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I am Reading RSA and Public-Key Cryptography by Mollin and I can't make out how El Gamal is different from Diffie Hellman Key Exchange. Any thoughts?

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marked as duplicate by DrLecter, otus, yyyyyyy, e-sushi Dec 31 '15 at 12:02

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The difference is purely conceptual. That is, when Diffie-Hellman published their paper, they equated between public-key encryption and trapdoor functions. Thus, they did not think that they had constructed a public-key encryption scheme, and this invention came only a year later with RSA. In fact, Diffie and Hellman even explicitly talk about publishing one part of the key...

The contribution of ElGamal was to formalize this as an encryption scheme, and free us of the conceptual block that public-key encryption requires a trapdoor function. By the way, conceptual contributions are very important, so this does not belittle it in any way. In addition, note that El Gamal was very clear about this in his paper. A quote from the paper: "Section II shows a way to implement the public key distribution scheme introduced by Diffie and Hellman to encrypt and decrypt messages."

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