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# System prepended metadata

title: Benchmark Report

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# 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**
![Screenshot 2025-08-22 at 18.21.55](https://hackmd.io/_uploads/Hkz2mD8Yll.png)
*Key generation: 639 ms | Signing: 6.38 ms | Verification: 963 μs*

**2^11 Activation Performance**
![Screenshot 2025-08-22 at 18.38.39](https://hackmd.io/_uploads/B1M0mPUYlg.png)
*Key generation: 1.84 s | Signing: 6.37 ms | Verification: 840 μs*

**2^12 Activation Performance**
![Screenshot 2025-08-22 at 18.43.46](https://hackmd.io/_uploads/By21Nw8tge.png)
*Key generation: 2.67 s | Signing: 5.43 ms | Verification: 840 μs*

**2^13 Activation Performance**
![Screenshot 2025-08-22 at 18.57.17](https://hackmd.io/_uploads/Hk_MVPLtlg.png)
*Key generation: 4.46 s | Signing: 6.02 ms | Verification: 834 μs*

**2^14 Activation Performance**
![Screenshot 2025-08-22 at 19.05.50](https://hackmd.io/_uploads/r124NwLteg.png)
*Key generation: 7.21 s | Signing: 6.39 ms | Verification: 832 μs*

**2^15 Activation Performance**
![Screenshot 2025-08-22 at 19.15.32](https://hackmd.io/_uploads/r14DEPIFlx.png)
*Key generation: 15.42 s | Signing: 6.47 ms | Verification: 1.74 ms*


**2^16 Activation Performance**
![Screenshot 2025-08-22 at 19.33.27](https://hackmd.io/_uploads/S1OFNPUKxl.png)
*Key generation: 28.94 s | Signing: 6.56 ms | Verification: 2.18 ms*

**2^17 Activation Performance**
![Screenshot 2025-08-22 at 19.51.46](https://hackmd.io/_uploads/SyKiVwLYxg.png)
*Key generation: 61.14 s | Signing: 7.18 ms | Verification: 813 μs*


**2^18 Activation Performance**
![Screenshot 2025-08-22 at 20.16.59](https://hackmd.io/_uploads/SJ4aVP8tge.png)
*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**
![Screenshot 2025-08-25 at 08.24.42](https://hackmd.io/_uploads/SkTPaoKKlg.png)

**2^11 Activation Performance**
![Screenshot 2025-08-25 at 08.33.14](https://hackmd.io/_uploads/SJBKpsFYxe.png)

**2^12 Activation Performance**
![Screenshot 2025-08-25 at 08.35.15](https://hackmd.io/_uploads/Syu56stYge.png)

**2^13 Activation Performance**
![Screenshot 2025-08-25 at 08.39.15](https://hackmd.io/_uploads/rycs6oKYlx.png)

**2^14 Activation Performance**
![Screenshot 2025-08-25 at 08.44.32](https://hackmd.io/_uploads/Byz66jtYeg.png)

**2^15 Activation Performance**
![Screenshot 2025-08-25 at 08.51.24](https://hackmd.io/_uploads/HJLRTiYFee.png)

**2^16 Activation Performance**
![Screenshot 2025-08-25 at 09.02.49](https://hackmd.io/_uploads/SyckRiYtee.png)

**2^17 Activation Performance**
![Screenshot 2025-08-25 at 09.21.43](https://hackmd.io/_uploads/rkeZ0sttle.png)

**2^18 Activation Performance**
![Screenshot 2025-08-25 at 09.56.28](https://hackmd.io/_uploads/By2-0iYYxe.png)


## 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)  
