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2

You also asked I would also be interested to see articles that apply algebra to the study of block ciphers. Specifically constructing groups to aid analysis that also consider the fact that a block cipher is a composition of several round functions. One nontrivial result is here; what this result states is that a composition of the DES round functions ...

3

Your first two paragraphs made a series of statements; these statements were less than perfectly accurate, and D.W. attempted to address those. You then went on and asked What I don't understand is how a key that is longer than a block size provides any extra security. From what I understand this would suggest the existence of many fixed points, ...

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The question makes a number of statements that are incorrect. It is not correct that a fixed point is guaranteed to exist. It is not correct that if you hold the plaintext constant and vary the key, then a fixed point is guaranteed to exist. Moreover, the existence of fixed points has only an extremely tenuous connection to security. Assume $E$ is a ...

4

Well, whether $AES'$ is as secure as $AES$ depends on the length of $k_1, k_2$. If they are both 128 bit, then what you effectively have is a standard 128-bit AES, except that prior to round 6, you replace the running key with an independent key (and you tweaked the last round, but that's cryptographically harmless). Now, it is never a good idea to do ...

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This is not a complete answer but it seems to me that it cannot be more secure than the original AES since otherwise it would mean that there is a serious weakness in the AES key schedule As far as being as secure there's at least one application in which it's a weakness : when you use AES inside a Davies-Meyer construction. An attacker has then more power ...

3

First, some public key algorithms such as RSA are technically block ciphers, capable of encrypting a block of as many bits as the size of the modulus - commonly 1024, 2048, or 4096 bits, dependent on the key. The problem is that most public key algorithms require a very large amount of CPU cycles to encrypt one block of data. In the case of RSA, the larger ...

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We can still safely use 64-bit-block ciphers when used in an otherwise sound protocol, and all of the following three conditions are met: The effective key size is made big enough; that disqualifies DES (55-bit), but not Blowfish (up to 448 bits), TEA (128 bits), 3DES (167 bits), and to some degree 2-keys-3DES (111 bits). Note: I computed the effective key ...

3

Yes, block ciphers are used in public key cryptography, though typically as auxiliary building blocks rather than as the heart of the public key scheme by themselves. One example is in digital signatures: many use a hash such as SHA-1, to digest the message being signed into a short cryptogram, and/or as part of a Mask Generating Function (loosely speaking: ...

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Another way of stating what you're asking is "if I encrypt a random number, how will an attacker know if he's correctly decrypted it?" The answer is "because the attacker may someday learn some of your output." Consider what would happen if you used the algorithm to encrypt a thousand random numbers, but then you encrypted a message beginning with "Dear ...

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