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.

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Elliptic Curve Comparison: secp256k1 vs P-256

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Overview Table

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When to Use Each Curve

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Use Secp256k1 When:

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Use P-256 When:

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Technical Differences

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Curve Equations

y² = x³ + 7 (mod p)

Coefficients: a = 0, b = 7

y² = x³ - 3x + b (mod p)

Coefficients: a = -3, b = 0x5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B

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Field Primes

p = 2²⁵⁶ - 2³² - 977
  = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F

• Form: Pseudo-Mersenne prime (near 2²⁵⁶)
• Optimization: Fast modular reduction (subtract small constant)

p = 2²⁵⁶ - 2²²⁴ + 2¹⁹² + 2⁹⁶ - 1
  = 0xFFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF

• Form: NIST prime (specific structure)
• Optimization: Specialized reduction algorithm

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Curve Orders

n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141

n = 0xFFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551

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Performance Comparison

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TypeScript (@noble/curves)

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Native (C libraries)

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Hardware Acceleration

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Security Comparison

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Trust Model

• Origin: SECG (Standards for Efficient Cryptography Group)
• Selection: Parameters verifiably random (“nothing up my sleeve”)
• Transparency: Clear justification for all constants
• Community trust: High (Bitcoin, Ethereum adoption)

• Origin: NIST (National Institute of Standards and Technology)
• Selection: Generated using SHA-1 hash of seed value
• Transparency: Some skepticism about NIST curve selection process
• Government trust: Required for US federal systems (FIPS)

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Known Vulnerabilities

• ✅ No known mathematical weaknesses
• ✅ No known backdoors
• ✅ No feasible discrete log attacks
• ✅ Side-channel resistance (if implemented correctly)

• ⚠️ Nonce reuse leaks private key (both)
• ⚠️ Timing attacks possible (both, if not constant-time)
• ⚠️ Invalid curve attacks (both, must validate points)

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Audit Status

• libsecp256k1 - Multiple audits, Bitcoin Core
• @noble/curves - Security audited, production-ready
• Widely used: Bitcoin, Ethereum, thousands of projects

• OpenSSL - Extensively audited, ubiquitous
• @noble/curves - Same library as secp256k1 (audited)
• Widely used: TLS, WebAuthn, enterprise PKI

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Ecosystem Support

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Blockchain

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Web/Mobile

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Libraries

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Use Case Examples

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Ethereum Transaction Signing (Secp256k1)

import * as Secp256k1 from '@tevm/voltaire/Secp256k1';
import * as Transaction from '@tevm/voltaire/Transaction';

// Sign transaction with secp256k1 (required)
const tx = {
  to: '0x...',
  value: 1000000000000000000n,
  // ...
};

const txHash = Transaction.hash(tx);
const signature = Secp256k1.sign(txHash, privateKey);

// Recover sender address (ecRecover)
const publicKey = Secp256k1.recoverPublicKey(signature, txHash);
const senderAddress = Address.fromPublicKey(publicKey);

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WebAuthn Authentication (P-256)

import * as P256 from '@tevm/voltaire/P256';
import { Bytes32 } from '@tevm/voltaire/Bytes32';

// User authenticates with Face ID/Touch ID
const credential = await navigator.credentials.create({
  publicKey: {
    challenge: Bytes32('0x0000000000000000000000000000000000000000000000000000000000000001'),
    rp: { name: 'My DApp' },
    user: { id: userId, name: 'alice@example.com', displayName: 'Alice' },
    pubKeyCredParams: [{ alg: -7, type: 'public-key' }], // ES256 (P-256)
    authenticatorSelection: { userVerification: 'required' },
  },
});

// Extract P-256 public key from credential
const publicKey = extractP256Key(credential);

// Verify WebAuthn signature
const isValid = P256.verify(signature, messageHash, publicKey);

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Account Abstraction (Both)

// Validate signature with ecrecover
address signer = ecrecover(messageHash, v, r, s);
require(signer == owner, "Invalid signature");

// Validate P-256 signature (proposed precompile at 0x100)
bool valid = verifyP256(messageHash, r, s, publicKey.x, publicKey.y);
require(valid, "Invalid passkey signature");

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Migration Considerations

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From Secp256k1 to P-256

• ❌ Different curves (not compatible)
• ❌ Requires smart contract wallet (EOAs are secp256k1 only)
• ❌ Limited L1 support (RIP-7212 not yet deployed)

• ✅ Hardware wallet support (YubiKey, Secure Enclave)
• ✅ Passwordless authentication (WebAuthn)
• ✅ Enterprise compliance (FIPS)

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Hybrid Approach

contract MultiSigWallet {
  address public secp256k1Owner;  // Traditional
  P256PublicKey public p256Owner;  // Passkey

  function execute(bytes calldata data, bytes calldata signature, SignatureType sigType)
    external
  {
    if (sigType == SignatureType.Secp256k1) {
      // Validate secp256k1 (ecrecover)
      require(validateSecp256k1(data, signature, secp256k1Owner));
    } else if (sigType == SignatureType.P256) {
      // Validate P-256 (RIP-7212 precompile)
      require(validateP256(data, signature, p256Owner));
    }

    // Execute transaction
    (bool success, ) = target.call(data);
    require(success);
  }
}

• Secp256k1 for compatibility
• P-256 for UX (Face ID, Touch ID)
• Graceful degradation

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Recommendations

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For Ethereum DApps

• ✅ Use secp256k1 (required for EOAs)
• ⚠️ Consider P-256 for smart contract wallets (future)

• ✅ secp256k1 for wallet compatibility (EIP-191, EIP-712)
• ✅ P-256 for WebAuthn/passkeys (better UX)

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For Enterprise Applications

• ✅ Use P-256 (FIPS compliance required)
• ❌ Avoid secp256k1 (not FIPS-approved)

• ✅ Use secp256k1 (universal support)

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For Mobile/Web Apps

• ✅ Use P-256 (Secure Enclave)
• ⚠️ secp256k1 for Ethereum compatibility

• ✅ Use P-256 (WebAuthn, WebCrypto API)
• ✅ secp256k1 for Web3 wallet integration

1. Secp256k1 for blockchain operations
2. P-256 for user authentication
3. Bridge the two via smart contract wallet

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Future Outlook

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RIP-7212: P-256 Precompile

• ✅ On-chain P-256 verification (3000 gas)
• ✅ Enables passkey-based smart wallets
• ✅ Hardware wallet integration (YubiKey)

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Account Abstraction (EIP-4337)

• Signature scheme flexibility
• Support for multiple curves (secp256k1 + P-256)
• Hardware-based authentication

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Post-Quantum Cryptography

• Shor’s algorithm breaks ECDLP
• Estimated 10-20 years until threat

• NIST post-quantum standards (CRYSTALS, etc.)
• Hybrid classical + post-quantum schemes

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Conclusion

• Ethereum-native apps: Secp256k1 (required)
• Modern web/mobile: P-256 (better UX)
• Enterprise: P-256 (compliance)
• Hybrid/AA: Both (best of both worlds)

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Related

• Secp256k1 - Ethereum’s ECDSA curve
• P256 - NIST P-256 curve
• Account Abstraction - EIP-4337
• RIP-7212 - P-256 precompile