# Benchmark Report

## Summary
Benchmarking of the optimized post-quantum signature scheme ``(SIGTopLevelTargetSumLifetime32Dim64Base8)`` demonstrates feasible performance for production use across practical activation ranges with varying activation durations from `2^10` to `2^18`. The benchmark measures the computational cost of key generation as the activation duration increases.

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## Test Configuration

- **Signature Scheme:** Poseidon Top Level Target Sum
- **Lifetime:** `2^32` (fixed)
- **Configuration:** Hashing Optimized, Dimension 64, Base 8
- **Activation Duration Range:** `2^10` to `2^18` (1,024 to 262,144)
- **Sample Size:** 10 iterations for key generation
### Hardware Specifications
**Test Environment**

**Platform:** Gitpod Cloud Development Environment

- **CPU:** 8 cores
- **RAM:** 16 GB
- **Storage:** 50 GB SSD
- **Architecture:** x86_64
- **Operating System:** Linux (Gitpod default)

> **Note:** All benchmark results are specific to this hardware configuration.
> Performance may vary on different systems, particularly with different CPU architectures, core counts, or memory configurations.

## Benchmark Results
**2^10 Activation Performance**
*Key generation: 639 ms | Signing: 6.38 ms | Verification: 963 μs*

**2^11 Activation Performance**
*Key generation: 1.84 s | Signing: 6.37 ms | Verification: 840 μs*

**2^12 Activation Performance**
*Key generation: 2.67 s | Signing: 5.43 ms | Verification: 840 μs*

**2^13 Activation Performance**
*Key generation: 4.46 s | Signing: 6.02 ms | Verification: 834 μs*

**2^14 Activation Performance**
*Key generation: 7.21 s | Signing: 6.39 ms | Verification: 832 μs*

**2^15 Activation Performance**
*Key generation: 15.42 s | Signing: 6.47 ms | Verification: 1.74 ms*

**2^16 Activation Performance**
*Key generation: 28.94 s | Signing: 6.56 ms | Verification: 2.18 ms*

**2^17 Activation Performance**
*Key generation: 61.14 s | Signing: 7.18 ms | Verification: 813 μs*

**2^18 Activation Performance**
*Key generation: 98.73 s | Signing: 6.98 ms | Verification: 805 μs*

### Performance vs Activation Duration

| Activation | Effective Sig Capacity | Key Gen Time (avg) | Sign Time (avg) | Verify Time (avg) | JIT Feasibility |
|------------|-------------------------|--------------------|-----------------|-------------------|-----------------------|
| 2^10 | 1,024 | 639 ms | 6.38 ms | 963 μs | ✅ Excellent |
| 2^11 | 2,048 | 1.84 s | 6.37 ms | 840 μs | ✅ Good |
| 2^12 | 4,096 | 2.67 s | 5.43 ms | 840 μs | ✅ Acceptable |
| 2^13 | 8,192 | 4.46 s | 6.02 ms | 834 μs | ⚠️ Pre-gen recommended |
| 2^14 | 16,384 | 7.21 s | 6.39 ms | 832 μs | ⚠️ Pre-gen required |
| 2^15 | 32,768 | 15.42 s | 6.47 ms | 1.74 ms | ❌ Pre-gen essential |
| 2^16 | 65,536 | 28.94 s | 6.56 ms | 2.18 ms | ❌ Pre-gen essential |
| 2^17 | 131,072 | 61.14 s | 7.18 ms | 813 μs | ❌ Pre-gen essential |
| 2^18 | 262,144 | 98.73 s | 6.98 ms | 805 μs | ❌ Pre-gen essential |

## Performance Analysis

### Signing Performance Consistency
Remarkably consistent signing performance across all activation durations:

- **Average:** 6.42 ms ± 0.67 ms (~10% variance)
- **Range:** 5.43 ms – 7.18 ms
- **Observation:** No correlation with activation duration

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### Verification Efficiency
Excellent verification performance with minimal latency:

- **Most activations:** 800–900 μs (sub-millisecond)
- **Slight increase:** 2^15–2^16 → 1.74–2.18 ms
- **Observation:** Returns to baseline at higher activations

### Deployment Recommendations

Based on key generation performance analysis:

**JIT Generation Recommended:** 2^10 - 2^12 (1K - 4K signatures)
- Key generation: 639ms - 2.67s
- Suitable for: Interactive applications, low-frequency signing

**Pre-generation Advised:** 2^13 - 2^14 (8K - 16K signatures)
- Key generation: 4.46s - 7.21s
- Suitable for: Batch processing, moderate-frequency signing

**Pre-generation Essential:** 2^15+ (32K+ signatures)
- Key generation: 15.42s - 98.73s
- Suitable for: High-throughput systems, enterprise deployments

# AWS Benchmark Report

## Summary
This report presents a comprehensive performance analysis of key generation for the Poseidon Top Level Target Sum signature scheme, conducted on AWS infrastructure. The benchmarks measure computational costs across activation durations from 2^10 to 2^18, revealing exceptional scaling characteristics and consistent performance patterns.

### Test Configuration

- **Signature Scheme:** Poseidon Top Level Target Sum
- **Lifetime:** 2^32 (fixed)
- **Configuration:** Hashing Optimized, Dimension 64, Base 8
- **Activation Duration Range:** 2^10 to 2^18 (1,024 to 262,144)
- **Sample Size:**
- 10 iterations for key generation
- 100 for signing/verification

### AWS Hardware Specifications

- **Environment:** Amazon Web Services EC2 Instance
- **Instance Type:** m7i-flex.large
- **vCPU / Memory:** 2 vCPU, 8 GiB Memory
- **Architecture:** x86_64
- **Operating System:** Linux

> **Note:** AWS infrastructure demonstrates superior and more consistent performance characteristics compared to cloud development environments.

## Benchmark Results
**2^10 Activation Performance**

**2^11 Activation Performance**

**2^12 Activation Performance**

**2^13 Activation Performance**

**2^14 Activation Performance**

**2^15 Activation Performance**

**2^16 Activation Performance**

**2^17 Activation Performance**

**2^18 Activation Performance**

## Performance vs Activation Duration

| Activation | Effective Sig Capacity | Key Gen Time (avg) | Sign Time (avg) | Verify Time (avg) | JIT Feasibility |
|------------|-------------------------|--------------------|-----------------|-------------------|-------------------------|
| 2^10 | 1,024 | 601 ms | 1.03 ms | 220 μs | ✅ Excellent |
| 2^11 | 2,048 | 1.21 s | 1.05 ms | 216 μs | ✅ Excellent |
| 2^12 | 4,096 | 2.29 s | 1.05 ms | 221 μs | ✅ Very Good |
| 2^13 | 8,192 | 4.80 s | 1.06 ms | 216 μs | ✅ Good |
| 2^14 | 16,384 | 9.66 s | 1.04 ms | 222 μs | ⚠️ Pre-gen recommended |
| 2^15 | 32,768 | 19.51 s | 1.04 ms | 215 μs | ⚠️ Pre-gen required |
| 2^16 | 65,536 | 38.70 s | 1.06 ms | 219 μs | ❌ Pre-gen essential |
| 2^17 | 131,072 | 78.33 s | 1.04 ms | 216 μs | ❌ Pre-gen essential |
| 2^18 | 262,144 | 155.98 s | 1.06 ms | 214 μs | ❌ |
### Signing Performance Consistency

Exceptional consistency across all activation durations:

- **Average:** 1.05 ms ± 0.01 ms (~1% variance)
- **Range:** 1.03 ms – 1.07 ms
- **Observation:** No correlation with activation duration

### Verification Efficiency

Outstanding performance with minimal, consistent latency:

- **All activations:** 214–222 μs (sub-millisecond)
- **Variance:** <4% across all measurements
- **Observation:** No performance anomalies detected

### Recommendations

- **JIT Generation Recommended:** 2^10 – 2^13 (1K – 8K signatures)
- **Pre-generation Advised:** 2^14 – 2^15 (16K – 32K signatures)
- **Pre-generation Essential:** 2^16+ (65K+ signatures)