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Here, the order of the generator, | g |, is the number of non-zero elements of the field. In the case of GF(2 8) this is 2 8 − 1 = 255. That is to say, for the Rijndael example: (x + 1) 255 = 1. So this can be performed with two look up tables and an integer subtract.
An xorshift+ generator can achieve an order of magnitude fewer failures than Mersenne Twister or WELL. A native C implementation of an xorshift+ generator that passes all tests from the BigCrush suite can typically generate a random number in fewer than 10 clock cycles on x86, thanks to instruction pipelining. [12]
Default generator in R and the Python language starting from version 2.3. Xorshift: 2003 G. Marsaglia [26] It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence.
Finally, if a generator period longer than 2 128 is required, the generator can be extended with an array of sub-generators. One is chosen (in rotation) to be added to the main generator's output, and every time the main generator's state reaches zero, the sub-generators are cycled in a pattern which provides a period equal to 2 to the power of ...
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The generator computes an odd 128-bit value and returns its upper 64 bits. This generator passes BigCrush from TestU01, but fails the TMFn test from PractRand. That test has been designed to catch exactly the defect of this type of generator: since the modulus is a power of 2, the period of the lowest bit in the output is only 2 62, rather than ...
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AES key schedule for a 128-bit key. Define: N as the length of the key in 32-bit words: 4 words for AES-128, 6 words for AES-192, and 8 words for AES-256; K 0, K 1, ... K N-1 as the 32-bit words of the original key; R as the number of round keys needed: 11 round keys for AES-128, 13 keys for AES-192, and 15 keys for AES-256 [note 4] W 0, W 1, ...