# Tag Info

10

There is no such thing as a 16 bit AES key. AES is a block cipher with a block size of 128 bits and a key size of 128, 192 or 256 bits. As a block cipher, AES can only encrypt 16 bytes (128) bits at a time. AES in itsef is not (CPA) secure as repetition of the plaintext would lead to repetitions of the ciphertext. To encrypt larger amounts of data, AES ...

9

$s_i = s_{i-1}\cdot(N + 1) + 1 = s_{i-1} \cdot N + s_{i-1} + 1$ but $s_{i-1} \cdot N = 0 \pmod N$, so $s_i = s_{i-1} + 1 \pmod N$ which means you can discover the next number to be generated just looking to the current one...

5

HMAC does not provide an obvious security improvement over the KMAC construction, which is optimal for Keccak based functions. HMAC is designed to create a secret initialization vector or IV for Merkle-Damgård type hash functions, KMAC does the same for sponge based hash functions but much more efficiently. HMAC also needs to deal with the length extension ...

5

Yes, the attack you sketched out would work - in theory. In practice, it's an efficient (computable in polynomial time) mapping $\psi:E\rightarrow\mathbb Z_n$ we're lacking. As for the unefficient mappings, $\psi:x\cdot P\mapsto x$ would be perfectly fine theoretically, but we don't know how to calculate it (it's the elliptic curve discrete logarithm ...

4

See Vitor's answer for the answer your professor was looking for. However, for any PRNG of the form $s_{i+1} = F(s_{i})$, where the attacker sees the $s_i$ values, and knows $F$, then he can distinguish it. Given a sequence of values $r_1, r_2, ...$, he can determine whether it was generated by that PRNG by checking if $r_2 = F(r_1)$; this is always true ...

4

Can a variable that is not explicitly computed correlate with the power consumption? Yes, and this can happen in several ways. When you say "not computed explicitly", I assume you mean that the computation is performed on a masked value or share instead. That is, the secret inputs (referred to as the key by the paper you link to) themselves do not ...

3

Our goal is to find a root $(x_0,y_0)$ in $\mathbb{Z}_e$ of the polynomial $f(x,y) = x(A+y)-1$. Finding roots of a polynomial in any $\mathbb{Z}_n$ isn't an easy job, in order to solve the problem Coppersmith had the idea to reduce to problem to finding a root $(x_0,y_0)$ over $\mathbb{Q}$ of some other polynomial $f'$ related to $f$. About Coppersmith ...

3

The block size does not directly determine the security of a block cipher. Even with a 32 bit block cipher the number of possible permutations is 2^32!, a stupendously big number. Small block sizes are however cumbersome to use in secure modes of operation as the input is limited. For instance, it would be easy to have repeating counters in counter mode ...

3

Remark: The round function of your toy cipher is the following. | K ---> + | ------- | S | ------- | >> 2 | Hence in the last round, the shift and S-box are useless (because invertible hence do not add security) which is why in a SPN scheme the key addition at the end is preferred. I did ...

2

Scheme is not IND-CPA for any message longer than one block. I'll include a image of CBC mode below for reference (Source: Wikipedia). Suppose instead of block cipher encryption we have plaintext xor-ed with the key as you propose. You'll note that for message block 1, $M_1$, the ciphertext block $C_1 = M_1 \oplus IV \oplus Key$. Similarly $C_2 = M_2 ... 2 Probably you could also read "known best attack" instead of "best known attack". In that case the attack would simply be the attack that reduces the security the most. This is often calculated in powers of two, represented by bits. For instance an attack could reduce security from 112 bits to 80 bits. If a second attack only reduces security from 112 bits ... 2 The first thing you should do is estimate the key length. While you may be able to do this using Kasiski examination, in this modern era of computers I very much recommend instead using the index of coindicence, which you can compute very easily, e.g. with this Python program: import sys msg = sys.stdin.read() # read ciphertext from standard input for ... 2 If you want to attack the block cipher, then there are no generic attacks which use the block size. However, if you want to use a block cipher for messages which are longer than 32 bits, then you will have to use it in a mode of operation, like GCM, or OMAC (more popular modes are CBC and CTR, but they should not be used for communication on their own since ... 1 Any group where you can derive$x$from$g, g^x, g^{1/x}$would also have the Discrete Log problem be equivalent to the (computational) Diffie-Hellman problem. Since this is not known to be true in general, we don't know of any general method for deriving$x$from those values. This equivalence is quite simple to demonstrate; if it based on the fact that ... 1 If you encrypt (partially) random values then the likelyhood that you encrypt the same value is larger for block ciphers that operate of fewer bits. If you encrypt the same value with the block cipher (which is a PRP) it will result in the same ciphertext. Identical ciphertext can be used by an attacker to retrieve information about the plaintext, breaking ... 1 Most of side channel attacks are depends on algorithm and implementation. In several cases, power consumption is evidently visible in algorithm. For example in the algorithm for elliptic curve points multiplication, for computing$Q=k\cdot P$we have following algorithm: Let$k$be$l$bit. Q=P for i from l-1 to 0 do Q = 2Q if k_i == 1 then Q = Q+P ... 1 The main complexity of attacks using a quantum computer with Grover's attack is explained here. I'll use the remainder of the answer to indicate some possible misconceptions in your question. It's hard to say exact QC specs, but let's assume we have decent a quantum computer using Grover's algorithm that is able to half AES-128 keyspace to that of ... 1 You're essentially asking if SHA-3 can use a keyed hash instead of an HMAC. The short answer is yes. But there's more to it than that. In the SHA-3 competition, two of the finalists (Keccak and Skein) were specifically designed to have a one-pass MAC as part of their design, and that's what the answer above is giving about Keccak. KMAC is Keccak's ... 1 I believe the only way you can do this is to assume you have fixed length inputs to the hash function$f$. Otherwise, it is problematic what probability distribution you'd want to impose on the input set$\{0,1\}^{\ast}$which is the collection of all finite input strings. In practice, hash functions do have an upper limit on the input string, but that's ... 1 The attack, as stated in sections 6.2 & 6.3, actually can only recover the quantity$K_1[1,3]\oplus K_2[1,3]\$. What you would hope to do is, to use a similar approach via another high probability linear relation [usually there is more than one] and recover more relations between subkey bits. Eventually, the goal is recovering all the original key bits. ...

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