Questions tagged [group-theory]

Groups are an abstract algebraic concept based on a set and a group law (a binary function which closes the set).

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Diffie-Hellman insecure on addition modulo $n$

Assume that the group $G$ is the set $\mathbb{Z}_{n} = \{0,\ldots, n-1\}$ for a 1024 bit integer and $+$ is addition modulo $n$. Then why would Diffie-Hellman key exchange in this group be insecure?
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Discrete logarithm weak group

I'm looking for weak groups in discrete logarithm, that $x$ can be extracted from $Y$ in polynomial time where $Y \equiv g^x \pmod{p}$ . I thought one way is to produce a prime $p$ that $p-1$ is an ...
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Does pairings based cryptography inherently require a CRS/trusted setup?

In all algorithms I've seen that rely on pairings-based cryptography (some examples: snarks without PCPs, more snarks, sublinear ring signatures), a common reference string is required. Is this always ...
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How is a group element converted into a key?

I've only just started research on cryptography so I apologize if this is a basic question or I'm getting terms confused. I'm researching braid group cryptography and currently looking at the Anshel-...
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How to find the generator of an elliptic curve? [duplicate]

If the elliptic curve has prime order of points, then all of its points are generator. Is this true? If so, how can I find the optimized generator(which generates more number of points) among them?
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Why is only one generator stated in literature for elliptic curve group P-256?

I refer to elliptic curve groups over prime fields and their application in cryptography. If the order of a group is prime, it follows (am I wrong?) that: the group is cyclic and every element ...
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Hash “Preimage by product” resistance

Let H() be a hash function that achieves collision resistance as well as first and second preimage resistance. Let's equip the output set of H of a multiplicative group structure, more precisely a ...
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Given the finite cyclic, additive group (G, +), with |G| = n and generator = g, what are the computations and exchanged messages for Diffie-Hellman? What I tried myself: Alice chooses a private $a$ ...
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Is Triple-DES a group?

I know for a fact that DES is not a group, but are any of the Triple-Des versions a group? Why, or why not?
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How to compare the order of elements in cyclic groups?

In a cyclic group with randomly looking behavior like the one used in secp256k1, is there any known efficient algorithm to compare the order of two randomly given elements $P_1$ and $P_2$ and find out ...