Universally Composable Efficient Priced Oblivious Transfer from a Flexible Membership Encryption

Abstract

Abstract. Membership encryption is a newly developed cryptographic primitive that combines membership proof and encryption into an unified setting. This paper presents a new flexible membership encryption scheme which is provably secure and significantly more efficient than the previous scheme. Further we apply our proposed membership encryption to construct a round optimal 1-outof-n priced oblivious transfer (POT) protocol which, unlike the existing 1-out-of-n POT schemes, is proven secure under the universally composable (UC) security model and thus preserves security when it is executed with multiple protocol instances that run concurrently in an adversarily controlled way. Moreover, using our membership encryption, the POT protocol exhibits constant communication complexity on the buyer's side and O(n) communication cost on the vendor's side, which is so far the best known in the literature.Keywords: membership encryption, priced oblivious transfer, universally composable security, bilinear maps, non-interactive proof of knowledge, P-Signature, non-interactive range proof.

Efficient Adaptive Oblivious Transfer Without q-type Assumptions in UC Framework

“…Definition 3 (SqDBDH [10]). The Square Decision Bilinear Diffie-Hellman assumption in (G, G T ) states that for all PPT algorithm A, with running time in ρ, the advantage Adv SqDBDH G,GT…”