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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]
Galois/Counter Mode. In cryptography, Galois/Counter Mode (GCM) [ 1 ] is a mode of operation for symmetric-key cryptographic block ciphers which is widely adopted for its performance. GCM throughput rates for state-of-the-art, high-speed communication channels can be achieved with inexpensive hardware resources.
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 arbitrary set of N ...
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
CCM mode (counter with cipher block chaining message authentication code; counter with CBC-MAC) is a mode of operation for cryptographic block ciphers. It is an authenticated encryption algorithm designed to provide both authentication and confidentiality. CCM mode is only defined for block ciphers with a block length of 128 bits. [1][2]
Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. The modulus used is the same. So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum.
A mode of operation describes how to repeatedly apply a cipher's single-block operation to securely transform amounts of data larger than a block. [3][4][5] Most modes require a unique binary sequence, often called an initialization vector (IV), for each encryption operation. The IV must be non-repeating, and for some modes must also be random.