Digital Signature Schemes Based on Error-correcting Codes

Applied cryptography: Protocols, algorithms, and source code in C

“…When the feedback size n is less than the block length, the average cycle length drops to around 2 m/2 . For a 64-bit block cipher, this is only 2 32 -not long enough.…”

“…Function f is straightforward. First, the right half and the ith subkey are added modulo 2 32 . The result is broken into eight 4-bit chunks, and each chunk becomes the input to a different S-box.…”

“…To continue the example, the listing (32, 7, 5, 3, 2, 1, 0) means that if you take a 32-bit shift register and generate the new bit by XORing the thirty-second, seventh, fifth, third, second, and first bits together (see Figure 16.4), the resultant LFSR will be maximal length; it will cycle through 2 32 The code is a little more complicated when the shift register is longer than the computer's word size, but not significantly so.…”

“…(If you wonder where those numbers came from: 0x5a827999 = 2 1/2 /4, 0x6ed9eba1 = 3 1/2 /4, 0x8f1bbcdc = 5 1/2 /4, and 0xca62c1d6 = 10 1/2 /4; all times 2 32 . )…”

“…Ivan Damgård designed a one-way hash function based on the knapsack problem (see Section 19.2) [414]; it can be broken in about 2 32 operations [290,1232,787].…”