FAQ?
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...
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.
"Finite field cryptography" is fancy language for groupbased cryptography done over the integers modulo a prime (instantiating a field) to disting...
The term "finite field cryptography" exists to distinguish from groupbased cryptography. It is true that every field contains two groups, but a gr...
What is the difference between groupbased and finite field cryptography?
The term "finite field cryptography" exists to distinguish from groupbased 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 groupbased 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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The ethical exploiter congratulated Arbitrium for the 400 ETH payout but asserted that a find of this kind should be entitled to the maximum bounty of about 1,500 ETH, or $2 million.
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Hedge fund cofounder CK Cheng told Cointelegraph that institutional investors will enter the market as long as the regulations provide them with a very clear road to cryptocurrency.
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