https://github.com/georgiifirsov/galois-lib

Finite field arithmetic library written for my research in cryptography
https://github.com/georgiifirsov/galois-lib

arithmetic cryptography finite-field-arithmetic finite-field-arithmetics finite-fields galois-field mathematics symmetric-cryptography

Last synced: about 12 hours ago
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Finite field arithmetic library written for my research in cryptography

• Host: GitHub
• URL: https://github.com/georgiifirsov/galois-lib
• Owner: GeorgiiFirsov
• License: gpl-3.0
• Created: 2023-07-02T17:44:34.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2023-10-12T21:07:40.000Z (about 1 year ago)
• Last Synced: 2024-08-10T04:23:16.482Z (3 months ago)
• Topics: arithmetic, cryptography, finite-field-arithmetic, finite-field-arithmetics, finite-fields, galois-field, mathematics, symmetric-cryptography
• Language: C
• Homepage: https://georgyfirsov.github.io/galois-lib/
• Size: 281 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# galois-lib

This library implements some arithmetic operations in finite fields.

## Implemented operations

`galois-lib` implements not so many algorithms, because it is designed to be a helper library 

for cryptographic libraries. Hence it contains only few necessary operations.

### Multiplication in $GF(2 ^ {8})$

Multiplication in finite field of size $2 ^ {8}$ is implemented using precomputed

logarithm and exponents tables. It works according to the following obvious formula:

$$

a \cdot b = \exp \left( \log a + \log b \right),

$$

where all operations are assumed to be in the finite field.

### multiplication in $GF(2 ^ {128})$

Multiplication in $GF(2 ^ {128})$ is implemented using some kind of Karatsuba algorithm

with help of `pclmulqdq` instruction. More information here: [Intel® Carry-Less Multiplication 

Instruction and its Usage for Computing the GCM Mode][1].

[1]: https://www.intel.com/content/dam/develop/external/us/en/documents/clmul-wp-rev-2-02-2014-04-20.pdf