Mathematical Preliminaries in Mathematical Operation
نویسندگان
چکیده
منابع مشابه
Mathematical preliminaries of crypto Finite fields
In the high school you probably have studied many arithmetic laws and how to apply them in order to compute or solve equations. In practice, most of them do not hold if you consider floating point numbers. For instance, (a+ b) + c 6= a+ (b+ c) when b and c are near the floating point precision and a is moderately large number. We also often treat a digital document as a raw sequence of bits and...
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is the exponentiation operation. Moreover, if h = gx then we say that x is the discrete logarithm of h on basis g, and write x = logg h. The discrete logarithm assumption in a cyclic finite group G of order p is that given a generator g of G and a randomly generated element h of G, it is computationally infeasible to find logg h. To formalize this, we need to define infeasibility. Thus, more fo...
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Theorem 1 (Chinese Remainder Theorem). If ni ⊥ nj for each 1 ≤ i < j ≤ k, then the system of congruences (1) has a unique solution modulo N = ∏k i=1 ni. The proof of the existence of the solution will also give us an algorithm for finding that solution. Proof. For each i ∈ {1, . . . , k} let mi = N/ni. The numbers mi are natural numbers, because ni was one of the factors of N . We have ni ⊥ mi,...
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1 Integers. Divisibility The cryptographic constructions we’re going to see in further lectures and courses are built on top of various algebraic structures. All these structures, however, are ultimately built on top of integers. The set of integers is Z = {. . . ,−2,−1, 0, 1, 2, . . .}. On this integers set, we are given the binary operations “+” (addition) and “ ·” (multiplication). The multi...
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ژورنال
عنوان ژورنال: International Journal for Research in Applied Science and Engineering Technology
سال: 2019
ISSN: 2321-9653
DOI: 10.22214/ijraset.2019.10100