Primitive polynomials $({\rm mod}\ 2)$

Multiples of Primitive Polynomials and Their Products over GF(2)

A standard model of nonlinear combiner generator for stream cipher system combines the outputs of several independent Linear Feedback Shift Register (LFSR) sequences using a nonlinear Boolean function to produce the key stream. Given such a model, cryptanalytic attacks have been proposed by finding out the sparse multiples of the connection polynomials corresponding to the LFSRs. In this direct...

Mod 2 and Mod 5 Icosahedral Representations

We shall call a simple abelian variety A/Q modular if it is isogenous (over Q) to a factor of the Jacobian of a modular curve. In this paper we shall call a representation ρ̄ : GQ→GL2(F̄l) modular if there is a modular abelian variety A/Q, a number field F/Q of degree equal to dimA, an embedding OF ↪→ End(A/Q) and a homomorphism θ : OF→F̄l such that ρ̄ is equivalent to the action of GQ on the ker θ...

Topological superconductor in quasi-one-dimensional ${\rm Tl}_{2-x}{\rm Mo}_6{\rm Se}_6$

2 00 1 On primitive roots of 1 mod p k , divisors of p 2 − 1 , Wieferich primes and quadratic analysis mod p 3

On primitive roots of 1 mod p k , divisors of p 2 − 1 , Wieferich primes and quadratic analysis mod p Abstract Primitive roots of 1 mod p k (k > 2 and odd prime p) are sought, in cyclic units group G k ≡ A k B k mod p k , coprime to p, of order (p − 1)p k−1. 'Core' subgroup A k has order p − 1 independent of precision k, and 'extension' subgroup B k of all p k−1 residues 1 mod p is generated by...

Primitive derivations, Shi arrangements and Bernoulli polynomials

LetW be a finite irreducible real reflection group, which is a Coxeter group. A primitive derivation D, introduced and studied by K. Saito (e.g., [4]), plays a crucial role in the theory of differential forms with logarithmic poles along the Coxeter arrangement. For example, we may describe the contact order filtration of the logarithmic derivation module using the primitive derivations ([10, 1...