# Questions tagged [hardness-assumptions]

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

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### Is the following Inverse Computational co-Diffie-Hellman problem hard?

Let $\langle g \rangle \stackrel{\Delta}{=} \mathbb{G}$ and $\langle h \rangle \stackrel{\Delta}{=} \mathbb{H}$ be groups of prime order $p$. Given $( p, g, g^\delta, g^{\delta^{-1}}, h, h^\delta )$, ...
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### Minimal Assumptions in Cryptography

When do we call an assumption to be minimal assumption? What's the difference if we say just using assumption X the protocol Y is constructed instead of using minimal assumption X the protocol Y is ...
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### What are security reductions of symmetric-key algorithms?

I was reading Wikipedia page of post-quantum cryptography. It says that it is desirable for cryptographic algorithms to be reducible to some particular mathematical problem, that is intractability of ...
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### Solve DLOG using a probabilistic algorithm for DLOG lsb

Following the question Can I know from a Bitcoin public key if the private key is odd or even? The answer there gives a simple algorithm for solving the Discrete Logarithm Problem when given an oracle ...
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### Would being able of factoring integers efficiently have some consequences over Elliptic Curve Cryptography?

Let's assume you can factor integers in a very efficient manner. Would that endanger the security of e.g. elliptic curve cryptography, or is there no link between the two ? You can often read that ...
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### DDH to DLIN reduction

I read multiple times that it should be feasible to show a reductions from Decisional Diffie Hellmann. Could you give examples?
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### Developments in ABE using Pairings

What are the recent developments in Attribute-Based Encryption (ABE) using Pairings assumptions? Is pairings the most viable assumption while designing ABE. What other assumptions are used for ABE ...
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