Public and Private Keys

Posted On September 10, 2024

In a blockchain system, public keys are used to receive assets, while private keys are used to sign transactions and prove ownership. They work together in asymmetric cryptography to secure transactions and access blockchain data.

Example of a Public Key

A public key is a cryptographic key that is used in asymmetric encryption and digital signatures. It is part of a key pair, with the other half being the private key. The public key can be shared openly and is used to encrypt data or verify a digital signature, while the private key is kept secret and is used to decrypt data or create a digital signature.

Public keys are often represented as long strings of alphanumeric characters. The format and length of a public key can vary depending on the cryptographic algorithm used. Here are some examples of public keys from different cryptographic systems:

1. RSA Public Key

RSA (Rivest-Shamir-Adleman) is a widely used encryption algorithm. An RSA public key typically consists of two parts: the modulus and the exponent.

2. ECDSA Public Key

ECDSA (Elliptic Curve Digital Signature Algorithm) is another popular cryptographic algorithm, often used in blockchain systems like Bitcoin and Ethereum.

3. Ed25519 Public Key

Ed25519 is known for its performance and security properties.

Key Characteristics

• Length: Public keys can vary in length depending on the cryptographic algorithm and key size. For example, RSA keys are commonly 2048 or 4096 bits long, while ECDSA keys are typically 256 bits.
• Encoding: Public keys are usually encoded in formats like Base64 or hexadecimal for easy representation and transmission. They are often enclosed in delimiters (e.g., -----BEGIN PUBLIC KEY----- for PEM format) when used in various systems.
• Use: Public keys are used for encrypting data or verifying signatures. In blockchain systems, public keys are associated with wallet addresses and are used to verify the authenticity of transactions.

Relation in the key pair ( public vs private key)

In a key pair, the public key and private key are mathematically related but distinct, and each public key is uniquely paired with a specific private key. Here’s a detailed explanation:

Key Pair Basics

1. Private Key:
   • Definition: A private key is a secret number used in cryptographic algorithms. It must be kept confidential as it is used to sign transactions or decrypt data.
   • Role: In asymmetric encryption, the private key is used to decrypt information that has been encrypted with the corresponding public key. In digital signatures, it is used to sign messages, and the public key is used to verify the signature.
2. Public Key:
   • Definition: A public key is derived from the private key and can be shared openly. It is used to encrypt data or verify digital signatures.
   • Role: The public key is used to encrypt data that can only be decrypted with the corresponding private key. In the context of digital signatures, it is used to verify that a signature was created using the corresponding private key.

Unique Pairing

1. One-to-One Relationship:
   • Pairing: Each private key is uniquely associated with exactly one public key. This means that a specific private key can only generate one corresponding public key.
   • Uniqueness: The relationship between the private key and its public key is strictly one-to-one. A particular public key corresponds to a unique private key.
2. No Multiple Private Keys for a Single Public Key:
   • Single Pair: A given public key cannot be paired with multiple private keys. If you have a public key, there is exactly one private key that matches it, and vice versa.
   • Mathematical Relationship: The algorithms used to generate key pairs (e.g., RSA, ECDSA) ensure that the relationship between a public key and its private key is one-to-one. The private key is used to generate the public key, and this relationship is cryptographically secure.

Key Pair Generation

1. Algorithm:
   • Generation: The key pair is generated through cryptographic algorithms. For example, in RSA, the key pair is generated using two large prime numbers. For ECDSA, the keys are generated using elliptic curve mathematics.
   • Process: During key generation, a private key is selected, and the corresponding public key is derived from it using the algorithm’s procedures.
2. Key Pair Usage:
   • Encryption/Decryption: In encryption, data encrypted with the public key can only be decrypted by the corresponding private key.
   • Digital Signatures: A digital signature created with a private key can be verified using the corresponding public key.

Example to Illustrate

• Key Pair: If Alice has a key pair, she has a private key (say, alice_private_key) and a corresponding public key (alice_public_key).
  • Encryption: If Bob wants to send Alice a confidential message, he encrypts it using Alice’s public key (alice_public_key). Only Alice can decrypt it using her private key (alice_private_key).
  • Digital Signature: If Alice signs a document with her private key (alice_private_key), anyone can verify the signature using Alice’s public key (alice_public_key).

Each public key is paired with a unique private key, and vice versa. A public key cannot be associated with multiple private keys; the relationship is strictly one-to-one. This unique pairing ensures the security and integrity of cryptographic operations, such as encryption and digital signatures.