Oblivious Transfer (OT) is a major primitive for secure multiparty computation. Indeed, combined with symmetric primitives along with garbled circuits, it allows any secure function evaluation between two parties. In this paper, we propose a new approach to build OT protocols. Interestingly, our new paradigm features a security analysis in the Universal Composability (UC) framework and may be instantiated from post-quantum primitives. In order to do so, we define a new primitive named Smooth Projective Hash Function with Grey Zone (SPHFwGZ) which can be seen as a relaxation of the classical Smooth Projective Hash Functions, with a subset of the words for which one cannot claim correctness nor smoothness: the grey zone. As a concrete application, we provide two instantiations of SPHFwGZ respectively based on the Diffie-Hellman and the Learning With Errors (LWE) problems. Hence, we propose a quantum-resistant OT protocol with UC-security in the random oracle model.
Oblivious Transfer (OT) is a major primitive for secure multiparty computation. Indeed, combined with symmetric primitives along with garbled circuits, it allows any secure function evaluation between two parties. In this paper, we propose a new approach to build OT protocols. Interestingly, our new paradigm features a security analysis in the Universal Composability (UC) framework and may be instantiated from post-quantum primitives. In order to do so, we define a new primitive named Smooth Projective Hash Function with Grey Zone (SPHFwGZ) which can be seen as a relaxation of the classical Smooth Projective Hash Functions, with a subset of the words for which one cannot claim correctness nor smoothness: the grey zone. As a concrete application, we provide two instantiations of SPHFwGZ respectively based on the Diffie-Hellman and the Learning With Errors (LWE) problems. Hence, we propose a quantum-resistant OT protocol with UC-security in the random oracle model.
Since the seminal result of Kilian, Oblivious Transfer (OT) has proven to be a fundamental primitive in cryptography. In such a scheme, a user is able to gain access to an element owned by a server, without learning more than this single element, and without the server learning which element the user has accessed. The NIST call for post-quantum encryption and signature schemes has revived the interest for cryptographic protocols based on post-quantum assumptions and the need for secure post-quantum OT schemes. In this paper, we show how to construct an OT scheme based on lattices, from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Note that our scheme does not rely on random oracles and provides UC security against adaptive corruptions assuming reliable erasures.
We construct a universal composable framework for two-message oblivious transfer protocols based on lattice-assumption. Compared with the paper proposed by Liu and Hu, we modify a framework proposed by Liu and Hu by adding three tools, which are XOR, Bit Commitment and Smooth Projective Hash Function (SPHF). We instantiate Hash Function as SPHF, which can be more secure in practical application and can achieve full-simulatable in security proof. Compared with Hash Function used as Random Oracle in security proof, this construction is more secure and efficient in security proof. In particular, we mainly consider full-simulatable in simulation, which simulator can simulate any corruption cases. So we mainly consider non-adaptively malicious adversary in Oblivious Transfer protocols.
Secure computation is a powerful cryptographic tool that encompasses the evaluation of any multivariate function with arbitrary inputs from mutually distrusting parties. The oblivious transfer primitive serves is a basic building block for the general task of secure multi-party computation. Therefore, analyzing the security in the universal composability framework becomes mandatory when dealing with multi-party computation protocols composed of oblivious transfer subroutines. Furthermore, since the required number of oblivious transfer instances scales with the size of the circuits, oblivious transfer remains as a bottleneck for large-scale multi-party computation implementations. Techniques that allow one to extend a small number of oblivious transfers into a larger one in an efficient way make use of the oblivious transfer variant called randomized oblivious transfer. In this work, we present randomized versions of two known oblivious transfer protocols, one quantum and another post-quantum with ring learning with an error assumption. We then prove their security in the quantum universal composability framework, in a common reference string model.
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.
Because of the concise functionality of oblivious transfer (OT) protocols, they have been widely used as building blocks in secure multiparty computation and high-level protocols. The security of OT protocols built upon classical number theoretic problems, such as the discrete logarithm and factoring, however, is threatened as a result of the huge progress in quantum computing. Therefore, post-quantum cryptography is needed for protocols based on classical problems, and several proposals for post-quantum OT protocols exist. However, most post-quantum cryptosystems present their security proof only in the context of classical adversaries, not in the quantum setting. In this paper, we close this gap and prove the security of the lattice-based OT protocol proposed by Peikert et al. (CRYPTO, 2008), which is universally composably secure under the assumption of learning with errors hardness, in the quantum setting. We apply three general quantum security analysis frameworks. First, we apply the quantum lifting theorem proposed by Unruh (EUROCRYPT, 2010) to prove that the security of the lattice-based OT protocol can be lifted into the quantum world. Then, we apply two more security analysis frameworks specified for post-quantum cryptographic primitives, i.e., simple hybrid arguments (CRYPTO, 2011) and game-preserving reduction (PQCrypto, 2014).
A Framework For Fully-Simulatable h-Out-Of-n Oblivious Transfer
We present a framework for fully-simulatable h-out-of-n oblivious transfer (OThn) with security against non-adaptive malicious adversaries. The framework costs six communication rounds and costs at most 40n public-key operations in computational overhead. Compared with the known protocols for fully-simulatable oblivious transfer that works in the plain mode (where there is no trusted common reference string available) and proven to be secure under standard model (where there is no random oracle available), the instantiation based on the decisional Diffie-Hellman assumption of the framework is the most efficient one, no matter seen from communication rounds or computational overhead. Our framework uses three abstract tools, i.e., perfectly binding commitment, perfectly hiding commitment and our new smooth projective hash. This allows a simple and intuitive understanding of its security. We instantiate the new smooth projective hash under the lattice assumption, the decisional Diffie-Hellman assumption, the decisional N-th residuosity assumption, the decisional quadratic residuosity assumption. This indeed shows that the folklore that it is technically difficult to instantiate the projective hash framework under the lattice assumption is not true. What's more, by using this lattice-based hash and lattice-based commitment scheme, we gain a concrete protocol for OThn which is secure against quantum algorithms.