Why must public-key cryptography be easy in one direction and hard in the other?
Conditions
- There must be an easy direction from private key to public key.
- There must be a computationally hard reverse direction from public key to private key.
Reasoning, step by step
- Recognize the need for an asymmetric generation process.
- Understand that computing the public key from the private key must be easy.
- Understand that computing the private key from the public key must be computationally hard.
Example
The speaker explains that public-key cryptography needs a way to generate a public key so that computing the private key from the public key is computationally hard, while computing the public key from the private key is easy.
Common misconceptions
- Assuming both directions of key generation are equally easy.
- Thinking that public-key cryptography relies on symmetric key exchange.
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