Questions tagged [distinguisher]

A distinguisher describes an adversary's advantage. In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm.

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Noise flooding with Renyi divergence

According to this question, I found papers that deal with noise flooding with Renyi divergence. However, the answer is still unclear to me on how to use Renyi divergence on the noise flooding ...
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An unconditional proof of a PRP by restricting adversary run time

I am a Ph.D. student studying CS theory, I made this account for this question. Recently, I seem to have obtained a proof of existence of a PRP (which is unconditional in the sense that it does not ...
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How small is the negligible advantage for DDH?

The well known Decisional Diffie Hellman assumption (DDH) assert that for any $n = \log q$ and generator $g$ of $\mathbb{Z}_q$, for uniformly i.i.d $A, B, C \sim U(\mathbb{Z}_q)$, the following are ...
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PRGs from OW functions

Given a OW function $f:\{0,1\}^n\to\{0,1\}^n$ with hardcore predicate $h(x)$, you can build a PRG $G$ by setting $$G(s):=f(s)\Vert h(s), \quad s\leftarrow\{0,1\}^n.$$ The expansion condition for $G$ ...
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Showing that $F'(k, x) := F(F(k, 0^{n}), x)$ is a PRF [duplicate]

I wanted to do some practice on security reduction proofs, and I am stumped on this one from the Boneh-Shoup book. If $F(k, x)$ is a secure PRF, then show that $F'(k, x) := F(F(k, 0^{n}), x)$ is a ...
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Distinguishers and next bit predictors without the uniform distribution

Consider a probability distribution $D$ over $n$ bit strings. Denote $U$ to be the uniform distribution over $n$ bit strings and $U_{n}$ to be the uniform distribution over integers $\{1, 2, \ldots, n\...
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How many encryptions are needed before OpenPGP key privacy is violated?

According to an excellent answer describing the pitfalls of key privacy in OpenPGP: Theoretically, an all-zero key ID can be used as a way to discourage traffic analysis, but this is not a complete ...
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In SKE, can we assume without loss that the ciphers of a fixed plaintext distribute identically?

Let $(KG,D,E)$ be a symmetric encryption scheme. Fix $sk\gets KG(\lambda)$ and an arbitrary plaintext $m$. Generally speaking, $E_{sk}$ is not deterministic, so that $E_{sk}(m)$ is a random variable, ...
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Why the differential cryptanalysis complexity is linear with inverse of the probability while linear cryptanalysis is quadratic with the bias inverse?

I am trying to understand the analysis of the complexity of Differential Cryptanalysis versus the complexity of linear cryptanalysis. In differential cryptanalysis the number of required texts is $\...
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Given an input x, can a distinguisher D output 1/2?

Consider a PPT distinguisher $D$. Now if I give it an input (a bit string) $x$, it outputs 1 if $x$ ends with $1$ and $0$ otherwise. We know such a distinguisher exists and is often given as an ...
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why do we take computational distinguishability over ensembles

In the Cornell lecture notes, computational indistinguishability is defined as Definition 69.4 (Computational Indistinguishability). Let $\{X_n\}_n$ and $\{Y_n\}_n$ be ensembles where $X_n$,$Y_n$ are ...
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Example of not computationally indistinguishable

All the examples that I see for proving that two distributions are not computationally indistinguishable involve a pattern: choose a Distinguisher $D(\cdot)$ such that $D(x)$ is $1$ if $x$ satisfies ...
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How does a hybrid argument work relating to PRG's?

How does a hybrid argument work relating to PRG's? I am working on a homework assignment where the problems say to use a hybrid argument to prove/disprove that something is a secure PRG, and I can't ...
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Proof of (in)distinguishability based on DDH/CDH/DL

I am wondering whether or not it is known that the following problem is computationally infeasible while working in a group for which the DDH (or CDH or DL) assumption holds (as usual, g is a group ...
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Simulating a joint distribution of an *almost* deterministic function

The following is in the context of secure MPC. Suppose that there is a functionality $f(x,y)$ which outputs 'answer' with probability $1-\textrm{negl}(n)$ for some security parameter $n$, and 'other ...
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I want to know the hardness of computing a or b given $g^{b^{-1}}$ and ab in cyclic groups with large prime order

$G$ is a multiplicative cyclic group of a large prime order $p$ and $g$ is a generator of $G$ Theorem 1: Given $g^{b^{-1}}$ and $ab$, it's hard to compute $a$ or $b$, where $a$ and $b$ are randomly ...
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Distinguishing between a Polynomial and a Laurent Polynomial

Let $f(x) \in \mathbb{Z}_p[x]$ (for a prime $p \gg d$) be a polynomial of degree $d$, and let $g(x)$ be a Laurent polynomial with the same degree and only the first negative exponent term ($g(x) = \...
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18 votes
2 answers
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A website that identifies an RNG from its output

This happened during a discussion of RNG entropy, and the difficulty of verifying the level of entropy in a long sequence of bits (e.g. a private key.) A colleague of mine told me about a website ...
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Computationally indistinguishably vs Perfect Indistinguishably [duplicate]

I know that perfect security means absolutely no information about the plaintext is leaked to the adversary while computational secrecy is okay with a tiny amount of leak. But, what is the difference ...
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Proving a function is or is not a pseudorandom function F_k(x) = F_k(x)||0

I have 4 functions to analyze. I need to determine if they are or are not pseudorandom and give a proof/counterexample. I'm having trouble just determining if they are - let alone proving or giving ...
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Is there only one formula for the statistical difference between a pair of distribution ensembles?

Statistical closeness implies computational indistinguishability was recently posed. It revolves around a numeric value $\Delta(n)$ of the statistical difference between a pair of distribution ...
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Statistical closeness implies computational indistinguishability

This is so trivial that authors usually don't bother to give an explicit proof. But for me there is some vagueness. We say that two ensembles $X_n$ and $Y_n$ are statistically close, if $$ \Delta(n) ...
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CCA security of this scheme

Let $k$ be uniformly sampled from $\{0,1\}^\lambda$, $F$ be a secure PRP with block length $\lambda$ and let $Enc(k, m)$ be such that it returns $c = (F(k,r), r \oplus F(k,m))$ with $r$ uniformly ...
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Does the bias in RC4 drop asymptotically further in the keystream?

It's well-known that the RC4 keystream has significant biases that become less prominent later in the keystream. The most severe bias is in the second byte, which has a 128-1 bias towards zero. Other ...
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Probability distribution of bitwise-&

Does the bitwise-& between two uniformly distributed input produce an output that seems uniformly distributed ? To be more specific, assume to take x and y uniformly from {0,1}^n and compute z = x ...
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How to define the statistical distance between two probabilistic algorithms?

Let $$ \begin{aligned} F_{i} \colon \{\, 0,1 \,\}^* \times \{\, 0,1 \,\}^* &\to \{\, 0,1 \,\}^* \\ (k, x) &\mapsto y \\ \end{aligned} $$ for $i \in \{\, 1,2 \,\}$. As we known, for every ...
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4 votes
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Hashing a counter to prevent distinguishers in CTR mode

Because a block cipher is a PRP and thus bijective, the fact that the input in CTR mode never repeats means that each block of keystream will be unique. This creates a distinguisher from random data ...
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Is there distinguisher?

Are these distributions computationally indistinguishable ? $f:\{0,1\}^n \to \{0,1\}^n $ $\{X_n\}_{n\in N}$ : uniform distribution for function which $f(0^n)=0^n$ and for other function probability ...
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How to define the statistical distance between two functions?

The statistical difference between two families of distributions of random variables: Let $\mathrm{\mathbf{X}} = \{ X_{l} \}_{l}$ and $\mathrm{\mathbf{Y}} = \{ Y_{l} \}_{l}$ be two families of ...
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Is this a PRP? How can I create a distinguisher to show it isn't?

Consider the keyed permutation $F_k : \{0,1\}^2 \to \{0,1\}^2$ with two-bit keys defined as $F_k(x) = k\oplus x$. Is this F a PRP? How can I create a distinguisher D and calculate the difference ...
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19 votes
1 answer
2k views

Distinguishing x25519 public keys from random?

I recently read a piece of protocol that avoided sending ephemeral x25519 keys in the clear as an effort to foil deep-packet inspection. I understand that x25519 public keys are effectively 255 bits, ...
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An XTS penguin?

I stumbled across a VPN website when looking up information about XTS, and came across their own explanation of different block modes (basically the ECB penguin, but with their company logo instead). ...
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Are there any references on using neural networks to distinguish CSPRNGs?

No feasible algorithm should be able to distinguish the outputs of two CSPRNGs. Are there any research papers that present results of actually testing this? In particular, I'm interested in ...
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Does a distinguisher for an PRF based on a hash make the hash function insecure?

I recently found a distinguisher for the PRF $f(s, i) = H(s || i)$ where $s$ is the seed and $i$ is a counter and $H$ is a cryptographic hash function, which is able to distinguish $f(s, i)$ from true ...
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Definition of a distinguisher

In Introduction to Modern Cryptography by Katz and Lindell, p. 70, they define a pseudorandom generator by: Let $l(\cdot)$ be a polynomial and let $G$ be a deterministic poly-time alg. s.t. for ...
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Difficulty of finding partially matching ciphertexts for a given plaintext when encrypted with two different keys

I'm trying to find a simple, practical proof-of-work scheme based purely on encryption (due to wide availability of optimized, hardware accelerated AES execution on most platforms, including modern ...
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2 votes
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Understanding hybrid arguments in detail

Assume we are given three distributions $H_{1}$, $H_{2}$ and $H_{3}$ and the following security games: $Game_{1}$: Distinguish between $H_{1}$ and $H_{3}$. $Game_{2}$: Distinguish between $H_{1}$ ...
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2 votes
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Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG?

If $F$ a PRF, and we construct $G$ using $F$ in the following way: $$G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$$ where $|s|= n$. Is $G$ then a PRG? If so how can I prove this? If not how can $G(s)$ ...
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Computationaly efficient distinguisher for a PRP generator

Let $n$ be an integer (the motivating context had $n\approx2^{27}$). All other lowercase variables are non-negative integers less than $n$ (elements of $\mathbb Z_n$). All uppercase variables are ...
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3 votes
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Are two outputs of a PRF computationally indistinguishable when the keys are somehow related?

This question is related to my previous question “Are two outputs of a PRF computationally indistinguishable when using two different keys??”, but in this question the keys are related. Assume $c_i$ ...
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2 votes
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Are two outputs of a PRF computationally indistinguishable when using two different keys?

Assume we have a pseudorandom function $f(\cdot)$ that maps an input to $\mathbb{F}_p$ where $p$ is a large prime number. Assume $r_1$ and $r_2$ output of the pseudorandom function using two ...
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1 vote
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proving indistinguishability of joint distribution using hybrid argument

Using Hybrid Argument, I want to prove following equivalence: $$\{X,Y,Z\}\equiv \{X',Y',Z'\}$$ by proving following equivalences: $\{X,Y,Z\}\equiv \{X,Y,Z'\}$(1) $\{X,Y,Z'\}\equiv \{X,Y',Z'\}$(2) $\...
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3 answers
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Can an adversary distinguish a private key from a pseudo-random string of the same length?

Apologies if this is a dumb question but allow me to describe the dilemma I have: Suppose that I am protecting a private key on a device using a password & PBKDF2. The obvious attack would be an ...
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6 votes
0 answers
682 views

Is this PRG secure?

$G$ is a secure PRG in range $\{0,1\}^n\rightarrow\{0,1\}^{n+1}$. Let us define $G'(S)=G(S\oplus G(S)_{1,...,n})$, s.t. $G(S)_{1,...,n}$ is the first n bits of $G(S)$. Is $G'(S)$ a secure PRG? ...
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3 votes
2 answers
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Is this simple PRNG secure?

$G$ is a PRNG used in a stream cipher and defined in the following way: G receives $s_0$ as an input, which is a random string drawn from a uniform distribution. The output of step $i$ is $s_i = (s_{...
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A confusion on the proof of Yao's theorem (Yao 82)

I'm reading the proof of Yao's theorem on Boaz Barak's lecture, the main part of the proof is the following claim: My question is: How can we say "without loss of generality" here? Since $H^i$ ...
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Does concatenation of two pair computational indistinguishable distributions still indistinguishable?

Let $X,X',Y,Y'$ be some distribution ensembles such that $X\sim X'$ and $Y\sim Y'$, where $\sim$ means computational indistinguishable. Define $(X,Y)$ be the distribution ensemble over $\{0,1\}^{2n}$ ...
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1 answer
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Distinguishing two sets of pseudorandom values when their keys differ by one

Suppose we use a pseudorandom function $PRF$ and a random key $k$ to generate a set of pseudorandom values: $\forall i, 1\leq i \leq n: w_i=PRF(k,i)$ Now, consider instead of picking a fresh key, ...
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2 votes
2 answers
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Understanding the distinguisher for a PRG

Given the following definition of a psuedorandom generator, I'm having trouble understanding what exactly the "distinguisher" D is outputting, and when?
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1 vote
1 answer
256 views

PRF that can be distinguished after $k$ queries?

In adaptive attacks, if we design poorly, adversary can modify his queries and break the given pseudo random function (that is being able to distinguish it from uniform randomness). Is there a poor ...
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