# Questions tagged [hardness-assumptions]

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

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### Discrete Logarithm problem with inverse

Let $\mathbb G$ be a cyclic group of order $q$. The Discrete Logarithm Problem (DLP) is, given $g, g^x \in \mathbb G$, to compute $x \in \mathbb Z_q$. I'm interested to know if there is a known ...
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### Extracting $x$ given $g^x, g^{x + y}, y$

Given a cyclic group $G$ of prime order $q$ with generator $g$ in which computing the discrete logarithm is hard. Is it (still) hard to find the discrete logarithm $dlog_g(g^x) = x$ if the ...
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### From the product of two permutation matrices raised to the same power, is it easy to find the power?

Let $A$ and $B$ be two public permutation matrices. If $r$ is a secret power of large number, can we easily find $r$ from $A^rB^r$?
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### Security of a signature scheme based on both factoring and discrete logarithms

I have seen this paper: A New Signature Scheme Based on Multiple Hard Number Theoretic Problems by Ismail and Tahat: In this paper, we propose a new signature scheme based on two hard number ...
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### Proving impossibility for a stronger primitive

I have a primitive $A$ which is impossible to prove under some hardness assumption in a black-box way. Now, if another primitive $B$ is stronger than $A$ - in other words $B$ implies $A$ - will it ...
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### Difficulty of generating a string “The (md5|sha1) hash of this string is (x)” that hashes to (x) vs. regular hash collision between files?

I know that collisions in md5 and sha1 have been demonstrated in particular pairs of files (by incrementing some none viewable portion of a PDF, etc). Would generating the above string be ...
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### Naor Pinkas OT - senders security; reduction to DDH

This question concerns the security of the sender in the Naor Pinkas OT. The protocol can be found here. We can reduce the security to the DDH assumption. How exactly is this done? Can someone ...
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### Comparing stronger vs. weaker assumptions

If I have to argue that an assumption A is stronger than B, should I argue this way:- An adversary breaking the security of A does not translate to breaking the security of B. But, if an adversary ...
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### Is DL difficult under the group of Unimodular matrices?

Is discrete logarithm assumed to be computationally hard in a non-abelian group as the subgroup of the general linear group under matrix multiplication formed by the unimodular matrices? The two ...
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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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