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4-bit crypto S-boxes: Generation with irreducible polynomials over Galois field GF(24) and cryptanalysis
public-key cryptography EPs
2018/6/13
4-bit crypto S-boxes play a significant role in encryption and decryption of many cipher algorithms from last 4 decades. Generation and cryptanalysis of generated 4-bit crypto S-boxes is one of the ma...
Multiplication and Division over Extended Galois Field GF(pqpq): A new Approach to find Monic Irreducible Polynomials over any Galois Field GF(pqpq).
Galois Field Finite field Irreducible Polynomials (IPs)
2017/6/9
Irreducible Polynomials (IPs) have been of utmost importance in generation of substitution boxes in modern cryptographic ciphers. In this paper an algorithm entitled Composite Algorithm using both mul...
Adjacency Graphs, Irreducible Polynomials and Cyclotomy
feedback shift register adjacency graph De Bruijn sequence
2016/4/22
We consider the adjacency graphs of linear feedback shift registers (LFSRs) with reducible characteristic polynomials. Let l(x) be a characteristic polynomial, and l(x)=l_1(x)l_2(x)\cdots l_r(x) be a ...
An Iterative Construction of Irreducible Polynomials Reducible Modulo Every Prime
Iterative Construction Irreducible Polynomials Reducible Modulo Every Prime
2011/1/21
We give a method of constructing polynomials of arbitrarily large degree irreducible over a global field F but reducible modulo every finite prime of F.The method consists of finding quadratic f ∈ F[x...
Optimal Irreducible Polynomials for GF(2m) Arithmetic
Irreducible polynomials Arithmetic in F2m
2008/8/27
The irreducible polynomials recommended for use by multi-
ple standards documents are in fact far from optimal on many platforms.
Specifically they are suboptimal in terms of performance, for the co...
Asymptotic Behavior of the Ratio Between the Numbers of Binary Primitive and Irreducible Polynomials
Asymptotic Behavior Binary Primitive Irreducible Polynomials
2008/8/14
In this paper we study the ratio (n) = 2(n) 2(n) , where 2(n) is the number
of primitive polynomials and 2(n) is the number of irreducible polynomials
in GF(2)[x] of degree n. Let n = Q`i=1 prii...
Asymptotic Behavior of the Ratio Between the Numbers of Binary Primitive and Irreducible Polynomials
Asymptotic Behavior of the Ratio Binary Primitive Irreducible Polynomials
2008/6/2
In this paper we study the ratio (n) = 2(n) 2(n) , where 2(n) is the number
of primitive polynomials and 2(n) is the number of irreducible polynomials
in GF(2)[x] of degree n.
