My question is: Does the public key in a asymmetric key have to be used to encrypt data or can it go either way (be used to decrypt)?
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In RSA the public and private key technically fulfill the same role, one can decrypt what the other encrypted. The only difference is that one is made available to all parties.

Aurelia
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Public keys can only be used to encrypt data, and private keys can only be used to decrypt data.
If you could decrypt data using a public key, that defeats the purpose of encryption.
Imagine you put your public key on your Facebook profile so that people can encrypt emails to you if they wish. If public keys could decrypt, then anyone that viewed your profile would have the key to all your emails (that were encrypted using that key pair).

Frayt
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1What is signature validation? – Aurelia Apr 21 '16 at 15:53
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Maybe you mean digital signatures? https://en.wikipedia.org/wiki/Digital_signature – Frayt Apr 23 '16 at 09:28
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1It was a rhetorical question. Encrypting with a private key and decryption with a public is what you do when validating digital signatures, contradicting your point. Keys in RSA and most other asymmetric crypto serve the same technical purpose, just being designated different. – Aurelia Apr 25 '16 at 09:01