Titlebook: Cryptology and Error Correction; An Algebraic Introdu Lindsay N. Childs Textbook 2019 Springer Nature Switzerland AG 2019 Caeser ciphers.Ch

ANIM

Water Resources Development and Managementh is given a proof using the Binomial Theorem. The final section describes an efficient algorithm for computing a high power of a number modulo .. This algorithm will have both an obvious use in using the cryptosystems presented in Chaps.?. and . and a less obvious use to help construct cryptosystems in the last section of Chap.?..

闡釋

傷心

Secure, Reliable Information, or the study of methods to add redundancy to a message to determine if it is compromised by errors, is illustrated by check digits in several settings, and by repetition coding, a special case of which has historically been known as triple modular redundancy.

flourish

Missile

Rings and Fields, that if . is a prime number, then doing modular arithmetic modulo . is the same as working in ., and the latter is a field. So concepts and results involving polynomials (in Chap.?.) and matrices (in Chap.?.) make sense when the “numbers” are integers modulo a prime number ..

構(gòu)成

BRACE

Polynomials and Finite Fields,le polynomial in .[.], . a field, then the ring of cosets modulo the principal ideal generated by .(.) is also a field. Every finite field can be described in that way. The method also yields the complex numbers, when the field . is the field of real numbers and .. So complex numbers are cosets. They aren’t “imaginary” at all.

SLAY

Reed-Solomon Codes II,tional effort required in decoding to solve the set of equations to recover the original word .(.) can be substantially reduced by first multiplying the matrix of coefficients by the inverse of a discrete Fourier transform.

Abrade

Nutrition and Cutaneous Ulcers,ch groups by proving the Primitive Root Theorem, which states that for every prime number ., the group of units of . is a cyclic group. The chapter concludes with two methods that can be more efficient than constructing log tables for solving the discrete logarithm problem; one method involves use of the Chinese Remainder Theorem.

configuration