Table 2 Comparison of different elliptic curves.

From: Enhanced image hash using cellular automata with sponge construction and elliptic curve cryptography for secure image transaction

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