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Yes. The keys are indeed used in a linear manner. In particular, they are used in $E$-$D$-$E$ mode: encrypt using first 56 bits as key, decrypt using next 56 bits as key and then again encrypt using final 56 bits. This way its possible to use triple DES (which is officially called TDEA) for the DES, 2-DES and 3-DES variations. The first would use ...

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You are quite correct. A PRP in counter mode is, in fact, distinguishable from a random sequence if you approach the "birthday bound". We get around this by never generating that much output at once. With a 128 bit block cipher, an output of $2^{40}$ bytes (which is a lot of output) gives us a distinguishing advantage of about $2^{-56}$ (the probability ...

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The reference for this is NIST SP800-38A, especially its appendix B. Basically we consider the IV a binary value of the width of the block cipher (64-bit for DES, 128-bit for AES), and add 1 to that, except for one detail: there is no carry at some application-specified rank, defining the maximum number of blocks that can be enciphered with a single IV; if ...

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A family of functions F is a pairwise independent permutation if: Each member of the family is itself a permutation, and For any fixed $A$, $B$ (with $A \ne B$, and both from the input set of the permutation), and $f$ is a random member from the family $F$, then the pair $f(A), f(B)$ is equidistributed over all distinct pairs from the output range of the ...

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Yes. This is called format-preserving encryption. The most flexible algorithm is FFX, which uses a Feistel network with AES-based round-functions, but performs addition modulo $m$. For certain values of $m$, the range of the round function is extended in order to limit statistical biases to negligible values. When $m$ is very small, this approach isn't ...

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In CTR, you can use any operation which has a full cycle through the space of the IV with the counter. You could use the plus operator like the example: $69dda8455c7dd4254bf353b773304eec + 1 = 69dda8455c7dd4254bf353b773304eed$ To calculate the next value, just again add 1. You could also use a increasing counter and xor it with the original IV: ...

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I just read that chapter of the book, and the authors don't really justify their claim. They also talk about "using random data to prevent collision and precomputation attacks" (which would then give you back the full key-size crypto strength) – this is about using random initialization vectors and such. But if you are using an insecure mode of operation, ...

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The text quoted in the question: States that in any (finite commutative) field $(A,+,\cdot)$, the distribution of the permutations $f_{(a,b)}$ defined by $f_{(a,b)}(x)=a\cdot x+b$, where $(a,b)$ is uniformly distributed on $A^*\times A$, is pair-wise independent, per the definition now given in the question. Observes that because $GF(2^n)$ is such a field, ...

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$GF(2^{128})$ is a finite field with $2^n$ elements. There are a number of ways to represent this field. For example, a binary vector of length 128, or polynomials of degree 127 where the coefficients are 0 or 1. You could even choose to represent them as integers between $0$ and $2^{128}-1$. These are the elements of the finite field. In addition to the ...

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It is certainly possible to conceive protocols, for which a 128 bit key might cause collisions that might be avoided by using a 256 bit key. For instance, suppose you have a protocol that uses AES-CCM with a 56 bit nonce for bulk encryption. If the nonce is generated randomly, there is at least a $2^{-28}$ collision rate. It is essential that you ensure ...

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When talking about effective security level, one first have to say what type of attack is considered. There are two main attack types on a blockcipher with block size $n$ in the mode of operation $\Pi$: Key-recovery attack: an attacker finds the secret key of length $k$. Distinguishing attack: an attacker distinguishes the ciphertexts, produced by $\Pi$, ...

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In the padding oracle attack you have an oracle that only tells you whether a particular chosen ciphertext decrypts to a correctly padded plaintext. That oracle is used to build a last word oracle, which used iteratively can reveal a whole message. The reason it works in CBC mode is that we can make predictable, arbitrary changes to the plaintext of the ...

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…are any other modes of operation vulnerable to padding oracle attacks? Nope, it’s purely restricted to CBC. A padding oracle attack, also known as “Vaudenay attack” because it was originally published by Serge Vaudenay in 2002 and introduced at EUROCRYPT 2002, is an attack against cipher-block chaining. The attack works against any block cipher in ...

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In general, you cannot, because padding makes sure the plaintext can always be recovered, so any valid padding method produces equally valid plaintext. For instance, suppose the last (decrypted) block is, in hexadecimal notation: 01:02:03:04:05:06:07:08:09:0A:0B:0C:0D:FF:00:00 The "natural" interpretation is that the padding method here might be "add an ...

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