# Questions tagged [hardness-assumptions]

Mathematical problems that are thought to be difficult to solve for all cases in polynomial time

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### Assuming the difference between success probabilities to be positive

Context: I am currently studying Theorem 3.1 in the paper Number-Theoretic Constructions of Efficient Pseudo-Random Functions by Naor and Reingold. The theorem basically states the randomized self-...
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### Is the ring learning with errors problem still hard if the errors are drawn from some subspace?

Let $R=\mathbb{Z}_p[x]/x^n+1$ be the ring used in normal RLWE, which is linear space over $\mathbb{Z}_p$ with dimension of $n$, let $S$ be a linear subspace of $R$ which described by linear ...
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### Proof by reduction definition in “Serious Cryptography”: Cipher reduced to hardness problem or other way around?

In Serious Cryptography by Jean-Philippe Aumasson on p. 46, paragraph "Provable Security", it says: Provable security is about proving that breaking your crypto scheme is at least as hard as ...
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### Assumptions underlying the soundness of STARKs

STARKs have recently received quite a lot of attention due to their small proof size and supposedly simple assumptions. The paper introduction itself seems to mainly state that their construction is ...
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### Efficient way of knowing large factors of $\phi(n)$ given small prime factors and $n$

Knowing large prime factor$(r > n^{1/4})$ of $\phi(n)$ can easily factorize n and hence learn $\phi(n)$. If we have knowledge on all small prime factors $(2< r_i << n^{1/4})$ of $\phi(n)$...
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### Size of $q$ in reductions from lattice problems to R-SIS

The Short integer solution problem is parameterized by four values: $n$, the dimension of the vectors that must be added $m$, the number of samples (dimension of the solution) $\beta$, upper-bound ...
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### KEA assumption details

In order to understand the construction of a zK-SNARK, I have recently been trying to understand the KEA1 assumption in The Knowledge-of-Exponent Assumptions and 3-Round Zero-Knowledge Protocols by ...
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### What is the hardness in Decisional Linear Assumption (DLIN)?

I had understood what does the DLIN assumption means and here is a related question. But I fail to understand the 'real hardness' in this problem. I would be grateful if someone can help me to ...
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### Define a Decryption algorithm on a given group-based Cramer Shoup lite scheme

I am currently working on public key encryption schemes and I want some help to figure out how decryption algorithms work. Suppose we have a public key $pk = (G,p,g,e)$ with $e \in Z^*_p$ . (where $G$ ...
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### If they exist a relation between decisional Diffie-Hellman assumption and composite decisional residuosity assumption

From the cryptographic hardness assumptions, we have DDH and CDR assumptions. It is known that the composite decisional residuosity assumption is related to a factoring problem, while the DDH is ...
It results that I have come with a mathematical approach to solve the CSP (Conjugacy Search Problem) where the platform group $G$ is either a permutation group or a Matrix Group. From my part I ...