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17

Basically it's analysis of a cryptographic cypher by the means of finding a relationship between the difference in the input data and the output data. Ideally, the slightest difference in input data (cleartext), even a single bit, should produce a completely different cypthertext. However, if the cypher is not well-designed, a correlation between the two ...


16

You have clarified the question as asking about whether replacing ShiftRows with a random byte permutation would strengthen AES against differential attacks. It would not. ShiftRows and MixColumns were carefully selected to work in tandem, such that every byte affects every other byte in the state within just two rounds. MixColumns ensures that every ...


13

This claim is bogus. DES itself has a 13-round differential with probability around $2^{-47}$, so TripleDES with its 48 rounds is resistant to any sort of differential attack. The paper authors are not really confident in the subject.


10

Differential cryptanalysis works on differences. Linear cryptanalysis works on linearity. Neat, isn't it ? Instead of speaking of how they differ, it is easier to list their common features. Both kinds of attacks: Use a lot of known pairs plaintext/ciphertext (many input messages encrypted with the same key, and, for each of them, the attacker knows both ...


9

I assume that you mean the S-box. The answer is NO! Randomly chosen S-boxes are not good choices for differential and linear cryptanalysis. When Biham and Shamir presented differential attacks on DES, one of the things that they showed was that if you replace the S-boxes in DES with randomly chosen ones, then the differential attack becomes much more ...


6

There are 256! possible 8x8 S-boxes (i.e., bijective functions from $\{0,1\}^8$ to $\{0,1\}^8$. This is an absolutely enormous number. You couldn't possibly enumerate all of them within the lifetime of the universe. So, yes, this is one reason why it is not straightforward to determine whether there exists such a S-box with differential uniformity 2.


6

No, it's not flawed. You're just running into a fact of life; differential cryptanalysis generally doesn't just give you the entire key (or even subkey) in one shot. It generally gives you partial information about the key, and if you want the entire key, well, you need to work at it more. In this phase of the attack, you know that the last round subkey ...


5

This is known as the "key complementation" property of DES; I had thought that it actually predated Biham and Shamir's work. In any case, your questions: Does this hold for only that particular combination of s box or it will be same for any S-box combination It'd remain even if you change the sbox's arbitrarily. The reason for this is that it is not ...


5

This is called an Even-Mansour cipher. Actually, for the differential cryptanalysis it does not matter what sort of difference you use, you only need that it propagates deterministically through linear transformations (whatever linearity means). In this case you use a difference modulo $2^{32}$: $$ A \boxminus B \equiv (A-B)\pmod{2^{32}}. $$ You compute ...


4

In the case of block ciphers, differential cryptanalysis aim to measure the changes between inputs and outputs with a probability. The goal is to predict what the result will be before the last round and try to extract the key. For hash functions, your aim is to find a second-pre-image. I will take Keccak as an example. It is a sponge construction ...


4

I understand the question as you have a single 4-bit S-box, which you first apply rowwise, and then columnwise. As already mentioned, this is equivalent to a large S-box $\mathcal{S}$ $$ c = \mathcal{S}(m\oplus k_1)\oplus k_2. $$ This is a well-known Even-Mansour cipher, and it can be broken with complexity $2^{n/2}$, which is $2^8$ for your $n=16$. The ...


4

There are two papers on conventional differential cryptanalysis of SEED. The last one penetrates only half of the cipher. Even though there are few third-party cryptanalysis papers, there is no indication that the cipher is weak. Fault attacks are quite irrelevant in the SSL setting. I would be more concerned with BEAST-like attacks, as SEED is a blockcipher,...


4

A fault injection attack is based on the fact that you have a healthy black box on which you can do queries, but you can mess with the black box, for example flipping random bits. In real life this could for example be a RFID chip which can be messed with using strong electronic fields. Attacks like these are generally: Very sophisticated in theory and ...


4

The design documents for Rijndael explain exactly how the designers proved its resistance to differential cryptanalysis. Read their submission to the AES competition process, particularly Section 8.2 and the Annex. To understand their approach, it will probably help to understand differential cryptanalysis and read some of the related literature. You can ...


4

They are generally relevant only to symmetric-key cryptography (e.g., block ciphers, hash functions, message authentication codes). There's no deep reason why -- it's just that differential and linear cryptanalysis tend to be effective against the sort of structure that are commonly used in block ciphers, but not very effective against the sort of designs ...


4

Your fault attack scenario correspond to this paper : A Differential Attack Technique Against SPN Structures with Application to AES and KHAZAD (Piret & Quisquater - CHES 2003) This paper describe how to retrieve four bytes of the last round key with at least two pairs of ciphertext/faultytext. Each pair of ciphertext $C$ and faultytext $C^*$ could be ...


3

As with Dmitry, I assume you are applying a 4-bit s-box to a 4-by-4 array of 16 bits, first to the rows (after xoring 16 bits of key material to the plaintext), then to the columns (and lastly xoring 16 more bits of key material to produce the ciphertext). Strictly speaking, you need to specify the 4-bit s-box in order to fully evaluate it against ...


3

With DES, the issue is the size of the s-box. The DES s-boxes are highly tuned for their security properties, but if you compare their nonlinearity to the larger AES s-box, the are quite inferior. Note than random s-boxes and key dependent s-boxes are not the same thing. Random = fixed random, key dependent = permuted s-boxes based on the key. A random set ...


3

Those tables are fairly easy to build conceptually but require quite some work to actually carry out. Note that: The columns show the XOR for the in-going pairs and the rows show the number of pairs that had the specified XOR afterwards. This pseudo-code generates the table: InLength; // input length of the S-Box in bits OutLengh; // output length of the ...


3

From your picture I deduce that $A$ and $B$ are both 8 bits. So this construction can be seen as a $16 \times 8$ bit S-box (not bijective). The fact that it's not square is probably what is causing confusion. Usually, for SPNs, invertible S-boxes are used. Non-invertible S-boxes are less common, but they certainly have applications. One of the things we can ...


3

Probably the biggest vulnerability is that the message expansion is too linear. The linearity of the SHA-1 message expansion is why we are able to find such good differential paths. There can be differences at the beginning of the message and by the end of the message expansion they are mostly canceled out.


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 a ...


2

This is the code i used to simulate your Sbox (no intelligence, pure application with lots of mask for security). virtual uint8 apply_s(uint16 input, int numBits) { uint16 mask = 1; for (int i = 1; i < numBits; ++i) { mask |= mask << 1; } uint32 res = input & mask; res = res * res; res = (res >> ...


2

"Not vulnerable" is not how I would describe it, but my understanding is that the existing attacks on DES cannot directly not work with 3DES. At the moment, the best attack against single DES is a linear attack which requires $2^{43}$ plaintext-ciphertext pairs, and has a time complexity of at between $2^{39}$ and $2^{43}$ operations. Linear cryptanalysis ...


2

The key does not effect the cipher' differentials threw the equation (x+k)+(x'+k)=x+x' (the + sign means xor) How you can yes the key is X1+k=x2 And threw the xor k=X1 +x2 X1 is the value beffor the xor with the key value k. X2 is the output of X1+k To make this attack work beffor you must find a differential for the two input pairs threw a chosen ...


1

XORing with a key indeed does not change the difference. But usually before the XORing there is nonlinear layer (Sboxes?) which changes the difference. For example $(N rounds...)(Sbox)(AddKey)$. You can use a differential up to the beginning of this layer. Then, for different subkeys you will get same sbox output differences, but the sbox input differences ...


1

Your calculations are correct. The 2nd table has 2 entries of 6 in its DDT, and 18 entries of 4. The Hamsi s-box has 24 entries of 4. What can you infer from these tables? First off, CryptWizard001 is a liar. Second, the larger the max value in the DDT, the more vulnerable the s-box is to differential cryptanalysis, therefore the modified s-box does not ...


1

A good tutorial on differential cryptanalysis can be found in Stinson's book where he conducts differential attacks on reduced-round DES. He gives details on attacking 4 rounds of DES (which is relatively easy) and 6 rounds of DES (which is significantly harder) and this is enough to get the intuition on why extending the attack to full DES (which is 16 ...



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