Does a private key always generate the same public key

Question

If I generate a private key, will it always produce the same public key every time I use that private key? Or is it possible for the public key to change if I generate a new one, even with the same private key?

Answer 1

Yes, a private key always generates the same public key. In public-key cryptography, each private key is uniquely associated with a single public key through a deterministic mathematical relationship. This means that for a given private key, the corresponding public key will always be the same, ensuring consistency and reliability in cryptographic operations.

• Deterministic Relationship: The process of generating a public key from a private key is deterministic; the same private key will always produce the same public key.

• Consistency: This consistency is crucial for secure communication, as it allows parties to reliably verify signatures and encrypt messages using the known public key.

• No Variability: Unlike symmetric key systems, where keys can be generated randomly, the public key derived from a private key does not change.

To conclude, the relationship between a private key and its corresponding public key is fixed and unchanging, ensuring the integrity and security of cryptographic systems.