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.
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.
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.
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.
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.
Oblivious Transfer (OT) is the fundamental building block of cryptographic protocols. In this paper we describe the simplest and most efficient protocol for 1-out-of- n OT to date, which is obtained by tweaking the Diffie-Hellman key-exchange protocol. The protocol achieves UC-security against active and adaptive corruptions in the random oracle model. Due to its simplicity, the protocol is extremely efficient and it allows to perform m 1-out-of- n OTs using only: Computation: (n+1)m+2 exponentiations ( mn for the receiver, mn+2 for the sender) and Communication: 32(m+1) bytes (for the group elements), and 2 mn ciphertexts. We also report on an implementation of the protocol using elliptic curves, and on a number of mechanisms we employ to ensure that our software is secure against active attacks too. Experimental results show that our protocol (thanks to both algorithmic and implementation optimizations) is at least one order of magnitude faster than previous work. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
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).