https://github.com/dantesbytes/finite-fields
bitcoin programming with python
https://github.com/dantesbytes/finite-fields
Last synced: over 1 year ago
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bitcoin programming with python
- Host: GitHub
- URL: https://github.com/dantesbytes/finite-fields
- Owner: dantesbytes
- Created: 2024-02-28T09:17:45.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-02-28T09:24:43.000Z (over 2 years ago)
- Last Synced: 2025-01-16T15:16:47.782Z (over 1 year ago)
- Language: Python
- Size: 1000 Bytes
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
## bitcoin programmingfinite fields and elliptic curves
The concept of finite fields and elliptic curves holds significant importance in various fields, particularly cryptography, where they form the foundation of modern cryptographic algorithms. Finite fields, also known as Galois fields, consist of a finite set of elements with defined addition and multiplication operations. These operations are performed modulo a prime number or a power of a prime. Meanwhile, elliptic curves, defined by equations of the form \( y^2 = x^3 + ax + b \), exhibit properties that make them ideal for cryptographic applications. They provide a group structure that allows for efficient scalar multiplication operations, which are fundamental in elliptic curve cryptography (ECC). ECC relies on the difficulty of solving the elliptic curve discrete logarithm problem (ECDLP), contributing to shorter key lengths, faster computations, and enhanced security compared to other cryptographic systems. Overall, finite fields and elliptic curves play a crucial role in ensuring the security and efficiency of modern cryptographic protocols.