Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We provide the first oblivious transfer protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust the setup (and some setup is needed for UC security). Trust in computational assumptions: only one of the parties needs to trust a computational assumption. Round complexity: it uses only two rounds. Communication complexity: it communicates O(1) group elements to transfer one out of two group elements. The Big-O notation hides 32, meaning that the communication is probably not optimal, but is essentially optimal in that the overhead is at least constant. Our construction is based on pairings, and we assume the presence of a key registration authority.
Oblivious transfer is one of the most important cryptographic primitives, both for theoretical and practical reasons and several protocols were proposed during the years. We provide the first oblivious transfer protocol which is simultaneously optimal on the following list of parameters: Security: it has universal composition. Trust in setup assumptions: only one of the parties needs to trust the setup (and some setup is needed for UC security). Trust in computational assumptions: only one of the parties needs to trust a computational assumption. Round complexity: it uses only two rounds. Communication complexity: it communicates O(1) group elements to transfer one out of two group elements. The Big-O notation hides 32, meaning that the communication is probably not optimal, but is essentially optimal in that the overhead is at least constant. Our construction is based on pairings, and we assume the presence of a key registration authority.
Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM.
Non-committing encryption achieved only semantic security,in contrast,applications often require security against chosen ciphertext attacks.A main ingredient in the previous adaptive universally composable(UC)oblivious transfer protocols are non-committing encryptions.the previous proposals are not UC secure against adaptive adversaries in the so-called non-erase model.A new UC secure oblivious transfer protocols were proposed and schemes utilize two primitives of the verifiably smooth projective hashing and deniable encryption as constructed by.the double trapdoor decryption mechanism based on trapdoor commitment.Our construction is based on the decisional composite residuosity in common reference string (CRS) model.We constructed a two-message(1-round) string oblivious transfer protocol,which improves computational efficient that supports message spaces of size exponential and save O(n)-1 rounds communications efficient than bit-OT protocols.
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 mem-bership 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-out-of-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 secu-rity 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.
Abstract. We study the necessary and sufficient assumptions for universally composable (UC) computation, both in terms of setup and computational assumptions. We look at the common reference string model, the uniform random string model and the key-registration authority model (KRA), and provide new results for all of them. Perhaps most interestingly we show that: – For even the minimal meaningful KRA, where we only assume that the secret key is a value which is hard to compute from the public key, one can UC securely compute any poly-time functionality if there exists a passive secure oblivious-transfer protocol for the stand-alone model. Since a KRA where the secret keys can be computed from the public keys is useless, and some setup assumption is needed for UC secure computation, this establishes the best we could hope for the KRA model: any non-trivial KRA is sufficient for UC computation. – We show that in the KRA model one-way functions are sufficient for UC commitment and UC zero-knowledge. These are the first examples of UC secure protocols for non-trivial tasks which do not assume the existence of public-key primitives. In particular, the protocols show that non-trivial UC computation is possible in Minicrypt. 1
Committed Oblivious Transfer (COT) is a two-party primitive that combines one-out-of-two oblivious transfer with bit commitment. In the beginning of COT, a sender is committed to bits b0, b1 and a receiver to a choice bit c. In the end, the receiver is committed to bc without learning anything about b1-c, while the sender learns nothing about c. This primitive implies secure multi-party computation assuming that a broadcast channel is available. In this paper, we introduce the first universally composable unconditionally secure committed oblivious transfer protocol based on a Trusted Initializer (TI), which pre-distributes data to the parties. Our protocol builds on simple bit commitment and oblivious transfer protocols, using XOR commitments to prove simple relations in zero-knowledge. Besides providing very high security guarantees, our protocols are significantly simpler and more efficient than previous results, since they rely on pre-computed operations distributed by the TI.
Reducing the minimum assumptions needed to construct various cryptographic primitives is an important andinteresting task in theoretical cryptography. Oblivious Transfer, one of the most basic cryptographic building blocks, is also studied under this scenario. Reducing the minimum assumptions for Oblivious Transfer seems not an easy task, as there are a few impossibility results under black-box reductions. Until recently, it is widely believed that Oblivious Transfer can be constructed with trapdoor permutations but not trapdoor functions in general. In this paper, we enhance previous results and show one Oblivious Transfer protocol based on a collection of trapdoor functions with some extra properties. We also provide reasons for adding the extra properties and argue that the assumptions in the protocol are nearly minimum.