scholarly journals Incomplete character sums over finite fields and their application to the interpolation of the discrete logarithm by Boolean functions

2002 ◽  
Vol 101 (3) ◽  
pp. 223-229 ◽  
Author(s):  
Tanja Lange ◽  
Arne Winterhof
Keyword(s):  
Finite Fields ◽  
Boolean Functions ◽  
Discrete Logarithm ◽  
Character Sums ◽  
Incomplete Character Sums

A NOTE ON SOME CHARACTER SUMS OVER FINITE FIELDS

2015 ◽  
Vol 92 (1) ◽  
pp. 32-43
Author(s):  
XIWANG CAO ◽  
GUANGKUI XU
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Boolean Functions ◽  
Exponential Sums ◽  
Character Sums ◽  
Walsh Spectrum

In this paper, we present a decomposition of the elements of a finite field and illustrate the efficiency of this decomposition in evaluating some specific exponential sums over finite fields. The results can be employed in determining the Walsh spectrum of some Boolean functions.

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

scholarly journals On character sums in finite fields

1939 ◽  
Vol 71 (0) ◽  
pp. 99-121 ◽  
Author(s):  
H. Davenport
Keyword(s):  
Finite Fields ◽  
Character Sums
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