Secrecy without one-way functions

We show that some problems in information security can be solved without using one-way functions. The latter are usually regarded as a central concept of cryptography, but the very existence of one-way functions depends on difficult conjectures in complexity theory, most notably on the notorious “P 6= NP” conjecture. This is why cryptographic primitives that do not employ one-way functions are often called “unconditionally secure”. In this paper, we suggest protocols for secure computation of the sum, product, and some other functions of two or more elements of an arbitrary constructible ring, without using any one-way functions. A new input that we offer here is that, in contrast with other proposals, we conceal “intermediate results” of a computation. For example, when we compute the sum of k numbers, only the final result is known to the parties; partial sums are not known to anybody. Other applications of our method include voting/rating over insecure channels and a rather elegant and efficient solution of the “two millionaires problem”. Then, while it is fairly obvious that a secure (bit) commitment between two parties is impossible without a one-way function, we show that it is possible if the number of parties is at least 3. We also show how our unconditionally secure (bit) commitment scheme for 3 parties can be used to arrange an unconditionally secure (bit) commitment between just two parties if they use a “dummy” (e.g., a computer) as the third party. We explain how our concept of a “dummy” is different from a wellknown concept of a “trusted third party”. Based on a similar idea, we also offer an unconditionally secure k-n oblivious transfer protocol between two parties who use a