An efficient implementation of the Euclidean GCD (greatest common divisor) algorithm employing the redundant binary number system is described. The time complexity is O(n), utilizing O(n)4-2 signed 1-b adders to determine the GCD of two n-b integers. The process is similar to that used ...
The time complexity of the "O(log k) GCD Algorithm" is significantly faster than other GCD algorithms such as the Euclidean algorithm, which has a time complexity of O(k). This means that for larger numbers, the "O(log k) GCD Algorithm" will be able to find the GCD in a ...
Is Euclidean algorithm faster than __gcd(a,b)? → Reply farzad.shbfn 10 years ago, # ^ | -21 if u're looking for faster code, i think this'll come in handy too: int gcd(int a, int b) { while(b ^= a ^= b ^= a = a % b); return a; } it's all arithmetic an...
GCD computations and variants of the Euclidean algorithm enjoy broad uses in both classical and quantum algorithms. In this paper, we propose quantum circuits for GCD computation with $O(n \log n)$ depth with O(n) ancillae. Prior circuit construction needs $O(n^2)$ running time with O(...
The key to execute the extended Euclidean algorithm in O(nlog2n)O(nlog2n) is to be able to switch between the two representations. Conversion of [a0(x);a1(x),…,ak(x)][a0(x);a1(x),…,ak(x)] to pkpk, qkqk and rkrk The recurrence pi=pi−2+aipi−1pi=pi−2+aipi...
Binary GCD algorithmEuclidean algorithmExponentiationGreatest common divisorMulti-exponentiationPublic-key cryptographySide-channel attackbit double and triple exponentiation, they achieve the average complexity of 1.53 and 1.75 multiplications (including squarings), respectively. The proposed algorithms can be ...
We show that parallel versions of both algorithms match the complexity of the best previous parallel GCD algorithm due to Chor and Goldreich. Specifically, if log n ≤ k ≤ 2 n and k is a power of two, then both algorithms run in O ( n /log k + log 2 n log log n ) time ...
Our algorithms take time O(n~2) for n bit input. This is an improvement from the known results based on the Euclidean algorithm, and taking time O(n·M(n)), where M(N) denotes the complexity of multiplying n bit integers. The new algorithms have applications in practical primality ...
The binary algorithm is a variant of the Euclidean algorithm that performs well in practice. We present a quasi-linear time recursive algorithm that computes the greatest common divisor of two integers by simulating a slightly modified version of the binary algorithm. The structure of the recursive...
J. Shallit and J. Sorensen, Analysis of a left shift binary GCD algorithm, J. Symb. Comput. 17 (6) (1994), 473 - 486Analysis of a left-shift binary GCD algorithm - Shallit, Sorenson - 1994 () Citation Context ...ber of algorithms, in addition to the Euclidean algorithm, for ...