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The one complication arises if the same hardware which generates the CRC by finding () = () + is used to check the CRC with a full-width division of () (). The latter will not produce a remainder of 0, nor of S ( x ) {\displaystyle S(x)} , but of S ( x ) ⋅ x n mod G ( x ) . {\displaystyle S(x)\cdot x^{n}{\bmod {G}}(x).}
as a result, even if the CRC is encrypted with a stream cipher that uses XOR as its combining operation (or mode of block cipher which effectively turns it into a stream cipher, such as OFB or CFB), both the message and the associated CRC can be manipulated without knowledge of the encryption key; this was one of the well-known design flaws of ...
little_endian_table[0] := 0 crc := 1; i := 128 do { if crc and 1 { crc := (crc rightShift 1) xor 0x8408 // The CRC polynomial} else { crc := crc rightShift 1 } // crc is the value of little_endian_table[i]; let j iterate over the already-initialized entries for j from 0 to 255 by 2 × i { little_endian_table[i + j] := crc xor little_endian ...
[2] [3] Between the 7th and 10th centuries CE a group of Jewish scribes formalized and expanded this to create the Numerical Masorah to ensure accurate reproduction of the sacred text. It included counts of the number of words in a line, section, book and groups of books, noting the middle stich of a book, word use statistics, and commentary. [ 1 ]
[5] FEC can be applied in situations where re-transmissions are costly or impossible, such as one-way communication links or when transmitting to multiple receivers in multicast. Long-latency connections also benefit; in the case of satellites orbiting distant planets, retransmission due to errors would create a delay of several hours.
Bernstein's hash djb2 [2] 32 or 64 bits shift/add or mult/add or shift/add/xor or mult/xor PJW hash / Elf Hash: 32 or 64 bits add,shift,xor MurmurHash: 32, 64, or 128 bits product/rotation Fast-Hash [3] 32 or 64 bits xorshift operations SpookyHash 32, 64, or 128 bits see Jenkins hash function: CityHash [4] 32, 64, 128, or 256 bits FarmHash [5 ...