Table 2 Comparison of different elliptic curves.
Feature | secp256k1 | secp26r1(P-256) | curve25519 | ed448 |
---|---|---|---|---|
Mathematical structure | Koblitz curve: \(y^2=x^3+7\) | Weierstrass curve: \(y^2=x^3-3x+b\) | Montgomery curve: \(y^2=x^3+ax^2 +x\) | Edwards curve: \(y^2+x^2=1+dx^2y^2\) |
Computational overhead | Low | Moderate | Low | Moderate |
Efficiency in scalar multiplication | High | Moderate | High | High |
Security level | 128-bit(256-bit field size) | 128-bit (256-bit field size) | 128-bit (256-bit field size) | 224-bit (448-bit field size) |
Resistance to side channel attacks | Moderate | High | Very high | Very high |
Suitable for lightweight applications | High | Moderate | High | Moderate |
Standardization | Broadly used in cryptography and blockchain | NIST approved | Good for modern encryption protocols | IETF standard |
Real world applications | Cryptographic protocols and blockchain | Cryptography, secure communications | Encryption key exchange | Secure messaging, cryptographic signatures |
Integration with sponge function and CA | Highly compatible due to simplicity | Computationally higher | Compatible | Compatible |