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A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).
The Hadamard code is a linear code, and all linear codes can be generated by a generator matrix .This is a matrix such that () = holds for all {,}, where the message is viewed as a row vector and the vector-matrix product is understood in the vector space over the finite field.
Cyclic redundancy check. A cyclic redundancy check ( CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to digital data. [ 1][ 2] Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents.
The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by Makoto Matsumoto (松本 眞) and Takuji Nishimura (西村 拓士). [ 1][ 2] Its name derives from the choice of a Mersenne prime as its period length. The Mersenne Twister was designed specifically to rectify most of the flaws found in older PRNGs.
The public key is derived from the private key by disguising the selected code as a general linear code. For this, the code's generator matrix is perturbated by two randomly selected invertible matrices and (see below). Variants of this cryptosystem exist, using different types of codes.
Mathematical definition. In mathematical terms, the extended binary Golay code G24 consists of a 12-dimensional linear subspace W of the space V = F24. 2 of 24-bit words such that any two distinct elements of W differ in at least 8 coordinates. W is called a linear code because it is a vector space. In all, W comprises 4096 = 212 elements.
The key selects which S-boxes are used. The patent describes the execution of the cipher operating on 24 bits at a time, and also a sequential version operating on 8 bits at a time. Another variant by John L. Smith from the same year [3] uses a 64-bit key operating on a 32-bit block, using one addition mod 4 and a singular 4-bit S-box. The ...
This attack is against AES-256 that uses only two related keys and 2 39 time to recover the complete 256-bit key of a 9-round version, or 2 45 time for a 10-round version with a stronger type of related subkey attack, or 2 70 time for an 11-round version. The Advanced Encryption Standard ( AES ), also known by its original name Rijndael ( Dutch ...