Polynomial Permutations on Finite Lattices Related to Cryptography
نویسندگان
چکیده
Motivated by cryptography, permutations induced by polynomial functions on finite lattices L = (L,∨,∧,∗ ) with an antitone involution ∗ are investigated. These permutations together with the operation of composition form a subgroup of the symmetric group on L. We describe the structure of this subgroup for different classes of lattices L and indicate possible applications by outlining a protocol for a symmetric cipher. AMS Subject Classification: 06C15, 08A40, 06D30
منابع مشابه
EEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations
GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...
متن کاملEfficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملDickson Polynomials that are Involutions
Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in F2[x] that are involutions over finite fields of characteristic 2. Such description is obtained using modular arithmetic’s tools. We give results related to the cardinality and the number of fixed points (in the context of cryptog...
متن کاملCombinatorial Statistics on Alternating Permutations
We consider two combinatorial statistics on permutations. One is the genus. The other, d̂es, is defined for alternating permutations, as the sum of the number of descents in the subwords formed by the peaks and the valleys. We investigate the distribution of d̂es on genus zero permutations and Baxter permutations. Our qenumerative results relate the d̂es statistic to lattice path enumeration, the ...
متن کاملRandom Ensembles of Lattices from Generalized Reductions
We propose a general framework to study constructions of Euclidean lattices from linear codes over finite fields. In particular, we prove general conditions for an ensemble constructed using linear codes to contain dense lattices (i.e., with packing density comparable to the Minkowski-Hlawka lower bound). Specializing to number field lattices, we obtain a number of interesting corollaries for i...
متن کامل