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The LLL algorithm takes as input a basis of a Euclidean lattice, and, within a polynomial number of operations, it outputs another basis of the same lattice but consisting of rather short vectors. We ...
We study a relaxed notion of lattice trapdoor called approximate trapdoor, which is defined to be able to invert Ajtai's one-way function approximately instead of exactly. The primary motivation of ou...
Recently, Lyubashevsky & Seiler (Eurocrypt 2018) showed that small polynomials in the cyclotomic ring Zq[X]/(Xn+1)Zq[X]/(Xn+1), where nn is a power of two, are invertible under special congruence cond...
As an extension of identity-based encryption (IBE), revocable hierarchical IBE (RHIBE) supports both key revocation and key delegation simultaneously, which are two important functionalities for crypt...
Lattice-based cryptosystems are less efficient than their number-theoretic counterparts (based on RSA, discrete logarithm, etc.) in terms of key and ciphertext (signature) sizes. For adequate security...
We describe an algorithm to solve the approximate Shortest Vector Problem for lattices corresponding to ideals of the ring of integers of an arbitrary number field KK. This algorithm has a pre-process...
In a group signature scheme, users can anonymously sign messages on behalf of the group they belong to, yet it is possible to trace the signer when needed. Since the first proposal of lattice-based gr...
Homomorphic secret sharing (HSS) is an analog of somewhat- or fully homomorphic encryption (S/FHE) to the setting of secret sharing, with applications including succinct secure computation, private ma...
Group signatures allow users of a group to sign messages anonymously in the name of the group, while incorporating a tracing mechanism to revoke anonymity and identify the signer of any message. Since...
A software watermarking scheme enables one to embed a "mark" (i.e., a message) within a program while preserving the program's functionality. Moreover, there is an extraction algorithm that recovers a...
We present the first lattice-based group signature scheme whose cryptographic artifacts are of size small enough to be usable in practice: for a group of 225225 users, signatures take 910 kB and publi...
In this paper, we first revisit the generic two-message key exchange (TMKE) scheme (which will be referred to as KF) introduced by Kurosawa and Furukawa (CT-RSA 2014). This protocol is mainly based on...
Multi-Theorem Preprocessing NIZKs from Lattices     NIZK  CRS       2018/3/23
Non-interactive zero-knowledge (NIZK) proofs are fundamental to modern cryptography. Numerous NIZK constructions are known in both the random oracle and the common reference string (CRS) models. In th...
We propose a concrete family of dense lattices of arbitrary dimension n in which the lattice Bounded Distance Decoding (BDD) problem can be solved in deterministic polynomial time. This construction i...
In this paper, we propose NTRU-LPR IND-CPA, a new secure scheme based on the decisional variant of Bounded Distance Decoding problem over rings (DR-BDD). This scheme is IND-CPA secure and has two KEM ...

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