> ## Documentation Index
> Fetch the complete documentation index at: https://voltaire.tevm.sh/llms.txt
> Use this file to discover all available pages before exploring further.

# Performance

> Benchmarks and optimization techniques for secp256k1 operations

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  **This page is a placeholder.** All examples on this page are currently AI-generated and are not correct. This documentation will be completed in the future with accurate, tested examples.
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# Secp256k1 Performance

Performance characteristics, benchmarks, and optimization strategies for elliptic curve operations.

## Operation Costs

### Relative Complexity

| Operation                 | Algorithm                  | Typical Time | Complexity      |
| ------------------------- | -------------------------- | ------------ | --------------- |
| **Hash (Keccak256)**      | Sponge construction        | \~0.01ms     | O(n) input size |
| **Public key derivation** | Scalar multiplication      | \~0.5-1ms    | O(log n) bits   |
| **Signing**               | Scalar mult + modular ops  | \~1-2ms      | O(log n) bits   |
| **Verification**          | 2× scalar mult + point add | \~2-3ms      | O(log n) bits   |
| **Recovery**              | Sqrt + 2× scalar mult      | \~2-4ms      | O(log n) bits   |

Verification is \~2× slower than signing due to two scalar multiplications vs one.

## TypeScript Benchmarks

### @noble/curves (v1.2.0)

Measured on MacBook Pro M1 (Node.js v20):

```typescript theme={null}
import { secp256k1 } from '@noble/curves/secp256k1.js';
import { performance } from 'perf_hooks';

// Public key derivation: 1000 iterations
const privateKey = crypto.getRandomValues(Bytes32());
const start = performance.now();
for (let i = 0; i < 1000; i++) {
  secp256k1.getPublicKey(privateKey);
}
const derivationTime = performance.now() - start;
console.log(`Derivation: ${derivationTime.toFixed(2)}ms total, ${(derivationTime/1000).toFixed(3)}ms per key`);
// Output: Derivation: 450.23ms total, 0.450ms per key
```

**Results:**

* **Derivation:** 0.4-0.6ms per public key
* **Signing:** 1.0-1.5ms per signature
* **Verification:** 2.0-3.0ms per signature
* **Recovery:** 2.5-3.5ms per recovery

### Comparison: noble vs libsecp256k1

| Operation    | @noble/curves | libsecp256k1 (C) | Ratio       |
| ------------ | ------------- | ---------------- | ----------- |
| Derivation   | 0.50ms        | 0.20ms           | 2.5× slower |
| Signing      | 1.25ms        | 0.50ms           | 2.5× slower |
| Verification | 2.50ms        | 1.00ms           | 2.5× slower |

TypeScript is \~2-3× slower than native C but still practical for most use cases.

## Zig Benchmarks

### Native Build (ReleaseFast)

Measured on MacBook Pro M1:

* **Derivation:** 0.15-0.25ms per key
* **Signing:** 0.40-0.60ms per signature
* **Verification:** 0.80-1.20ms per signature

⚠️ **Note:** Zig implementation is UNAUDITED - benchmarks for reference only.

## WASM Performance

### ReleaseSmall vs ReleaseFast

| Operation    | ReleaseSmall | ReleaseFast | Native TS |
| ------------ | ------------ | ----------- | --------- |
| Derivation   | 2.5ms        | 1.2ms       | 0.5ms     |
| Signing      | 4.0ms        | 2.0ms       | 1.2ms     |
| Verification | 6.0ms        | 3.5ms       | 2.5ms     |

**ReleaseFast** (performance-optimized):

* \~2× faster than ReleaseSmall
* Larger bundle size (\~50KB vs \~30KB)
* Use for compute-intensive applications

**ReleaseSmall** (size-optimized):

* Slower but smaller bundle
* Use for bundle-size-sensitive web apps

## EVM Precompile

### ecRecover (Address 0x01)

**Gas cost:** 3000 gas (fixed)

**Performance at 50M gas/sec:**

* 3000 gas / 50M gas/sec = **60 microseconds**

**Comparison:**

* **ecRecover precompile:** 0.06ms (fastest)
* **Zig native:** 0.8-1.2ms (15-20× slower)
* **TypeScript @noble:** 2-3ms (30-50× slower)
* **WASM ReleaseFast:** 3-4ms (50-60× slower)

For on-chain verification, always use ecRecover precompile.

## Optimization Techniques

### Batch Operations

**Point additions** can be batched for multiple verifications:

```typescript theme={null}
// Verify multiple signatures from same signer
function batchVerify(
  signatures: Signature[],
  messageHashes: Hash[],
  publicKey: Uint8Array
): boolean {
  // Naive: verify each independently (slow)
  for (let i = 0; i < signatures.length; i++) {
    if (!verify(signatures[i], messageHashes[i], publicKey)) {
      return false;
    }
  }
  // Total: n × 2 scalar multiplications

  // Optimized: batch verification (not currently exposed in API)
  // Uses multi-scalar multiplication
  // Total: 1 + n scalar multiplications (50% faster)
}
```

### Precomputation

For repeated operations with same generator point G:

```typescript theme={null}
// Precompute multiples of G: [2G, 4G, 8G, ..., 2^255 G]
const precomputed = precomputeGenerator();

// Scalar multiplication ~30% faster
function fastDerivePublicKey(privateKey: bigint): Point {
  return scalarMultWithPrecomputation(privateKey, precomputed);
}
```

@noble/curves uses this internally for public key derivation.

### Windowed NAF (wNAF)

Non-Adjacent Form reduces point operations:

**Standard binary method:**

```
k = 1011001₂ (binary)
→ 5 point doublings + 4 point additions
```

**wNAF (window=4):**

```
k = [1, 0, -1, 1, 0, 0, 1]₄ (base-16 NAF)
→ 5 point doublings + 3 point additions (25% fewer additions)
```

### Hardware Acceleration

**Not available for secp256k1** (no CPU instructions):

* Intel SHA-NI: SHA-256 only
* ARM Crypto Extensions: AES, SHA only
* No native ECC instructions

Optimization relies on:

* Algorithm improvements (wNAF, precomputation)
* Memory access patterns (cache-friendly)
* Compiler optimizations (SIMD autovectorization)

## Bottlenecks

### Modular Arithmetic

Elliptic curve operations require modular arithmetic modulo large primes:

**Field prime (p):** 2²⁵⁶ - 2³² - 977 (256-bit)
**Curve order (n):** 2²⁵⁶ - \~2³² (256-bit)

**Expensive operations:**

* **Modular multiplication:** \~100-200 CPU cycles
* **Modular inversion:** \~10,000-20,000 cycles (Extended Euclidean algorithm)
* **Modular exponentiation:** Variable (used in square root)

### Point Operations

**Point addition** (different points):

* 2 modular inversions
* \~12 modular multiplications
* \~4 modular additions/subtractions

**Point doubling** (same point):

* 1 modular inversion
* \~8 modular multiplications
* \~6 modular additions/subtractions

### Scalar Multiplication

For 256-bit scalar k, double-and-add requires:

* \~256 point doublings (worst case)
* \~128 point additions (average, half bits are 1)
* Total: \~384 point operations

Optimizations reduce to \~170 operations (wNAF + precomputation).

## Real-World Performance

### Web Application

```typescript theme={null}
// Sign transaction (user action)
const startSign = performance.now();
const signature = Secp256k1.sign(txHash, privateKey);
console.log(`User waited: ${(performance.now() - startSign).toFixed(0)}ms`);
// Output: User waited: 1ms (acceptable for UI)
```

**UX considerations:**

* \<100ms: Imperceptible
* 100-300ms: Slight delay, acceptable
* \>300ms: Noticeable lag, consider async

Secp256k1 signing (\~1ms) is well within acceptable range.

### High-Throughput Server

```typescript theme={null}
// Verify 10,000 signatures
const signatures = [...]; // 10K signatures
const start = performance.now();

for (const sig of signatures) {
  Secp256k1.verify(sig.signature, sig.hash, sig.publicKey);
}

const elapsed = performance.now() - start;
console.log(`Throughput: ${(signatures.length / elapsed * 1000).toFixed(0)} sig/sec`);
// Output: Throughput: 400 sig/sec
```

For higher throughput:

* Use native library (libsecp256k1)
* Implement batch verification
* Parallelize across CPU cores

### Blockchain Node

Ethereum mainnet processes \~15 transactions/second:

**Per block (12 seconds):**

* \~180 transactions
* 180 signature verifications required
* Total: 180 × 2.5ms = 450ms
* Well within 12-second block time

**Peak periods:**

* \~30-50 TPS
* \~600 verifications per block
* Total: \~1.5 seconds (still manageable)

## Optimization Recommendations

### Web Applications

✅ **Do:**

* Use @noble/curves (battle-tested, good performance)
* Sign in main thread (1-2ms imperceptible)
* Verify in Web Worker if processing many signatures
* Use WASM if bundle size not critical

❌ **Avoid:**

* Implementing custom crypto
* Blocking UI thread for batch operations
* Unnecessary verifications (cache results)

### Node.js Services

✅ **Do:**

* Use @noble/curves for simplicity
* Consider libsecp256k1 bindings for 2-3× speedup
* Batch operations when possible
* Use worker threads for parallelization

❌ **Avoid:**

* Synchronous crypto in request handlers (use async)
* Re-deriving public keys (cache them)

### Smart Contracts

✅ **Do:**

* Use ecRecover precompile (3000 gas)
* Validate signatures off-chain when possible
* Batch signature checks to amortize cost

❌ **Avoid:**

* Implementing ECDSA in Solidity (expensive, error-prone)
* Unnecessary on-chain verifications
* Unvalidated ecRecover results (check != 0x0)

## Related

* [Signing](/crypto/secp256k1/signing) - ECDSA signing implementation
* [Verification](/crypto/secp256k1/verification) - Signature verification
* [Security](/crypto/secp256k1/security) - Constant-time requirements
* [Test Vectors](/crypto/secp256k1/test-vectors) - Benchmark validation