A pseudo-random function is an efficiently-computable function which emulates a random oracle.

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How to prove that a function F isn't a pseudo random function

Let $F$ be a length-preserving pseudorandom function. For the following constructions of a keyed function $F' : \{0, 1\}^n \times \{0, 1\}^{n−1} \to \{0, 1\}^{2n}$, state whether $F'$ is a ...
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Proving the existence of a pseudorandom function

I've been reading the Introduction to Modern Cryptography book by Katz and Lindell as part of my own learning and have come across this exercise which I am not sure how to approach. The exercise is: (...
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Is F' a pseudorandom function when F is composed with G, a pseudorandom generator?

If $F$ is a pseudorandom function, is $F'$ also a pseudorandom function in the following: $$ F'_k(x)=F_k(G(x)) \space \space \text, $$ where $G$ is $a$ pseudorandom generator? Also, does the other ...
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Pollard's Rho - Restricting the random function to the exponents

Pollard's Rho is usually constructed using a function $f:G \rightarrow G$ which behaves 'random enough' in order to detect a collision with Floyd's cycle detection trick. It is easy enough to observe, ...
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What might be assumed about a PRF if the key has been chosen?

The defining feature of a PRF $f:\{0,1\}^k\times\{0,1\}^s\mapsto\{0,1\}^*$ is that, if the first parameter is selected at random, it should be indistinguishable from a function $g:\{0,1\}^s\mapsto\{0,...
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Pseudorandom Functions with different input and output lengths

I am working on a problem found in my Cryptography textbook that goes as follows: Let F be a pseudorandom function such that for $k \in \{0,1\}^n$, function $F_k$ maps $l_{in}(n)$-inputs to $l_{...
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Pseudorandom Function Proof

Given a set of pseudorandom functions $F=\{f_s^i\}_i$ for each $s\leftarrow\{0,1\}^n$ generated at random; moreover each $f_s^i$ uses a specific PRG $G^i:\{0,1\}^n\to\{0,1\}^{2n}$, where: $G^i(s)=...
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Special random distribution algorithm

I am implementing ring signatures as a part of an authorization system. Since the number of users could get high enough to make computation on end-user devices infeasible, I am thinking of "...
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Protocol/algorithms based on a variable-length input PRF

Are the proofs based on a PRF assumption still valid when using a variable-length input PRF ? The answer might be obvious, but I have a doubt.
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Simple application of verifiable random function?

I have been reading a little bit about verifiable random functions (e.g.). In the literature, these are described as "pseudo-random functions that provide a non-interactively verifiable proof for the ...
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Is $E_{k}(x) = F_{k}(x) \oplus F_{k}( \bar x)$ PRF?

$E_{k}(x) = F_{k}(x) \oplus F_{k}( \bar x)$ and F is PRF which maps $\left \{0,1 \right \}^n \times \left \{0,1 \right \}^n $ to $\left \{0,1 \right \}^n$. Let two messages $m_{0} = 0^l $ and $m_{1} ...
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Implementing a pseudo random function in practice

Can anyone point me to a C++ crypto library with an implementation of a pseudo random function (PRF)? I don't have much background in crypto theory, but I am in the middle of a graduate course ...
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TLS 1.2 PRF Cipher Suite Specification

I am upgrading our assembler SSL/TLS implementation to support TLS 1.2 and am reviewing RFC5246 specification for TLS 1.2. It states that the PRF is now part of the cipher suite specification but ...
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NIST SP800-108 KDF modes comparison

According to NIST SP800-108, there are three modes that can build KDF from PRF: counter mode, feedback mode and double-pipeline iteration mode. Assume that the same PRF and input distribution are used,...
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Proof that this is not a secure pseudorandom function

$p$ is a large prime number. Consider the following function $F:\mathbb Z^*_p \times \mathbb D\rightarrow\mathbb Z^*_p$ where $\mathbb D=2,....,p-1$. $F_k(x)=x^k \bmod p$ Proof that it's not ...
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Making PRFs out of PRGs

Is it possible that we take a $PRG$ $G(k)$ of stretch $n\cdot2^n$, and read its output as the table of a $PRF$ $F(K)$ with input and output size of $n$? Intuitively it sounds possible however I read ...
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Existence of a random function under constraints

Let $F_1$ and $F_2$ be two random functions taking as input $N$ bits and returning $N$ bits. Let $C_1$ and $C_2$ two constants of $N$ bits. Is there a random function $P$ taking as input $2N$ bits ...