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It s simply the digest of the last block that Ray has. That s why good digest-based PRNGs use an internal state. If the underlying digest algorithm is truly one-way (meaning that no one can determine the message from the digest), no one will be able to figure out what the state was that produced any particular pseudo-random output. If no one can figure out what the state is at any point in time, no one can compute what the next bytes will be.
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In 2 you learned about block ciphers. A block cipher encrypts each block independently, so if the same block of plaintext appears more than once in a message, the resulting ciphertext block also will be repeated. This repetition could help an attacker. For example, suppose a company encrypts employee information in a database using the same key for each entry. If two entries contain the same block of ciphertext for salary, anyone seeing that matching block would know that those two people earn the same salary. Feedback modes make certain that each block of ciphertext is unique. (Except for that, they offer no additional security.) The most common feedback mode (described in 2) is cipher block chaining (CBC). When you encrypt data in CBC mode, each block of plaintext is XOR d with the preceding block of ciphertext before the block is encrypted. There is no previous ciphertext for the first block, so it is XOR d with an initialization vector (IV). The term for no feedback is electronic codebook (ECB). Following are some other feedback modes.
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Cipher Feedback Mode*
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In cipher feedback (CFB) mode, you encrypt a block of data and XOR the plaintext with this encrypted block to produce the ciphertext. The block of data you encrypt is the preceding ciphertext. The first block has no preceding ciphertext, so it uses an IV. To create the first block of ciphertext, you encrypt the IV and XOR it with the plaintext. Now you save the
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*(Source: RSA Labs)
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resulting ciphertext for the next block. For the second block, you encrypt the preceding ciphertext (the result of the preceding XOR) and XOR the result of that with the plaintext. For example, suppose that the first plaintext block begins with the word Goal. Here s the process. 1. Encrypt the IV. IV 0xA722B551 . . . becomes 0x38F01321 . . . . 0x476F616C
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2. XOR the plaintext with the encrypted IV. Goal becomes 0x7F9F724D, which is the ciphertext.
3. Encrypt the preceding ciphertext. 0x7F9F724D . . . becomes 0xE1250B77 . . . . 4. XOR the plaintext with the encrypted preceding ciphertext, and repeat until the entire message is encrypted. It s possible to define CFB mode so that it uses feedback that is less than one full data block. In fact, with CFB, it s possible to define a block size as one byte, effectively converting a block cipher into a stream cipher. Suppose you re using AES, a block cipher with a block size of 16 bytes. Here s what to do. First, use a 16-byte IV and encrypt it. You now have a block of 16 bytes that is the encrypted IV. Grab one byte of plaintext and XOR it with the most significant byte of the encrypted IV. Now that you ve used that byte, throw it away by shifting the block of encrypted IV to the left. That leaves the least significant byte open. Fill it with the ciphertext (the result of the XOR). Now go on to the next byte of plaintext. CFB mode is as secure as the underlying cipher, and using the XOR operation conceals plaintext patterns in the ciphertext. Plaintext cannot be manipulated directly except by the removal of blocks from the beginning or the end of the ciphertext.
Output Feedback Mode*
Output feedback (OFB) mode is similar to CFB mode except that the quantity XOR d with each plaintext block is generated independently of both the plaintext and the ciphertext. Here s how to use this mode. For the first block of ciphertext, encrypt the IV and call this quantity the cipher block. Now XOR the cipher block with the plaintext. For the second block, encrypt the cipher block to create a new cipher block. Now XOR this new cipher block with the next block of plaintext.
*(Source: RSA Labs)
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