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11

I restrict to hash functions $H$ with an output of some fixed size $n\ge1$ bit(s), accepting as input some strings, including all $n$-bit strings; MD5 (resp. SHA-1, SHA-256) is an example of such function for $n=128$ (resp. $n=160$, $n=256$). Whether there exists a solution to $H(x)=x$ depends on the particular hash function. If $H$ is a random function (as ...


11

The main difference is that secp256r1 is a prime field curve, while secp256k1 is a Koblitz curve. Koblitz curves are known to be a few bits weaker than prime field curves, but since we are talking about 256-bit curves, neither is broken in "5-10 years" unless there's a breakthrough. The other difference is how the parameters have been chosen. In secp256r1 ...


9

What choice did they have? F1 is a bitwise function with three inputs and one output. There are $2^8 = 256$ such functions. Only 70 of them are "unbiased" (i.e. have as many 0 and 1 outputs in their image). If you further require that each input, as well as the order of inputs, matters for the output, you are left with only 36. However, those 36 are all ...


8

I would like to ask if that is true for every AES CTR mode implementation?, Doesn't have to be. You can store the nonce anywhere. You could even send it to the recipient via a different channel (e.g., email the ciphertext and use SMS to transmit the nonce). Storing it at the beginning has its advantages. For example, if streaming the data, you can ...


5

If you want strict indistinguishability, then yes, you need to store the IV (initial counter) somewhere. However, there are some relaxed modes that are used in practice for things like disk encryption, where it is often very useful to decrypt things "in the middle" like you say. For instance, XEX uses a counter which is derived from the sector and offset ...


5

In very short: Assume you have an NP problem, stated as some condition to be met. Since it is a NP condition, the computational complexity to find a satisfying input (called the witness for the language) grows quite fast. The setup of such an encryption scheme is based on a multilinear map (a generalization of a bilinear map, but with arbitrary many ...


4

First secp256r1 is a random and secp256k1 is a Koblitz curve. So according to this article: Koblitz curves should be avoided, [...] as they does not have enough warranty on crypto analytic activity and effectively they are: Not part of NSA Suite-B cryptography selection Not part of ECC Brainpool selection Not part of ANSI X9.62 selection ...


4

Like the other answers say, it does not always have to be the case. One other case where it is often not stored is when you have a single use key, for example as part of some hybrid encryption scheme. Then there is no need to use a nonce at all and it is usually taken to have zero value.


4

You can use these schemes instead: “Evaluating 2-DNF Formulas on Ciphertexts”, or “A Simple BGN-type Cryptosystem from LWE”. These schemes enable you to do addition, a single multiplication, and more additions. For inner product, that's all you need (encrypt each item separately, multiply pairs, and add all together). Not everything needs FHE. In any ...


4

MD5 was designed with the goal that any change in the input uniformly affects all the bits of the output. It's not perfect, but it's pretty good. If you're choosing the input "randomly enough" (e.g., by appending random bits before hashing) then your question approaches this one: Given two randomly generated 8-bit strings, what is the probability that ...


3

I don't know of a use of Lamport's scheme precisely as Lamport originally published it; however if we include generalizations of the idea (such as Winternitz signatures), then it has been used as the basis of Hash Based Signatures, such as this proposal


3

I don't believe he is answering the right question. You essentially asked "why are public keys so much larger than symmetric keys", and after his first sentence (which started to address the question, but was a bit vague), he tried to answer the distinct question "why are public key operations so much slower" (not that he got the details of that correct; ...


3

The correction question you should ask about why various operations in RC4 (or, for that matter, any other cipher) are there would be "if I were to remove that, what would the impact be? Would this weaken the cipher in some way?" At your current state of knowledge, that may be a rather imponderable question, but it is still the correct one. I can try to ...


3

Before answering the actual question, I will offer some general advice. It is important to pay attention, both in class and to the textbook you are reading. If learning how to solve such exercises is a key goal of the course, such solutions have very probably been discussed at length in class. Moreover, your textbook also has proof examples, and in this ...


2

As can be seen by RFC 5280 (X.509), this structure is the SubjectPublicKeyInfo. This field is formatted as follows: SubjectPublicKeyInfo ::= SEQUENCE { algorithm AlgorithmIdentifier, subjectPublicKey BIT STRING } The AlgorithmIdentifier is defined as follows: AlgorithmIdentifier ::= SEQUENCE { algorithm ...


2

While I can confirm that your “feeling“ is indeed correct, the rest of your question is not that easy to answer. I’ll try to give you some insight nevertheless. Generally… The number of rounds depends on the design and security parameters of the individual ciphers. This makes it rather impossible to generalize things in form of “structure $A$ should use ...


2

The sect curves are curves over a binary field. From SEC 2: Recommended Elliptic Curve Domain Parameters (chapter 3): The example elliptic curve domain parameters over $\mathbb{F}_{2^m}$ have been given nicknames to enable them to be easily identified. The nicknames were chosen as follows. Each name begins with sec to denote ‘Standards for Efficient ...


2

Since it's a linear cipher, you should be wary about a guessable padding, otherwise if your last block is only one char long, you will reveal almost your whole matrix on this last block. If you're too afraid of mangling the last word, use something like 'Z'+(random chars). But I really would not use any predictable padding with such a cipher.


2

The key space for DES is far too small (56 bits). Therefore, any use of DES is not secure. It doesn't matter what mode you use. If the attacker has one plaintext, ciphertext pair, they can brute force the key space and recover the key in a feasible amount of time (24 hours using the cloud). But most importantly, how it could be made secure? Will change ...


2

Imagine that you have a ciphertext: Perfect secrecy means, that without knowing the key, any plaintext has to be a possible preimage. Because otherwise the ciphertext would give you information about the plaintext. Encryption is an injective function, because otherwise it could not be reversed. That means, for a given key and ciphertext you have at most ...


2

The usefulness of online AE (locally): Assume you wrote a program that encrypt arbitrary files. Now further assume the user wants to view a movie, encrypted with this tool. The tool can now use the online-property to stream the movie in real-time as it uses online-encryption. The usefulness of online AE (programatically): Assume you want to process ...


2

As SOJPM says in their answer, the proofs for AES-GCM assumes that AES is a PRP. I can't believe that there is anywhere in the proof that using a PRF (possibly truncated) would break things -- but I haven't looked carefully for this. Depending on how the GCM proof is structured, (using/not using) the PRP/PRF switching lemma [1] may suffice, but I don't ...


2

If you want to encrypt a long message with authenticated encryption, you should split it into many small segments (e.g. 4KiB each), with each fragment having its own tag. That way you only release plaintext to the application after verifying its tag. (As usual there are some pitfalls with designing such a construction). Such a construction works with any ...


2

The function $L_a(x)=\langle a,x\rangle=a_1 x_1+\cdots+a_n x_n$ is a linear multivariate function of $(x_1,\ldots,x_n)$. The function $$f(x)+\langle a,x\rangle=f(x_1,\ldots,x_n)+a_1 x_1+\cdots+a_n x_n$$ equals $0$ mod 2 if $f(x)=\langle a,x\rangle$ and $1$ mod 2 otherwise. The sum $$ \hat{f}(a)=\sum_{(x_1,\ldots,x_n) \in \mathbb{F}_2^n} (-1)^{f(x)+\langle ...


2

Edwards curves can be implemented using a unified formula for addition and doubling; i.e., one can implement addition such that $$\mathrm{dbl}(P)=\mathrm{add}(P,P).$$ Performance wise it is however more efficient to consider both functions separately, since the doubling can be implemented more efficiently than the addition. Depending on the representation ...


2

I've been looking for the test vectors also. https://github.com/NTRUOpenSourceProject/ntru-crypto/blob/master/reference-code/Java/Encrypt/build.xml refers to ""com.securityinnovation.testvectors.NtruEncryptTestVectorGenerator" " I haven't looked any deeper than this, but it looks like they don't publish test vectors, but give you a means of generating them ...


1

The "logic" of the Enigma machine and the development of the Polish solution, in principle, are well described in David Kahn's "Seizing The Enigma". There may be better descriptions that have come out since, but I found this very clear and continue to recommend it. In addition to the nuts and bolts of the machine itself, Kahn describes the history from ...


1

GCM is a specific mode for block ciphers that combines CTR encryption mode and GMAC authentication. Since Salsa and ChaCha are already based on CTR mode internally, that would not be a relevant mode. However, there is no problem using GMAC. Salsa and ChaCha output larger blocks than GMAC accepts, so you would need to break them in the correct size chunks to ...


1

In order to bridge the gap between two worst case scenarios to produce similar distribution of privatized answers certain noise is added. For example the salaries of a CEO (max) and a line worker or who ever gets minimum wage (min) may not be produce similar distribution without the noise. Random values taken from Laplacian distribution with standard ...


1

Here's a more "down to earth" example. The following cryptosystem with plaintext space $\mathcal{M} = \{a,b,c,d\}$, keyspace $\mathcal{K} = \{1,2,3,4\}$ and ciphertext space $\mathcal{C} = \{A,B,C,D\}$ has perfect secrecy: $$\begin{array}{c|c c c c} & 1 & 2 & 3 & 4 \\ \hline a & A & B & C & D \\ b & B & C & D ...



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