Can Add and Multiply On Cipher Text achieve all operations?

A Fully homomorphic encryption scheme needs to support an evaluate function that can do add and multiply operations on cipher text.

Can we do all kinds of complex operations on cipher text like search, sort etc using just add and multiply ?

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 I believe you would also need a not operation. – mikeazo♦ Dec 27 '12 at 2:59 universal operations are add, xor or nand , nor , not sure why they defined it with "and" and "mult" – sashank Dec 27 '12 at 3:27 You ask about *add*/multiply, but the title says *AND*/multiply – AFS Dec 27 '12 at 3:44 oops , thanks ,corrected now ! – sashank Dec 27 '12 at 5:54