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Can someone explain why is that the case? Cryptosystems based on finite sets have two very nice properties: There is an upper bound to the size o...

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Mostly, I would say that finite groups get used in crypto because they're a good way to describe things that naturally appear in many crypto schemes.

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"Finite field cryptography" is fancy language for group-based cryptography done over the integers modulo a prime (instantiating a field) to disting...

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The term "finite field cryptography" exists to distinguish from group-based cryptography. It is true that every field contains two groups, but a gr...

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What is the difference between group-based and finite field cryptography?

The term "finite field cryptography" exists to distinguish from group-based cryptography. It is true that every field contains two groups, but a group is not necessarily part of a field.

What is a a group in cryptography?

A group is a very general algebraic object and most cryptographic schemes use groups in some way. In particular Diffie–Hellman key exchange uses finite cyclic groups.

How do you know if a group is finite?

If a group has a finite number of elements, it is referred to as a finite group, and the order of the group is equal to the number of elements in the group. Otherwise, the group is an infinite group. A group is said to be abelian if it satisfies the following additional condition:

What is the difference between elliptic curve and finite field cryptography?

2 Answers 2. "Finite field cryptography" is fancy language for group-based cryptography done over the integers modulo a prime (instantiating a field) to distinguish this more "classic" approach from the new fancier elliptic curve cryptography.

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