It is well known that any encryption scheme which supports any form of homomorphic operation cannot be secure against adaptive chosen ciphertext attacks. The question then arises as to what is the most stringent security definition which is achievable by homomorphic encryption schemes. Prior work has shown that various schemes which support a single homomorphic encryption scheme can be shown to...

Consider a decision problem that cannot be 1 ? approximated by circuits of a given size in the sense that any such circuit fails to give the correct answer on at least a fraction of instances. We show that for any such problem there is a speciic \hard-core" set of inputs which is at least a fraction of all inputs and on which no circuit of a slightly smaller size can get even a small advantage ...

This paper reviews some of the work in the area of statistical circuit design. While space does not permit a more then superficial survey of the entire field, specific emphasis is placed on those techniques more familiar to the authors.