Modular exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography...
21 KB (2,802 words) - 00:03, 24 March 2024
Algorithm (IDEA), and RC4. RSA and Diffie–Hellman use modular exponentiation. In computer algebra, modular arithmetic is commonly used to limit the size of...
29 KB (3,602 words) - 18:28, 25 August 2024
square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic or powering of matrices. For...
21 KB (3,379 words) - 09:03, 14 June 2024
is known. The relative cost of exponentiation. Though it can be implemented more efficiently using modular exponentiation, when large values of m are involved...
24 KB (3,639 words) - 06:47, 26 January 2024
In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Exponentiation is written as bn, where b is the...
104 KB (13,637 words) - 12:46, 26 August 2024
U 2 j {\displaystyle U^{2^{j}}} . This can be accomplished via modular exponentiation, which is the slowest part of the algorithm. The gate thus defined...
41 KB (5,886 words) - 09:59, 12 August 2024
discrete logarithm problem. The computation of ga mod p is known as modular exponentiation and can be done efficiently even for large numbers. Note that g...
47 KB (5,161 words) - 17:29, 25 August 2024
However, when performing many multiplications in a row, as in modular exponentiation, intermediate results can be left in Montgomery form. Then the initial...
28 KB (3,847 words) - 07:52, 4 May 2024
Standard for digital signatures, based on the mathematical concept of modular exponentiation and the discrete logarithm problem. In a public-key cryptosystem...
16 KB (2,176 words) - 18:12, 30 July 2024
2 {\displaystyle 2} through p − 2 {\displaystyle p-2} and uses modular exponentiation to check whether a ( p − 1 ) / 2 ± 1 {\displaystyle a^{(p-1)/2}\pm...
116 KB (14,108 words) - 23:59, 15 August 2024
well-studied at the time. Moreover, like Diffie-Hellman, RSA is based on modular exponentiation. Ron Rivest, Adi Shamir, and Leonard Adleman at the Massachusetts...
61 KB (7,877 words) - 15:19, 2 August 2024
provide equivalent security, compared to cryptosystems based on modular exponentiation in Galois fields, such as the RSA cryptosystem and ElGamal cryptosystem...
39 KB (4,670 words) - 03:46, 2 August 2024
primality test. Both the provable and probable primality tests rely on modular exponentiation. To further reduce the computational cost, the integers are first...
8 KB (1,154 words) - 14:51, 4 February 2024
are coprime. 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...
28 KB (4,452 words) - 21:55, 14 August 2024
Euclidean Lehmer's Modular square root Cipolla Pocklington's Tonelli–Shanks Berlekamp Kunerth Other algorithms Chakravala Cornacchia Exponentiation by squaring...
13 KB (2,044 words) - 21:24, 21 July 2024
is based on the assumption that this Rabin function is one-way. Modular exponentiation can be done in polynomial time. Inverting this function requires...
14 KB (1,880 words) - 06:53, 22 July 2024
theorem, characterizing even perfect numbers Euler's theorem, on modular exponentiation Euler's partition theorem relating the product and series representations...
14 KB (1,603 words) - 16:45, 2 July 2024
Fermat primality test (category Modular arithmetic)
respectively, hence testing them adds no value. Using fast algorithms for modular exponentiation and multiprecision multiplication, the running time of this algorithm...
8 KB (1,134 words) - 07:32, 3 June 2024
Euclidean Lehmer's Modular square root Cipolla Pocklington's Tonelli–Shanks Berlekamp Kunerth Other algorithms Chakravala Cornacchia Exponentiation by squaring...
24 KB (3,042 words) - 00:45, 15 August 2024
46}).} Van Meter, Rodney; Itoh, Kohei M. (2005). "Fast Quantum Modular Exponentiation". Physical Review. 71 (5): 052320. arXiv:quant-ph/0408006. Bibcode:2005PhRvA...
26 KB (4,601 words) - 22:35, 6 August 2024
Discrete logarithm (category Modular arithmetic)
Regardless of the specific algorithm used, this operation is called modular exponentiation. For example, consider Z17×. To compute 34 in this group, compute...
17 KB (2,043 words) - 22:45, 29 July 2024
Solovay–Strassen primality test (category Modular arithmetic)
return composite return probably prime Using fast algorithms for modular exponentiation, the running time of this algorithm is O(k·log3 n), where k is the...
10 KB (1,500 words) - 03:30, 29 February 2024
Euclidean Lehmer's Modular square root Cipolla Pocklington's Tonelli–Shanks Berlekamp Kunerth Other algorithms Chakravala Cornacchia Exponentiation by squaring...
13 KB (1,768 words) - 03:41, 21 July 2024
carry out these modular exponentiations, one could use a fast exponentiation algorithm like binary or addition-chain exponentiation). The algorithm can...
6 KB (838 words) - 04:29, 12 June 2023
Modulo (redirect from Modular operation)
Gauss's introduction of modular arithmetic in 1801. Modulo (mathematics), general use of the term in mathematics Modular exponentiation Turn (angle) Mathematically...
46 KB (3,351 words) - 10:59, 15 August 2024
Euclidean Lehmer's Modular square root Cipolla Pocklington's Tonelli–Shanks Berlekamp Kunerth Other algorithms Chakravala Cornacchia Exponentiation by squaring...
25 KB (2,981 words) - 18:28, 21 June 2024
bits would double each iteration). The same strategy is used in modular exponentiation. Starting values s0 other than 4 are possible, for instance 10,...
21 KB (3,467 words) - 17:16, 2 May 2024
tree Dedekind sum Egyptian fraction quack Montgomery reduction Modular exponentiation Linear congruence theorem Method of successive substitution Chinese...
10 KB (935 words) - 23:13, 8 August 2024
reducing fractions to their simplest form and for performing division in modular arithmetic. Computations using this algorithm form part of the cryptographic...
123 KB (15,119 words) - 08:05, 21 August 2024
Euclidean Lehmer's Modular square root Cipolla Pocklington's Tonelli–Shanks Berlekamp Kunerth Other algorithms Chakravala Cornacchia Exponentiation by squaring...
17 KB (1,993 words) - 02:27, 26 July 2024