New results on quasi-subfield polynomials
نویسندگان
چکیده
Quasi-subfield polynomials were introduced by Huang et al. together with a new algorithm to solve the Elliptic Curve Discrete Logarithm Problem (ECDLP) over finite fields of small characteristic. In this paper we provide both quasi-subfield polynomial families and theorem limiting their existence. Our results do not allow derive any speedup for ECDLP compared previous approaches.
منابع مشابه
New results on the quasi-commuting inverses
A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, inother words, if its columns (or rows) are linearly independent. In recent years needs have been felt innumerous areas of applied mathematics for some kind of partial inverse of a matrix that is singularor even rectangular. In this paper, some results on the Quasi-commuting inverses, are given an...
متن کاملIsomorphism of Polynomials : New Results
In this paper, we investigate the difficulty of the Isomorphism of Polynomials (IP) Problem as well as one of its variant IP1S. The Isomorphism of Polynomials is a well-known problem studied in multivariate cryptography. It is related to the hardness of the key recovery of some cryptosystems. The problem is the following: given two families of multivariate polynomials a and b, find two invertib...
متن کاملSome Results on the Field of Values of Matrix Polynomials
In this paper, the notions of pseudofield of values and joint pseudofield of values of matrix polynomials are introduced and some of their algebraic and geometrical properties are studied. Moreover, the relationship between the pseudofield of values of a matrix polynomial and the pseudofield of values of its companion linearization is stated, and then some properties of the augmented field of ...
متن کاملSome new results on permutation polynomials over finite fields
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, four classes of monomial complete permutation polynomials and one class of trinomial complete permutation polynomials are presented, one of which confirms a conjecture proposed by Wu et al. (Sci. China Math., to appear. Doi: 10.1007/s11425-...
متن کاملOrthogonal Polynomials on the Unit Circle: New Results
I am completing a comprehensive look at the theory of orthogonal polynomials on the unit circle (OPUC; we will use OPRL for the real-line case). These two 500+-page volumes [124, 125] to appear in the same AMS Colloquium Series that includes Szegő’s celebrated 1939 book [138] contain numerous new results. Our purpose here is to discuss the most significant of these new results. Besides what we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2021
ISSN: ['1090-2465', '1071-5797']
DOI: https://doi.org/10.1016/j.ffa.2021.101881