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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 ...
Approximate Trapdoors for Lattices and Smaller Hash-and-Sign Signatures
Digital Signature Lattice
2019/9/16
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...
On the Non-Existence of Short Vectors in Random Module Lattices
Lattice-based cryptography Fiat-Shamir signatures module lattices
2019/8/30
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...
Simplified Revocable Hierarchical Identity-Based Encryption from Lattices
Lattices Identity-based encryption Revocation
2019/8/14
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...
Tweaking the Asymmetry of Asymmetric-Key Cryptography on Lattices: KEMs and Signatures of Smaller Sizes
lattice public-key encryption digital signature
2019/5/21
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...
Approx-SVP in Ideal Lattices with Pre-processing
heuristic assumptions pre-processing phase outputs
2019/2/28
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...
Group Signatures without NIZK: From Lattices in the Standard Model
Group signatures Lattices Attribute-based signatures
2019/2/28
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...
Watermarking PRFs from Lattices: Stronger Security via Extractable PRFs
watermarking lattices PRFs
2018/11/5
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...
Floppy-Sized Group Signatures from Lattices
Lattices Group Signature Verifiable Encryption
2018/5/22
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...
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...
Polynomial Time Bounded Distance Decoding near Minkowski’s Bound in Discrete Logarithm Lattices
lattice techniques Bounded Distance Decoding Minkowski's bound
2018/2/9
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...
NTRU-LPR IND-CPA: A New Ideal Lattices-based Scheme
Lattices-based Post-quantum Cryptography NTRUEncrypt NTRU-Prime
2018/1/31
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 ...