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The strength of the scheme comes from the fact that g ab mod p = g ba mod p take extremely long times to compute by any known algorithm just from the knowledge of p, g, g a mod p, and g b mod p. Such a function that is easy to compute but hard to invert is called a one-way function .
For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 / 2 ≡ 2 (mod 3). Equivalently, 2 n − 1 / 3 ≡ 1 (mod 2) if and only if n ≡ 2 (mod 3) . Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above).
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Computation of a cyclic redundancy check is derived from the mathematics of polynomial division, modulo two. In practice, it resembles long division of the binary message string, with a fixed number of zeroes appended, by the "generator polynomial" string except that exclusive or operations replace subtractions.
Introduction to Algorithms is a book on computer programming by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.The book has been widely used as the textbook for algorithms courses at many universities [1] and is commonly cited as a reference for algorithms in published papers, with over 10,000 citations documented on CiteSeerX, [2] and over 67,000 citation on ...
The first dynamic programming algorithms for protein-DNA binding were developed in the 1970s independently by Charles DeLisi in the US [5] and by Georgii Gurskii and Alexander Zasedatelev in the Soviet Union. [6] Recently these algorithms have become very popular in bioinformatics and computational biology, particularly in the studies of ...
n. In modular arithmetic, the integers coprime (relatively prime) to n from the set of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n.
A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n , until reaching the base case ...