We use an RLWE-based key exchange scheme to construct a simple and efficient post-quantum oblivious transfer based on the Ring Learning with Errors assumption. We prove that our protocol is secure in the Universal Composability framework against static malicious adversaries in the random oracle model. The main idea of the protocol is that the receiver and the sender interact using the RLWE-based key exchange in such a way that the sender computes two keys, one of them shared with the receiver. It is infeasible for the sender to know which is the shared key and for the receiver to get information about the other one. The sender encrypts each message with each key using a symmetric-key encryption scheme and the receiver can only decrypt one of the ciphertexts. The protocol is extremely efficient in terms of computational and communication complexity, and thus a strong candidate for post-quantum applications.

In this paper we show how to totally break the fully homomorphic encryption scheme of eprint 2017/458.

Error reconciliation is an important technique for learning with error (LWE) and ring-LWE (RLWE)-based constructions. In this paper, we present a comparison analysis on two error reconciliation-based RLWE key exchange protocols: Ding et al. in 2012 (DING12) and Bos et al. in 2015 (BCNS15). We take them as examples to explain the core idea of error reconciliation, building key exchange over RLWE problem, implementation and real-world performance, and compare them comprehensively. We also analyse a LWE key exchange 'Frodo' that uses an improved error reconciliation mechanism in BCNS15. To the best of our knowledge, our work is the first to present at least 128-bit classic (80-bit quantum) and 256-bit classic (> 200-bit quantum) secure parameter choices for DING12 with efficient portable C/C++ implementations. Benchmark shows that our efficient implementation is 11× faster than BCNS15 and one key exchange execution only costs 0.07 ms on a four-year-old middle range CPU. Error reconciliation is 1.57× faster than BCNS15.

The SimpleMatrix encryption scheme as proposed by Tao et al. \cite{TD13} is one of the very few existing approaches to create a secure and efficient encryption scheme on the basis of multivariate polynomials. However, in its basic version, decryption failures occur with non-negligible probability. Although this problem has been addressed in several papers \cite{DP14,TX15}, a general solution to it is still missing. In this paper we propose an improved version of the SimpleMatrix scheme, which eliminates decryption failures completely and therefore solves the biggest problem of the SimpleMatrix encryption scheme. Additionally, we propose a second version of the scheme, which reduces the blow-up factor between plain and ciphertext size to a value arbitrary close to 1.

Authenticated Key Exchange (AKE) is a cryptographic scheme with the aim to establish a high-entropy and secret session key over a insecure communications network. \emph{Password}-Authenticated Key Exchange (PAKE) assumes that the parties in play share a simple password, which is cheap and human-memorable and is used to achieve the authentication. PAKEs are practically relevant as these features are extremely appealing in an age where most people access sensitive personal data remotely from more-and-more pervasive hand-held devices. Theoretically, PAKEs allow the secure computation and authentication of a high-entropy piece of data using a low-entropy string as a starting point. In this paper, we apply the recently proposed technique introduced in~\cite{DXX2012} to construct two lattice-based PAKE protocols enjoying a very simple and elegant design that is an parallel extension of the class of Random Oracle Model (ROM)-based protocols \msf{PAK} and \msf{PPK}~\cite{BMP2000,M2002}, but in the lattice-based setting. The new protocol resembling \msf{PAK} is three-pass, and provides \emph{mutual explicit authentication}, while the protocol following the structure of \msf{PPK} is two-pass, and provides \emph{implicit authentication}. Our protocols rely on the Ring-Learning-with-Errors (RLWE) assumption, and exploit the additive structure of the underlying ring. They have a comparable level of efficiency to \msf{PAK} and \msf{PPK}, which makes them highly attractive. We present a preliminary implementation of our protocols to demonstrate that they are both efficient and practical. We believe they are suitable quantum safe replacements for \msf{PAK} and \msf{PPK}.