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Discrete Logarithm Proofs in Ergo#

Overview#

Discrete logarithm proofs are a fundamental cryptographic primitive in Ergo's signature verification mechanism, based on the computational hardness of the discrete logarithm problem in elliptic curve cryptography.

Key Characteristics#

  • Cryptographic Foundation: Proofs of knowledge of a discrete logarithm (DLog) verify signature authenticity without revealing the secret key
  • Schnorr Signature Basis: Ergo uses Schnorr signatures built on discrete logarithm proofs

Technical Details#

  • Proof Structure: Demonstrate knowledge of secret exponent w such that g^w = x
  • g: Generator of an elliptic curve group
  • x: Public key point
  • w: Private key

Implementation in ErgoScript#

In ErgoScript, discrete logarithm proofs are implemented using the proveDlog() predicate, which returns true if a valid proof of knowledge can be provided.

// DLog-based signature verification
val pubKey = ...  // Public key point
val signature = ...  // Signature proof
proveDlog(pubKey)

Practical Examples#

Security Considerations#

  • Based on discrete logarithm problem hardness
  • Efficient and compact signature verification
  • Supports multi-signatures and ring signatures

Advanced Applications#

References#