A New Public-Key Cryptosystem via Mersenne Numbers 📺
In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number $$p = 2^n - 1$$ p=2n-1, where n is a prime, a positive integer h, and two n-bit integers T, R, decide whether their exist n-bit integers F, G each of Hamming weight less than h such that $$T = F\cdot R + G$$ T=F·R+G modulo p.
Oblivious Transfers and Intersecting Codes
Assume A owns t secret k-bit strings. She is willing to disclose one of them to B, at his choosing, provided he does not learn anything about the other strings. Conversely, B does not want A to learn which secret he chose to learn. A protocol for the above task is said to implement One-out-of-t String Oblivious Transfer. An apparently simpler task corresponds to the case k=1 and t=2 of two one-bit secrets: this is known as One-out-of-two Bit OT. We address the question of implementing the former assuming the existence of the later. In particular, we prove that the general protocol can be implemented from O(tk) calls to One-out-of-two Bit OT. This is optimal up to a small multiplicative constant. Our solution is based on the notion of self-intersecting codes. Of independent interest, we give several efficient new constructions for such codes. Another contribution of this paper is a set of information-theoretic definitions for correctness and privacy of unconditionally-secure oblivious transfer.