Permutation Polynomials Modulo w
نویسنده
چکیده
We give an exact characterization of permutation polynomials mod ulo n w w a polynomial P x a a x adx d with integral coe cients is a permutation polynomial modulo n if and only if a is odd a a a is even and a a a is even We also characterize polynomials de ning latin squares mod ulo n w but prove that polynomial multipermutations that is a pair of polynomials de ning a pair of orthogonal latin squares modulo n w do not exist
منابع مشابه
One-stroke polynomials over a ring of modulo $2^w$
Permutation polynomials over a ring of modulo 2w are compatible with digital computers and digital signal processors, and so they are in particular expected to be useful for cryptography and pseudo random number generator. In general, the period of the polynomial should be long in such fields. In this paper, we derive the necessary and sufficient condition which specify one-stroke polynomials w...
متن کاملPermutation Polynomials modulo m
This paper mainly studies problems about so called “permutation polynomials modulo m”, polynomials with integer coefficients that can induce bijections over Zm = {0, · · · , m−1}. The necessary and sufficient conditions of permutation polynomials are given, and the number of all permutation polynomials of given degree and the number induced bijections are estimated. A method is proposed to dete...
متن کاملPeriodicity of odd degree Chebyshev polynomials over a ring of modulo $2^w$
Odd degree Chebyshev polynomials over a ring of modulo 2 have two kinds of period. One is an “orbital period”. Odd degree Chebyshev polynomials are bijection over the ring. Therefore, when an odd degree Chebyshev polynomial iterate affecting a factor of the ring, we can observe an orbit over the ring. The “ orbital period ” is a period of the orbit. The other is a “degree period”. It is observe...
متن کاملFurther improving security of Vector Stream Cipher
Vector Stream Cipher (VSC) is a stream cipher which consists of permutation polynomial over a ring of modulo 2w . The algorithm for generating stream keys is very simple and the encryption speed is very fast. Some theoretical attacks for VSC have been reported so far since the invention of VSC in 2004. Then, the authors proposed some improvements and developed “Vector Stream Cipher 2.0 (VSC 2.0...
متن کاملSymplectic Spreads and Permutation Polynomials
Every symplectic spread of PG(3, q), or equivalently every ovoid of Q(4, q), is shown to give a certain family of permutation polynomials of GF (q) and conversely. This leads to an algebraic proof of the existence of the Tits-Lüneburg spread of W (2) and the Ree-Tits spread of W (3), as well as to a new family of low-degree permutation polynomials over GF (3). Let PG(3, q) denote the projective...
متن کامل