Blockchain Public-Private Key Signatures: Verification, Encryption, and Decryption Processes

Public and Private Keys

Bitcoin uses the ECDSA digital signature algorithm, an asymmetric encryption method. Asymmetric encryption involves paired keys: public and private keys.

Public Key: Shared openly for digital verification and encryption.
Private Key: Kept securely by the owner for digital signing and decryption.

Below is a simplified explanation of the underlying principles—without delving into specific algorithmic implementations.

Encryption and Decryption

Setup

• Private Key: k
• Public Key: K

• Elliptic Curve Base Point: G

  • Relationship: K = k * G (private → public is irreversible).
• Message: Message
• Message Digest: Digest
• Encrypted Message: Encryption
• Random Number: X

Encryption Process

1. Message Digest:
   Digest = G * X
2. Digital Signature:
   Encryption = K * X + Message
3. Send Digest and Encryption to the recipient.

Decryption Process

Message = Encryption - K * X

• Breakdown:
  = Encryption - (k * G) * X
= Encryption - k * (G * X)
= Encryption - k * Digest

Digital Signatures & Verification

Setup

• Private Key: k
• Public Key: K (with K = k * G)
• Temporary Private Key: r
• Temporary Public Key: R = r * G
• Message: Message
• Hashed Message: hash
• Signature: Signature

Signing Process

1. Compute temporary public key: R = r * G.
2. Generate signature:
   Signature = [detailed formula] (omitted for brevity).
3. Send R, Message, and Signature to the recipient.

Verification Process

Verification checks if the computed r * G matches the received R using:

• Public key K.
• Original Message.
• Signature.

👉 Explore more about blockchain security

FAQ

Q1: Why use asymmetric encryption in blockchain?
Asymmetric encryption ensures secure transactions without exposing private keys, enabling trustless verification.

Q2: How does ECDSA enhance Bitcoin security?
ECDSA provides robust mathematical security, making private key forgery computationally infeasible.

Q3: What happens if a private key is lost?
Lost private keys render associated assets irrecoverable—underscoring the need for secure storage.

👉 Learn advanced key management