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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...
A new class of irreducible pentanomials for polynomial based multipliers in binary fields
irreducible pentanomials polynomial multiplication modular reduction
2018/6/5
We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time del...
"The Irreducible Minimum" An Evaluation of Counterterrorism Operations in Iraq
The Irreducible Minimum Counterterrorism Operations Task Force–714
2019/10/21
With the end of full-scale combat operations in Iraq in late April 2003, no one at the senior level in Washington or Baghdad expected an organized insurgency to materialize—a “war after the war” was u...
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 ...
$GF(2^n)$ Bit-Parallel Squarer Using Generalized Polynomial Basis For a New Class of Irreducible Pentanomials
implementation implementation
2016/1/26
We present explicit formulae and complexities of bit-parallel GF(2n) squarers for a new class of irreducible pentanomials xn+xn−1+xk+x+1, where n is odd and 1rer is bas...
A Chinese Remainder Theorem Approach to Bit-Parallel GF(2^n) Polynomial Basis Multipliers for Irreducible Trinomials
implementation Irreducible Trinomials
2016/1/5
We show that the step “modulo the degree-n field generating irreducible polynomial” in the classical definition of the GF(2^n) multiplication operation can be avoided. This leads to an alternative rep...
Low Space Complexity CRT-based Bit-Parallel GF(2^n) Polynomial Basis Multipliers for Irreducible Trinomials
Finite field multiplication polynomial basis
2015/12/30
By selecting the largest possible value of k∈(n/2,2n/3], we further reduce the AND and XOR gate complexities of the CRT-based hybrid parallel GF(2^n) polynomial basis multipliers for the irreduc...
Comparison Between Irreducible and Separable Goppa Code in McEliece Cryptosystem
McEliece cryptosystem Goppa code separable irreducible
2015/12/21
The McEliece cryptosystem is an asymmetric type of cryptography based on
error correction code. The classical McEliece used irreducible binary Goppa code which
considered unbreakable until now espec...
Toeplitz matrix-vector product based GF(2^n) shifted polynomial basis multipliers for all irreducible pentanomials
subquadratic space complexity multiplier shifted polynomial basis
2014/3/11
Besides Karatsuba algorithm, optimal Toeplitz matrix-vector product (TMVP) formulae is another approach to design GF(2^n) subquadratic multipliers. However, when GF(2^n) elements are represented using...
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.