I'm trying to learn about cryptography and have discovered that you can use asymmetric key encryption to verify your identity by encrypting something with your private key, but isn't that a security vulnerability?
(I'm talking about this: https://youtu.be/GSIDS_lvRv4?t=243)
This how I understand it:
* Users: A, B & Eve (A want to send a message to B, Eve is always listening)
* Both users each have a corresponding public/private key pair.
* Both users know about each others public key.
A ---> B-pub(A-priv(message)) ---> B
Can B or Eve decipher what A-priv is now?
* To A: B-pub, Message, (A-priv & pub)
* To B: A-pub, [A-priv?], message, (B-priv & pub)
* To Eve: A-pub, B-pub, B-pub(A-priv(message))
(have I missed any values?)
Assuming Eve can gain access to B-priv, can she then figure out what A-priv is from the message?