In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent...
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mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity...
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a modular multiplicative inverse of a modulo m. If a ≡ b (mod m) and a−1 exists, then a−1 ≡ b−1 (mod m) (compatibility with multiplicative inverse, and...
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With that provision, x is the modular multiplicative inverse of a modulo b, and y is the modular multiplicative inverse of b modulo a. Similarly, the...
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remainder of c = 8. Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using...
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In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing...
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public key. Determine d as d ≡ e−1 (mod λ(n)); that is, d is the modular multiplicative inverse of e modulo λ(n). This means: solve for d the equation de ≡...
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Modulo (redirect from Modular operation)
Fermat's little theorem. Inverse: [(−a mod n) + (a mod n)] mod n = 0. b−1 mod n denotes the modular multiplicative inverse, which is defined if and only...
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logarithm from pn − 1 and exponentiating the result. By making a modular multiplicative inverse table for the finite field and doing a lookup. By mapping to...
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{\frac {a}{b}}} does not denote the modular multiplication of a {\displaystyle a} times the modular multiplicative inverse of b {\displaystyle b} but rather...
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Inversive congruential generators are a type of nonlinear congruential pseudorandom number generator, which use the modular multiplicative inverse (if...
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every nonzero element a has a unique modular multiplicative inverse, a−1 such that aa−1 = a−1a ≡ 1 mod m. This inverse can be found by solving the congruence...
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Schönhage–Strassen algorithm (redirect from Schönhage-Strassen multiplication)
{1}{n}}\equiv 2^{-m}{\bmod {N}}(n)} , where m is found using modular multiplicative inverse. In Schönhage–Strassen algorithm, N = 2 M + 1 {\displaystyle...
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y {\displaystyle C'\cdot y} , since Peggy multiplied by the modular multiplicative inverse of y {\displaystyle y} . However, if in either one of the above...
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This formula still holds after a modular reduction if a modular multiplicative inverse is used to compute ( a d − b c ) − 1 {\displaystyle...
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subgroup of a multiplicative group of integers modulo n {\displaystyle n} , where n {\displaystyle n} is prime, the modular multiplicative inverse can be computed...
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the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse...
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(related through the identity |−x| = |x|). Monoid Inverse function Involution (mathematics) Multiplicative inverse Reflection (mathematics) Reflection symmetry...
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the extended Euclidean algorithm http://en.wikipedia.org/wiki/Modular_multiplicative_inverse#Computation """ x = 0 last_x = 1 y = 1 last_y = 0 while b !=...
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{\displaystyle \gcd(R,m)=1,} let R − 1 {\displaystyle R^{-1}} be the modular multiplicative inverse of R {\displaystyle R} (i.e., 0 < R − 1 < m {\displaystyle 0<R^{-1}<m}...
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Fermat's little theorem (category Modular arithmetic)
relating to Fermat's little theorem RSA Table of congruences Modular multiplicative inverse Long 1972, pp. 87–88. Pettofrezzo & Byrkit 1970, pp. 110–111...
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\ 1{\pmod {n}}} . In other words, the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the...
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modular multiplicative inverse of a modulo m. I.e., it satisfies the equation 1 = a − 1 mod m {\displaystyle 1=a^{-1}{\bmod {m}}} The multiplicative inverse...
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Method of successive substitution (category Modular arithmetic)
2j ≡ 1 (mod 3) The Euclidean modular multiplicative inverse of 2 mod 3 is 2. After multiplying both sides with the inverse, we obtain: j ≡ 2 × 1 (mod 3)...
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Unit fraction (section Modular arithmetic)
is a positive fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a...
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are all required to be coprime to n, as mentioned above. See modular multiplicative inverse. R. Crandall and J. Papadopoulos, On the implementation of AKS-class...
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Group scheme (redirect from Multiplicative group scheme)
The multiplicative group Gm has the punctured affine line as its underlying scheme, and as a functor, it sends an S-scheme T to the multiplicative group...
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Group (mathematics) (section Modular arithmetic)
\cdot \right)} , the rationals with multiplication, being a group: because zero does not have a multiplicative inverse (i.e., there is no x {\displaystyle...
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Arithmetic (redirect from Multiplicative operator)
48\div 8=48\times {\tfrac {1}{8}}} . The multiplicative identity element is 1 and the multiplicative inverse of a number is the reciprocal of that number...
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denoted by a−1 or 1/a, called the multiplicative inverse of a, such that a ⋅ a−1 = 1. Distributivity of multiplication over addition: a ⋅ (b + c) = (a ⋅...
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