A finite field is a mathematical construct based on a set of axioms which are held to be true. A number of interesting and useful properties arise from finite fields that makes them particularly suitable for use in cryptography, notably in block ciphers. Questions concerning finite fields should use ...
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1answer
186 views
Do recent announcements about solving the DLP in $GF(2^{6120})$ apply to schemes proposed for cryptographic use?
A recent paper by Göloğlu, Granger, McGuire, and Zumbrägel: Solving a 6120-bit DLP on a Desktop Computer seems to "demonstrate a practical DLP break in the finite field of $2^{6120}$ elements, using ...
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votes
3answers
813 views
How robust is discrete logarithm in $GF(2^n)$?
"Normal" discrete logarithm based cryptosystems (DSA, Diffie-Hellman, ElGamal) work in the finite field of integers modulo a big prime p. However, there exist other finite fields out there, in ...
7
votes
1answer
221 views
Security of pairing-based cryptography over binary fields regarding new attacks
In the last week, the discrete logarithm problem was broken for the binary fields $\mathbb{F}_{2^{(14 \times 127)}}$ and $\mathbb{F}_{2^{(27 \times 73)}}$.
Pairing-based cryptography using binary ...
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votes
5answers
865 views
Galois fields in cryptography
I don't really understand Galois fields, but I've noticed they're used a lot in crypto. I tried to read into them, but quickly got lost in the mess of heiroglyphs and alien terms. I understand they're ...
5
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1answer
299 views
Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme
Shamir's original paper (PDF, 197kb) describing a threshold secret sharing scheme states:
To make this claim more precise, we use modular arithmetic instead of
real arithmetic. The set of ...
