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Luhn algorithm. The Luhn algorithm or Luhn formula, also known as the " modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers. It is described in US patent 2950048A, granted on 23 August 1960. [1]
Luhn mod N algorithm. The Luhn mod N algorithm is an extension to the Luhn algorithm (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered base. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any ...
The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the ISBN 0-201-53082-1: The sum of products is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 + 1×1 = 99 ≡ 0 (mod 11). So ...
There are two modulo 11 algorithms which use different repeated weighting factor patterns: the IBM algorithm which uses (2,3,4,5,6,7), and the NCR algorithm which uses (2,3,4,5,6,7,8,9). Get the sum of the string by looping through each character and multiply it by a weight from 2 to 7 (IBM) or 2 to 9 (NCR) depending on its position.
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = be mod m. From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5, e = 3 and m = 13, dividing 53 = 125 by 13 leaves a remainder of c = 8.
Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [ 1 ] For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0 ...
Barrett reduction is an algorithm designed to optimize this operation assuming is constant, and <, replacing divisions by multiplications. Historically, for values a , b < n {\displaystyle a,b<n} , one computed a b mod n {\displaystyle ab\,{\bmod {\,}}n\,} by applying Barrett reduction to the full product a b {\displaystyle ab} .
Consistent hashing. In computer science, consistent hashing[1][2] is a special kind of hashing technique such that when a hash table is resized, only keys need to be remapped on average where is the number of keys and is the number of slots. In contrast, in most traditional hash tables, a change in the number of array slots causes nearly all ...