Abstract. We aim at constructing adaptive oblivious transfer protocols, enjoying fully simulatable security, from various well-known assumptions such as DDH, d-Linear, QR, DCR, and LWE. To this end, we present two generic constructions of adaptive OT, one of which utilizes verifiable shuffles together with threshold decryption schemes, while the other uses permutation networks together with what we call loosely-homomorphic key encapsulation schemes. We then show that specific choices of the building blocks lead to concrete adaptive OT protocols with fully simulatable security in the standard model under the targeted assumptions. Our generic methods can be extended to build universally composable (UC) secure, and leakage-resilient OT protocols.
Abstract. We aim at constructing adaptive oblivious transfer protocols, enjoying fully simulatable security, from various well-known assumptions such as DDH, d-Linear, QR, DCR, and LWE. To this end, we present two generic constructions of adaptive OT, one of which utilizes verifiable shuffles together with threshold decryption schemes, while the other uses permutation networks together with what we call loosely-homomorphic key encapsulation schemes. We then show that specific choices of the building blocks lead to concrete adaptive OT protocols with fully simulatable security in the standard model under the targeted assumptions. Our generic methods can be extended to build universally composable (UC) secure, and leakage-resilient OT protocols.
We aim at constructing adaptive oblivious transfer protocols, enjoying fully simulatable security, from various well-known assumptions such as DDH, d-Linear, QR, and DCR. To this end, we present two generic constructions of adaptive OT, one of which utilizes verifiable shuffles together with threshold decryption schemes, while the other uses permutation networks together with what we call loosely-homomorphic key encapsulation schemes. The constructions follow a novel designing approach called “blind permutation”, which completely differs from existing ones. We then show that specific choices of the building blocks lead to concrete adaptive OT protocols with fully simulatable security in the standard model under the targeted assumptions. Our generic methods can be extended to build universally composable (UC) secure OT protocols, with a loss in efficiency.
Abstract. Adaptive oblivious transfer (adaptive OT) schemes have wide applications such as oblivious database searches, secure multiparty computation and etc. It is a two-party protocol which simulates an ideal world such that the sender sends M1, · · · , Mn to the trusted third party (TTP) first, and then the receiver receives Mσi from TTP adaptively for i = 1, 2, · · · k. In the standard model, however, the fully simulatable schemes known so far had to rely on dynamic assumptions such as q-strong DH assumption, q-PDDH assumption and q-hidden LRSW assumption. This paper shows two fully simulatable adaptive OT schemes which do not rely on dynamic assumptions in the standard model. Our first scheme holds under the DDH assumption and our second scheme holds under the Paillier’s decisional Nth residuosity assumption, respectively.
Oblivious transfer, first introduced by Rabin, is one of the basic building blocks of cryp-tographic protocols. In an oblivious transfer (or more exactly, in its 1-out-of-2 variant), one party known as the sender has a pair of messages and the other party known as the receiver obtains one of them. Somewhat paradoxically, the receiver obtains exactly one of the messages (and learns nothing of the other), and the sender does not know which of the messages the receiver obtained. Due to its importance as a building block for secure protocols, the efficiency of oblivious transfer protocols has been extensively studied. However, to date, there are almost no known oblivious transfer protocols that are secure in the presence of malicious adversaries under the real/ideal model simulation paradigm (without using general zero-knowledge proofs). Thus, efficient protocols that reach this level of security are of great interest. In this paper we present efficient oblivious transfer protocols that are secure according to the ideal/real model simulation paradigm. We achieve constructions under the DDH, Nth residuosity and quadratic residuosity assumptions, as well as under the assumption that homomorphic encryption exists. 1
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.
Oblivious Transfer (OT) is a fundamental building block for secure computation, in which a sender holds two messages and a receiver learns exactly one of them, without revealing which one was chosen and without learning the other. While generic constructions for Universally Composable (UC) OT exist, instantiating them from post-quantum assumptions remains challenging, particularly under adaptive corruption. In this work, we present the first adaptively UC-secure OT protocol based on Group Actions, specifically assuming weakly pseudorandom Effective Group Actions (EGA) like CSIDH. We adhere to the framework of [BC15], which derives an adaptively UC-secure OT protocol from SPHF-friendly extractable and equivocable ( ⋿ 2 ) commitment schemes. The central challenge in instantiating this construction from group actions is the lack of SPHF-friendly IND-CCA encryption. Classical CCA transformations such as Fujisaki-Okamoto destroy the algebraic structure required for building SPHFs over ciphertexts, while known group action-based schemes offer no native mechanism to prove ciphertext validity. To overcome this obstacle, we construct from group actions an IND-CCA encryption scheme with enough algebraic structure to efficiently recognize valid ciphertexts. Our contributions are threefold: (1) a verifiable chameleon hash function with perfect soundness in the standard model, (2) an SPHF-friendly, publicly verifiable IND-CCA encryption scheme in the random oracle model, and (3) we combine these to build an SPHF-friendly ⋿ 2 commitment scheme and derive a fully adaptively secure OT protocol in the UC framework. This is the first construction of its kind under group action assumptions, enabling post-quantum secure OT with adaptive security guarantees. These building blocks may also be of independent interest e.g., to obtain digital signatures, non-malleable commitment schemes, or verifiable encryption.
We introduce a general construction of fully simulatable oblivious transfer based on lossy encryption. Furthermore, we extend the common definition of lossy encryption by introducing the notion of computationally lossy encryption. If the cryptosystem used is computationally lossy, our general construction yields oblivious transfer protocols with computational security for both parties. Otherwise, when regular statistically lossy cryptosystems are employed in this construction, it yields oblivious transfer protocols with statistical security for the sender. The construction introduced in this paper is realizable from rerandomizable, homomorphic and lossy cryptosystems in general. Thus, it yields specific constructions based on different assumptions, such as DDH, LWE and McEliece. Moreover, it proves the equivalence of fully simulatable oblivious transfer and lossy encryption.