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Performance Benchmarks

This page presents performance benchmarks for ECUtils across different configurations and elliptic curves. These benchmarks help you understand the trade-offs between different coordinate systems and caching strategies.

Test Environment

  • Python Version: 3.13
  • Platform: Linux
  • Methodology: Each operation was measured using timeit with multiple iterations to ensure statistical significance.

Configuration Options

ECUtils supports two main performance optimization options:

  1. Coordinate System:
  2. Jacobian (default): Uses projective coordinates to avoid expensive modular inversions during intermediate calculations.

  3. Affine: Traditional coordinate system with modular inversion at each step.

  4. LRU Cache:

  5. Enabled (default): Caches results of point operations, dramatically improving performance for repeated operations.
  6. Disabled: No caching, useful for memory-constrained environments.

Benchmark Results

This is the default and fastest configuration for most use cases.

Curve Point Addition (us) Point Doubling (us) Scalar Multiplication (ms) Koblitz Encoding (ms) Signature Generation (ms) Signature Verification (ms) Diffie-Hellman (ms) Massey-Omura (ms)
secp192k1 3.64 2.18 0.01 0.02 0.01 0.03 0.01 0.01
secp192r1 3.60 2.20 0.02 0.01 0.01 0.03 0.01 0.02
secp224k1 3.39 2.26 0.02 N/A 0.02 0.04 0.02 N/A
secp224r1 3.34 2.38 0.02 N/A 0.02 0.04 0.02 N/A
secp256k1 3.52 2.32 0.02 0.02 0.02 0.04 0.02 0.02
secp256r1 3.65 2.29 0.02 0.03 0.02 0.04 0.02 0.02
secp384r1 3.51 2.28 0.05 0.06 0.05 0.09 0.05 0.05
secp521r1 4.04 2.52 0.09 0.20 0.09 0.18 0.09 0.09

Jacobian Coordinates without LRU Cache

Curve Point Addition (us) Point Doubling (us) Scalar Multiplication (ms) Koblitz Encoding (ms) Signature Generation (ms) Signature Verification (ms) Diffie-Hellman (ms) Massey-Omura (ms)
secp192k1 139.88 96.80 9.89 1.57 9.73 29.10 0.99 9.96
secp192r1 151.30 95.38 10.25 1.01 10.26 30.69 1.02 10.33
secp224k1 168.39 106.10 12.34 N/A 12.55 38.15 1.25 N/A
secp224r1 165.98 120.51 13.42 N/A 13.20 40.23 1.40 N/A
secp256k1 189.12 135.68 15.79 1.81 16.34 47.26 1.57 15.61
secp256r1 196.16 140.40 17.35 2.29 17.51 53.48 1.74 17.39
secp384r1 312.98 249.14 39.42 6.29 39.34 119.26 4.02 39.66
secp521r1 465.60 355.00 79.38 19.38 80.78 240.85 7.95 79.34

Affine Coordinates with LRU Cache

Curve Point Addition (us) Point Doubling (us) Scalar Multiplication (ms) Koblitz Encoding (ms) Signature Generation (ms) Signature Verification (ms) Diffie-Hellman (ms) Massey-Omura (ms)
secp192k1 3.69 2.18 0.04 0.02 0.04 0.06 0.03 0.03
secp192r1 3.57 2.21 0.04 0.01 0.04 0.07 0.04 0.04
secp224k1 3.47 2.40 0.05 N/A 0.05 0.08 0.04 N/A
secp224r1 3.29 2.20 0.05 N/A 0.05 0.08 0.05 N/A
secp256k1 3.44 2.26 0.07 0.02 0.07 0.12 0.06 0.07
secp256r1 3.65 2.32 0.07 0.03 0.07 0.11 0.06 0.07
secp384r1 3.55 2.32 0.15 0.07 0.15 0.26 0.15 0.16
secp521r1 3.63 2.32 0.30 0.20 0.29 0.49 0.31 0.31

Affine Coordinates without LRU Cache

Curve Point Addition (us) Point Doubling (us) Scalar Multiplication (ms) Koblitz Encoding (ms) Signature Generation (ms) Signature Verification (ms) Diffie-Hellman (ms) Massey-Omura (ms)
secp192k1 113.92 99.93 30.68 1.60 9.77 28.49 0.94 9.42
secp192r1 110.87 94.18 31.64 1.00 10.17 31.00 1.02 10.25
secp224k1 121.29 108.45 44.08 N/A 12.55 37.55 1.25 N/A
secp224r1 126.18 124.80 43.43 N/A 13.16 40.18 1.26 N/A
secp256k1 146.20 134.37 57.40 1.80 16.26 49.53 1.61 16.12
secp256r1 156.11 145.07 57.87 2.32 17.24 51.21 1.65 16.42
secp384r1 240.58 247.35 141.55 6.27 39.11 118.42 4.04 40.46
secp521r1 392.27 359.29 301.78 19.41 80.98 245.52 8.31 83.39

Key Insights

LRU Cache Impact

The LRU cache provides dramatic performance improvements:

  • Point Addition: ~38x faster with cache (e.g., 139.88us -> 3.64us for secp192k1)
  • Scalar Multiplication: ~500-1000x faster with cache for repeated operations
  • Signature Operations: Significantly faster due to cached intermediate results

Coordinate System Comparison

When LRU cache is enabled:

  • Jacobian and Affine coordinates perform similarly for basic operations
  • Jacobian coordinates show slight advantages in scalar multiplication

When LRU cache is disabled:

  • Jacobian coordinates are faster for scalar multiplication (fewer modular inversions)
  • The difference becomes more pronounced with larger curves

Curve Size Impact

As expected, larger curves require more computation:

  • secp521r1 operations take approximately 2-4x longer than secp256k1
  • This is due to the larger field arithmetic operations

Recommendations

  1. For most applications: Use the default settings (Jacobian coordinates with LRU cache enabled).

  2. For memory-constrained environments: Consider reducing cache size, but expect performance degradation.

  3. For high-throughput applications: The LRU cache is essential for achieving optimal performance.

  4. For security-critical applications: secp256r1 or secp384r1 offer a good balance of security and performance.