Asymmetric Encryption in Blockchain: Understanding Digital Signatures and Encryption

Introduction to Asymmetric Encryption

Asymmetric encryption algorithms use distinct keys for encryption and decryption, where deriving the decryption key from the encryption key is computationally infeasible. This foundational technology enables two critical functions in blockchain:

• Digital Signatures: Authenticate sender identity using private-key signing and public-key verification.
• Encryption/Decryption: Securely transmit data by encrypting with a public key and decrypting with the corresponding private key.

While both leverage asymmetric cryptography, their purposes and mechanisms differ significantly.

1. Digital Signatures and Verification

Digital signatures ensure:
✅ Authentication: Proves the sender holds the private key.
✅ Integrity: Binds the sender to the message, preventing tampering.
✅ Non-repudiation: Prevents denial of sent messages.

1.1 RSA Digital Signatures

• Security Basis: Relies on the difficulty of factoring large integers.
• Key Length: Minimum 2048-bit recommended for security.

• Process:

  1. Hash the message (H(m)).
  2. Pad the hash to match key length.
  3. Sign using the private key.

• Limitations:

  • Slower key generation due to prime number requirements.
  • Longer keys needed for evolving computational threats.

1.2 Elliptic Curve Digital Signatures (ECDSA)

• Security Basis: Leverages elliptic curve discrete logarithm problem.

• Advantages:

  • Faster key generation.
  • Shorter keys (e.g., 256-bit ECDSA ≈ 3072-bit RSA in security).
  • Ideal for blockchain due to compact storage.

• Process:

  1. Generate ephemeral random number r.
  2. Compute R = r * G (G = curve base point).
  3. Hash message: h = H(m).
  4. Calculate signature: s = (h + k * Rx) / r mod n.

👉 Explore how ECDSA secures Bitcoin transactions

1.3 Signature Verification

• RSA: Verifier uses the public key to decrypt the signature and compares it to a recomputed hash.

• ECDSA: Reconstructs R’ from (Rx, s), public key K, and h to validate:

  R’ = (h * G + Rx * K) / s  

  Success if R’x == Rx.

Critical Note:

• Randomness in r is vital. Reuse compromises private key security.

2. Encryption and Decryption

Non-symmetric encryption ensures confidential message transfer without pre-shared keys. Unlike signatures, it focuses on data privacy, not identity binding.

2.1 Public-Key Encryption

Process (Elliptic Curve Integrated Encryption Scheme - ECIES):

1. Generate random r; compute R = r * G.
2. Encode message m to curve point M.
3. Compute shared secret: S = M + r * K (recipient’s public key).
4. Transmit (R, S).

Common Practice:

• Use S to derive a symmetric key for hybrid encryption (e.g., AES).

2.2 Private-Key Decryption

Process:

1. Compute M = S - k * R (using recipient’s private key k).
2. Decode M to retrieve m.

Why It Works:

S - k * R = (M + r * K) - k * (r * G) = M + r * (k * G) - k * r * G = M  

FAQs

Q1: Why use ECDSA over RSA in blockchain?

A1: ECDSA offers equivalent security with shorter keys (e.g., 256-bit vs. 3072-bit), reducing storage and bandwidth—critical for decentralized networks.

Q2: Can someone forge a signature if they know the random number r?

A2: Yes. Reusing or predictable r exposes the private key. Always use cryptographically secure randomness.

Q3: Is asymmetric encryption slower than symmetric encryption?

A3: Yes. Hence, hybrid systems (e.g., RSA+AES) combine asymmetric key exchange with symmetric data encryption for efficiency.

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Q4: How does a recipient verify an ECDSA signature without knowing the private key?

A4: The verifier uses the public key K, signature (Rx, s), and message hash h to reconstruct R’. If R’x matches Rx, the signature is valid.

Conclusion

Asymmetric cryptography underpins blockchain security through:

• Signatures (authentication).
• Encryption (confidentiality).

While RSA remains widely used, ECDSA’s efficiency makes it the preferred choice for blockchain applications. Always adhere to best practices in key management and randomness generation to mitigate risks.

For developers: Implement libraries like OpenSSL or SECP256k1 rigorously tested for cryptographic operations.