Obfuscation is different from homomorphic encryption, and in some sense much more powerful.
With homomorphic encryption, Alice can send some secret data to Bob in encrypted form, and let Bob carry out computation on that encrypted data. However, the result of the computation remains encrypted, and only Alice's private key can decrypt the result.
By contrast, obfuscation allows Alice to give Bob a program that contains some secret information (such as cryptographic keys) in such a way that Bob can run it (without any further interaction with Alice) on any inputs of his choice, and get the result in the clear. However, he cannot learn anything about the hidden secret information other than what is revealed by the input-output pairs he has obtained.
It's not hard to see that obfuscation gives you homomorphic encryption for free (you can probably get a rough idea of how to do it based on the somewhat imprecise descriptions above), but we don't know how to go in the other direction. (Current obfuscation candidates do use fully homomorphic encryption under the hood, but they need to rely on much more than that).
With homomorphic encryption, Alice can send some secret data to Bob in encrypted form, and let Bob carry out computation on that encrypted data. However, the result of the computation remains encrypted, and only Alice's private key can decrypt the result.
By contrast, obfuscation allows Alice to give Bob a program that contains some secret information (such as cryptographic keys) in such a way that Bob can run it (without any further interaction with Alice) on any inputs of his choice, and get the result in the clear. However, he cannot learn anything about the hidden secret information other than what is revealed by the input-output pairs he has obtained.
It's not hard to see that obfuscation gives you homomorphic encryption for free (you can probably get a rough idea of how to do it based on the somewhat imprecise descriptions above), but we don't know how to go in the other direction. (Current obfuscation candidates do use fully homomorphic encryption under the hood, but they need to rely on much more than that).