In 1992, A. Hiltgen provided first construction of provably (slightly) secure cryptographic primitives, namely, feebly one-way functions. These functions are provably harder to invert than to compute, but the complexity (viewed as the circuit complexity over circuits with arbitrary binary gates) is amplified only by a constant factor (in Hiltgen's works, the factor approaches 2). In traditional cryptography, one-way functions are the basic primitive of private-key shemes, while public-key schemes are constructed using trapdoor functions. We continue Hiltgen's work by providing examples of feebly secure trapdoor functions where the adversary is guaranteed to spend more time than honest participants (also by a constant factor). We give both a (simpler) linear and a (better) nonlinear construction. Bibliography: 25 titles.

Original languageEnglish
Pages (from-to)17-34
Number of pages18
JournalJournal of Mathematical Sciences
Issue number1
StatePublished - Jan 2013
Externally publishedYes


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