Is there a notion of information theoretic one-way function?
This is not a formal but intuitive concept of one-wayness. The intuition is that if you have a combinatorial object that requires $n$ bits to describe. A one way operation introduces noise in random...
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Overview of relations between cryptographic primitives?
Is there a web page that gives a graphical (or, alternatively, a textual) overview of known implications and separations between cryptographic primitives?More specifically, I am looking for something...
View ArticleOWF from PRG and OWF
Let $f : \mathcal{U}_{2\lambda} \to \mathcal{U}_{2\lambda}$ be a OWF, and $G : \mathcal{U}_{\lambda} \to \mathcal{U}_{2\lambda}$ be a PRG with $\lambda$-bit stretch. Establish whether the following...
View ArticlePAN authenticatable irreversible tokenization algorithm
I need to implement algorithm to create authenticatable irreversible tokens from PAN, without using any secrets.Is it possible? Is there any standards for that from associations?I was thinking about...
View ArticleOne-way function with combination sets as output / image
One-way functions generally operate on bit strings, for the input and the output.Are there any examples of one-way functions that produce a combination set in output? Let's call this function $f$. The...
View ArticleProving that the length-preserving OWF does not have polynomially bounded cycle
Here a cycle is the smallest positive integer such that $f^i(x) = x$.Formally we want to prove that if $f$ is OWF then $\forall p(.)$ and sufficiently large $n$, $Exp(cyc_f(U_n))>p(n)$ where $n$ is...
View ArticleA random access machine with lots of random data on its tape is a stronger...
Suppose we have a random access machine with $(n+1)2^n$ random bits on its tape. This assumption is weaker than assuming the existence of a random oracle, but using this assumption we can construct a...
View ArticleIs $g(x_1||x_2) = f(x_1 \wedge x_2)$ a one way function assuming f is a one...
Intuitively I think not because assuming the bit string $x_1,x_2 \sim \{0,1\}^{n/2}$, $x_1 \wedge x_2$ is not uniformly random so if $g$ were still a one-way function then the fact that the definition...
View ArticleIs every pseudorandom generator a one way function?
$$G:\{0,1\}^n\rightarrow\{0,1\}^{n+1}$$If above function is a pseudorandom generator then is the same $G$ a one way function. I tried to prove this but failed a lot of time. Would be helpful if someone...
View ArticleGiven the existence of provably-hard-to-solve problems, why do we routinely...
Let $(X, Y, Z)$ be a set of binary strings of length $n$. Let random $X$ be the private key for encoding (or decoding) message random $Y$ as $Z$. Let the encryption algorithm $m$ be a matching...
View ArticleIs every pseudorandom generator a one-way function, even if the output length...
Intuitively, if we can invert a PRG, then we can easily distinguish it with random distribution by checking g(inverse(y)) = y. So every PRG is a OWF?Unlike the problem "Is every pseudorandom generator...
View ArticleA modification of the Blum-Micali construction
Consider the following modification of the Blum-Micalli construction (denoted by BM):$G_l(x) = f^l(x) || BM^l(x)$I am asked the following questions about it:Show it is a PRG of fixed stretch for every...
View ArticleIs sha3 a one-way funtion
If i store sensitive stuff (e.g passwords, salted passwords, Internet protacel adresss(so i know its not tamperd with), private keys(the keys are using a portion of the key on multiple disks in...
View ArticleExistence of PRGs satisfying the following weaker definition
Consider the following definition. Let $p(n) > n$ be a polynomial, and $G_n: \{0, 1\}^n \rightarrow \{0, 1\}^{p(n)}$ a PRG. Moreover, given $x \leftarrow \{0, 1\}^n$, we say $S$ is a length $n-1$...
View ArticleTechnical feasibility of a theoritical compression mechanism
Considering that quantum computers (in theory) can break\reverse some of one-way-hashes a lot faster than conventional-computers. Is it technically feasible in any theoritical (but realistic) senarion,...
View ArticleDeterministically secure PRG from deterministically secure OWF
Consider the construction of "A Pseudorandom Generator from any One-way Function" [HILL99] in Hastad et al.One way to proof pseudorandomness of this construction is by contradiction.That is, an assumed...
View ArticleDoes removing just last bit from output of one way function change its one...
If $g(x)$ if length preserving one way function, is there a scenario where $h(x) := g(x)_{1\ldots |x|−1}$ . I.e., $h$ returns all bits that g returns, except for the last bit., is not a one way...
View ArticleWorst-case one-way permutations under P different from NP
This is probably obvious, but I cannot find it anywhere, since all textbooks define OWFs for average-case hardness.Do we known if worst-case one-way permutations exist assuming $\mathbf{P} \neq...
View ArticleAre there hash algorithms with variable length output?
I understand that for example MD5 produces a 128 bit hash value from a given text of variable size. My question is if there is a hash-like algorithm that will produce a hash value where one can specify...
View ArticleOn the construction and notation of a certain OWF
I am studying a little bit about one-way functions from Dr Goyal's notes.He constructs the following OWF:Let $D=\Bbb Z_2^{n^3}$ and $R=\Bbb Z_2^{2 n}$. Given $x \in D$, $f$ interprets $x$ as a set $S$...
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