Unformatted text preview: . The hash of the entire message is the hash of the last block. The pre-image should contain some kind of binary representation of the length of the entire message. This technique overcomes a potential security problem resulting from messages with different lengths possibly hashing to the same value [1069, 414]. This technique is sometimes called MD-strengthening . Various researchers have theorized that if the compression function is secure, then this method of hashing an arbitrary-length pre-image is also secure—but nothing has been proved [1138, 1070, 414]. A lot has been written on the design of one-way hash functions. For more mathematical information, consult [1028, 793, 791, 1138, 1069, 414, 91, 858, 1264]. Bart Preneel’s thesis  is probably the most comprehensive treatment of one-way hash functions. Figure 18.1 One-way function. 18.2 Snefru
Snefru is a one-way hash function designed by Ralph Merkle . (Snefru, like Khufu and Khafre, was an Egyptian pharaoh.) Snefru hashes arbitrary-length messages into either 128-bit or 256-bit values. First the message is broken into chunks, each 512-m in length. (The variable m is the length of the hash value.) If the output is a 128-bit hash value, then the chunks are each 384 bits long; if the output is a 256-bit hash value, then the chunks are each 256 bits long. The heart of the algorithm is function H, which hashes a 512-bit value into an m-bit value. The first m bits of H’s output are the hash of the block; the rest are discarded. The next block is appended to the hash of the previous block and hashed again. (The initial block is appended to a string of zeros.) After the last block (if the message isn’t an integer number of blocks long, zeros are used to pad the last block), the first m bits are appended to a binary representation of the length of the message and hashed one final time. Function H is based on E, which is a reversible block-cipher function that operates on 512-bit blocks. H is the last m bits of the output of E XORed with the first m bits of the input of E. The security of Snefru resides in function E, which randomizes data in several passes. Each pass is composed of 64 randomizing rounds. In each round a different byte of the data is used as an input to an S-box; the output word of the S-box is XORed with two neighboring words of the message. The S-boxes are constructed in a manner simil...
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