Questions tagged [cryptography]
Questions about the construction and analysis of protocols and algorithms for secure computation and communication (including authentication, integrity, and privacy aspects).
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If Q* can break encryption would that prove P=NP?
At 12:11 in this video the creator talks about unverified rumors the Q* algorithm can break AES-192 encryption. If this is true, would this mean P = NP?
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Converting encrypted messages to unencrypted results of an equally hard to reverse function
If we have some function, $f$ with an exponentially sized domain, mapping the set $\{0, 1\}^N$ to $\{0, 1\}$, could we do something like this:
For ease, let's say $E(x) = x^e (\text{mod} \; n)$. This ...
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Data structure for detecting duplicate entries efficiently
In search of an efficient data structure to store some sort of list hash that I can compare to a value to obtain a probability of it already being in the list.
Perhaps it makes more sense defined as ...
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(Zero-knowledge?) Proof of Connection
I have a conundrum to solve but am not knowledgeable enough about cryptography to know whether it's possible to do, and if so, what method to use.
I am a Provider and my task is to prove to some ...
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1
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What is the definition of security of universal hashing
As a cryptographic primitive, universal hashing should have somewhat a criterion on its security. How is its (computational) security defined? Or, in other words, what "breaks" a universal ...
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Are there any typical papers on the impossibility of black-box reduction of circuits?
I am now considering the impossibility of black-box reductions between error-correcting codes and universal hashing without multiplicative overhead in depth. I could hardly find any classical papers ...
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Does there exist some ``partial" universal hashing?
Suppose we have sets $X$ and $Y$, $|X|=m$, $|Y|=n$. $H$ is a universal family of hash functions from $X$ to $Y$. Let $S\subsetneq X$ be a proper subset of $X$. Does there exist some "partial"...
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On the equivalence between two definitions of universal hashing
Let $H=\{h|h:X\to Y\}$, $|X|=n$, $|Y|=m$. $H$ is a universal hash family if
Def 1. For any $x_1,\ x_2\in X$, $x_1\neq x_2$, $\left|\left\{h\in H\middle| h(x_1)=h(x_2)\right\}\right|\leq |H|/m$. (or ...
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How difficult are lattice algorithms for low-dimensional lattices?
Most lattice problems, such as the shortest vector problem, the closest vector problem, shortest basis problem, etc, are NP-hard and thus conjectured to be worst-case exponential time in the rank of ...
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If the data that I input for locality sensitive hashing is sensitive, should its resulting hash also be considered sensitive?
Is it correct to assume that if the input that I hash is sensitive, that I should also consider the locality-sensitive hash generated for that input to be sensitive? I presume that, if an attacker has ...
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Asymmetric communication between two symmetric parties?
(sci-fi-esque question inspired by Counterpart).
A portal between our world (called $A$) and a parallel world that's exactly the same (called $B$) opens up. Bob sees himself through this portal.
$A$-...
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Reversible computing as a path to a useful PRNG or hash function?
There's a question I've long had about reversible computing: do non-trivial algorithms usually end up generating strongly pseudorandom data as an artifact of the computation?
The most straightforward ...
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Protocol Proposed by Arthur-Merlin, and Zero Knowledge
Why there is a need for Arthur Merlin protocol.
What are the cause and differences between arthur-merlin protocol and Zero knowledge protocol ?
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Is Miller-Rabin not a suitable algortihm for the RSA key generation or am I missing something?
I'm trying to recreate the RSA key generator, from what I understood you must create two prime numbers of 256 bytes long, p and q...
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Self referential hash function possible?
Is there a hashing function $f$ that for each input $x$ if $f(x) = y$, then $f(x \, || \, y) = y$? In other words, if we concatenate its output with the input, the result will not change.
Furthermore, ...
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Interactive ZKP of possession of a signed message
Suppose Alice has a verifiable (message, signature) pair from Cedric, who would not cooperate and routinely uses an algo (ecdsa, eddsa, rsa, or insert yours here) to sign messages.
Alice wants to ...
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Is this restatement of one-way functions accurate?
I realize this is sort of a trivial ask, but I want to make sure I understand OWFs and it's usually explained with some jargon that I don't find clarifying. So, I'd just like to know whether or not my ...
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Does a random phenomenon have a pre defined probability distribution? what does it mean for something to be random?
While studying Shannon's notion of perfect secrecy I came upon the idea that a bit is perfectly random if it happens to be 0 or 1 with an equal probability. What does this mean? Also, what can we say ...
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LWE with a low rank matrix
Consider the decision LWE setting, where we have to distinguish between $(A, As + e)$ and $(A, u)$, for a randomly chosen $m \times n$ matrix $A$, an $n \times 1$ secret vector $s$, an $m \times 1$ ...
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Reference for the formal definition of sigma protocol
I'm looking for a book that contains the formal definition of sigma protocol (something like: A sigma protocol for a relation $R$ and a challenge space $C$ is... that satisfies the properties of ...
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How can I prove the file on DVD is the original?
I have an old file written to a DVD-R several decades ago, and it turned out this file can potentially has some value as NFT (non-fungible token). The file was published online and have been copied ...
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Where does 2^32 come from with bitcoin?
Several months ago I was doing research into calculating mining revenue for several crypto currencies. When trying to calculate BTC revenue I found this value 1/2^32 which was described somewhere ...
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How do these Crypto terms relate to each other and what do they all mean?
Alright this is another day of my pursuit to learn about how crypto works. I have several terms that I have found linked together. I was trying to do research on how the Target Hash is determined and ...
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What happens in the event of a collision in a crypto hash function?
I was reading about hash functions in crypto and a website had mentioned that they were collision free, which obviously isn't possible if there are infinite input values that are mapped to outputs of ...
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How MAC (Mandatory Access Control) model prevents trojan horse attacks?
I've heard that the MAC Model prevents Trojans to charm files on the system.
How is it possible? Can somebody show any example that MAC model protects us against it?
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What is the use or how can we implement zero-knowledge proof system in Elections?
I recently heard about the concept of zero-knowledge proof. However, I still do not get how it is possible to make it a solution to some real-world problems. One thing I heard is that zero-knowledge ...
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Why is M^e mod N the ciphertext and not just M^e
I watched a video on why the RSA algorithm works and it said that $(M^e \bmod N)^d \mod N = M^{ed} \bmod N$ which makes sense if $M^e$ is smaller than $N$.
Would $M^e$ not be smaller than $N$, the ...
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If someone has an encrypted message and it's original plaintext, could he guess the private key if it's the one used to encrypt the message?
In digital signatures, the private key is used to encrypt a (hashed) message and the public key is used to decrypt it. This made me wonder since the receiver has the cipher text (digital signature) ...
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Product of polynomial with negligible function is negligible
I want to prove that for every positive polynomial $p(n)$ and any negligible function $negl(n)$ the product $negl(n)p(n)$ is also negligible.
This is what I tried so far:
$\forall n>n_0:negl(n)<...
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Examples of cryptographic methods using outside randomness
Most cryptographic protocols like pseudorandom number generators run only on "internal" information: that is you set a seed and the next state is a function of its previous state etc.. I am ...
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Is it possible to write a program that is able to recognize some source-code as being its own source code?
Is it possible to write a program that is able to recognize some source code as being its own source-code?
Biological organisms evolved the ability of kin-recognition, and later, self-recognition, ...
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Is the differential privacy definition with lower and upper bound equivalent to the definition with just an upper bound?
According to Wikipedia, given a randomized algorithm $\mathcal{A}$, two neighboring datasets $D_1, D_2$, a real number $\epsilon > 0$, $\mathcal{A}$ provides $\epsilon$-differential privacy, if
$$
\...
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Not CPA secure for CBC mode if some code are changed that is if we replaced a function $\pi(k,x)=k\oplus x$
Consider the CBC mode where the block cipher is replaced by a function $\pi$ where $\pi(k,x)=k\oplus x$. Show that the mode is not CPA secure.
I am not got how to proceed to solve this question. ...
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What algorithm is prefered to do a x b mod P with big numbers (256 bits)
I'm trying to implement multiple precision arithmetic operations modulo P, with P < 2^256.
More specifically, ...
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How are extremely large integers stored and implemented in programming languages?
We have data types like int and long etc. which can store just a few bytes of integers.
But when we are implementing ...
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Factor $n$ in RSA if we know $φ(n)$
If we know that $n = 1363$ and $φ(n) = 1288$, how can we factor $n$?
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Is it possible to have a zero knowledge proof with a P Prover?
In the literature, when reading about zero knowledge proofs, the prover (prover/verifier) is always given an unlimited computational power or just capacity to solve NP.
Is it necessary for the prover ...
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Zero knowledge proof - case of graph 3-coloring (not understanding the concept)
In zero knowledge, in the context of graph 3-coloring, I do not understand how the prover is actually showing that he solved the problem.
The context:
both know the graph (the prover and the verifier)...
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How to prove that existence of one-way functions implies P≠NP?
Wikipedia:
The existence of such one-way functions... would prove that the complexity classes P and NP are not equal.
How is this proved?
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Why do public key systems involve private keys?
I read up the definition of a public key cryptosystem. It mentions there is a public key and a private key. That's confusing. Why is it called a "public key" system if it involves a private ...
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What are the advantages of using PRNG over TRNG?
True random number generators use an unpredictable physical means to generate numbers, whereas pseudo-random numbers utilize mathematical formulas to produce a certain sequence of numbers that will ...
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How 'Avalanche Effect' got its name?
I wonder how or why Avalanche Effect got its name.
Avalanche Effect is a desirable property of cryptographic algorithms, wherein if an input is changed slightly (...
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NSA Recommended Cryptography Algorithms changes from a single paper
I know that the NSA has recommended cryptography algorithms, such as their A/B suite algorithms and their Commercial National Security Algorithms Suite. I also know that they change their ...
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Hardcore bit of a one way function
Let $b:\{0,1\}^*\mapsto \{0,1\}$, be a hardcore bit of a one way function $f$. I want to show that $\vert Pr_{x\in U_n}[b(x)=1]-Pr_{x\in U_n}[b(x)=0]\vert=n^{-\omega(1)}$. Intuitively, it looks ...
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Show that if the discrete log problem is $(T,1-\epsilon)$-hard, then it's $(O(\frac{T}{\frac{1}{\epsilon}log\frac{1}{\epsilon}}-nlogm),\epsilon)$-hard
Show that if the discrete log problem is $(T,1-\epsilon)$-hard, then it's $(O(\frac{T}{\frac{1}{\epsilon}log\frac{1}{\epsilon}}-nlogm),\epsilon)$-hard
Let $G$ be a cyclic group of size $m$, and let $g ...
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Strengthening a given attack on discrete log
I am trying to prove the following claim:
Let $(G,*)$ be a cyclic group of size $m$ with generator $g$. Assume
there exists some adversary $A'$ of size
$T'=\frac{\left(T-O\left(\log m\right)\right)}{...
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Time estimation for successful brute force attack
If I have a password =
"passwordPASSWORD"
and the time it takes to encrypt the password successfully is:
353259.545 nano seconds
is there a formula that can work out the time taken to ...
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Check if a linear function or an affine function can be a pseudo random function
Let $G = \{0, \cdots , p-1 \}$ be a field. Let $K = G^{m \times n}$ and $F:K \times G^n \to G^m$ be a family of functions.
For $A \in G^{m \times n}$ and $x \in G^n$ we have $F(A,x) = Ax$.
I need to ...
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If there is an algorithm $A$ that guesses the entire message, given an encryption, with probability of $0.2$, then it's not $(O(A) +O(n), 0.1)$-secure
Let $(E,D)$ be a cipher with message space $M = \{0,1\}^n$ and key space $K = \{0,1\}^n$.
Assume that there is an algorithm $A\colon \{0,1\}^n \to \{0,1\}^n$ of size $T$ that given an
encryption of a ...
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Connection between Pseudo random generators and hardness
For a boolean function $f:\{0,1\}^n\longrightarrow\{0,1\}$ $H_{avg}(f)$ is defined as the largest $S(n)$ s.t. for all circuit $C_n$ of size $S(n)$, $\Pr_{x\in U_n}[C_n(x)=f(x)]<1/2+1/S(n)$. Here $...
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