I heard that along with a public key, you need a initalization vector so that messages are not encryption identically in different instances. Since all a public key does is multiple prime numbers together, why are some keys the same as others? There are an infinite number of prime numbers (I think) so there should be no problem.
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Small side note – public key cryptography does not typically use initialization vectors, they rely on other things (random padding in the case of RSA, or whole random keys in the case of elliptic curves) to get the property that IVs are used for in symmetric cryptography, which is to make sure the same message gets different ciphertexts when you encrypt it multiple times. An IV is specific to cryptographic algorithms that have many stages (e.g. in AES, you split the message into smaller blocks, and then encrypt each one) , so if you randomize the first state the remaining ones get correspondingly scrambled.
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