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A de Bruijn sequence can be used to shorten a brute-force attack on a PIN -like code lock that does not have an "enter" key and accepts the last n digits entered. For example, a digital door lock with a 4-digit code (each digit having 10 possibilities, from 0 to 9) would have B (10, 4) solutions, with length 10 000.
Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms.
A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic. The oldest and simplest method, known since antiquity as long multiplication or grade-school ...
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [1][2][3] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most single-digit ...
In binary encoding each long number is multiplied by one digit (either 0 or 1), and that is much easier than in decimal, as the product by 0 or 1 is just 0 or the same number. Therefore, the multiplication of two binary numbers comes down to calculating partial products (which are 0 or the first number), shifting them left, and then adding them ...
Cyclic permutation. Type of (mathematical) permutation with no fixed element. In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. [1][2] In some cases, cyclic permutations are referred to as cycles; [3] if a cyclic permutation has k elements, it may be called a k-cycle.
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