## CryptoDB

### Jiang Zhang

#### Affiliation: State Key Laboratory of Cryptology, China

#### Publications

**Year**

**Venue**

**Title**

2020

PKC

Tweaking the Asymmetry of Asymmetric-Key Cryptography on Lattices: KEMs and Signatures of Smaller Sizes
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Abstract

Currently, 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 the former typically needs thousands of bytes while in contrast the latter only requires at most hundreds of bytes. This significant difference has become one of the main concerns in replacing currently deployed public-key cryptosystems with lattice-based ones. Observing the inherent asymmetries in existing lattice-based cryptosystems, we propose asymmetric variants of the (module-)LWE and (module-)SIS assumptions, which yield further size-optimized KEM and signature schemes than those from standard counterparts. Following the framework of Lindner and Peikert (CT-RSA 2011) and the Crystals-Kyber proposal (EuroS&P 2018), we propose an IND-CCA secure KEM scheme from the hardness of the asymmetric module-LWE (AMLWE), whose asymmetry is fully exploited to obtain shorter public keys and ciphertexts. To target at a 128-bit quantum security, the public key (resp., ciphertext) of our KEM only has 896 bytes (resp., 992 bytes). Our signature scheme bears most resemblance to and improves upon the Crystals-Dilithium scheme (ToCHES 2018). By making full use of the underlying asymmetric module-LWE and module-SIS assumptions and carefully selecting the parameters, we construct an SUF-CMA secure signature scheme with shorter public keys and signatures. For a 128-bit quantum security, the public key (resp., signature) of our signature scheme only has 1312 bytes (resp., 2445 bytes). We adapt the best known attacks and their variants to our AMLWE and AMSIS problems and conduct a comprehensive and thorough analysis of several parameter choices (aiming at different security strengths) and their impacts on the sizes, security and error probability of lattice-based cryptosystems. Our analysis demonstrates that AMLWE and AMSIS problems admit more flexible and size-efficient choices of parameters than the respective standard versions.

2019

ASIACRYPT

Valiant’s Universal Circuits Revisited: An Overall Improvement and a Lower Bound
Abstract

A universal circuit (UC) is a general-purpose circuit that can simulate arbitrary circuits (up to a certain size n). At STOC 1976 Valiant presented a graph theoretic approach to the construction of UCs, where a UC is represented by an edge universal graph (EUG) and is recursively constructed using a dedicated graph object (referred to as supernode). As a main end result, Valiant constructed a 4-way supernode of size 19 and an EUG of size $$4.75n\log n$$ (omitting smaller terms), which remained the most size-efficient even to this day (after more than 4 decades).Motivated by the emerging applications of UCs in various privacy preserving computation scenarios, we revisit Valiant’s universal circuits, and propose a 4-way supernode of size 18, and an EUG of size $$4.5n\log n$$. As confirmed by our implementations, we reduce the size of universal circuits (and the number of AND gates) by more than 5% in general, and thus improve upon the efficiency of UC-based cryptographic applications accordingly. Our approach to the design of optimal supernodes is computer aided (rather than by hand as in previous works), which might be of independent interest. As a complement, we give lower bounds on the size of EUGs and UCs in Valiant’s framework, which significantly improves upon the generic lower bound on UC size and therefore reduces the gap between theory and practice of universal circuits.

2019

ASIACRYPT

Collision Resistant Hashing from Sub-exponential Learning Parity with Noise
Abstract

The Learning Parity with Noise (LPN) problem has recently found many cryptographic applications such as authentication protocols, pseudorandom generators/functions and even asymmetric tasks including public-key encryption (PKE) schemes and oblivious transfer (OT) protocols. It however remains a long-standing open problem whether LPN implies collision resistant hash (CRH) functions. Inspired by the recent work of Applebaum et al. (ITCS 2017), we introduce a general construction of CRH from LPN for various parameter choices. We show that, just to mention a few notable ones, under any of the following hardness assumptions (for the two most common variants of LPN) 1.constant-noise LPN is $$2^{n^{0.5+\varepsilon }}$$-hard for any constant $$\varepsilon >0$$;2.constant-noise LPN is $$2^{\varOmega (n/\log n)}$$-hard given $$q=\mathsf {poly}(n)$$ samples;3.low-noise LPN (of noise rate $$1/\sqrt{n}$$) is $$2^{\varOmega (\sqrt{n}/\log n)}$$-hard given $$q=\mathsf {poly}(n)$$ samples. there exists CRH functions with constant (or even poly-logarithmic) shrinkage, which can be implemented using polynomial-size depth-3 circuits with NOT, (unbounded fan-in) AND and XOR gates. Our technical route LPN $$\rightarrow $$ bSVP $$\rightarrow $$ CRH is reminiscent of the known reductions for the large-modulus analogue, i.e., LWE $$\rightarrow $$ SIS $$\rightarrow $$ CRH, where the binary Shortest Vector Problem (bSVP) was recently introduced by Applebaum et al. (ITCS 2017) that enables CRH in a similar manner to Ajtai’s CRH functions based on the Short Integer Solution (SIS) problem.Furthermore, under additional (arguably minimal) idealized assumptions such as small-domain random functions or random permutations (that trivially imply collision resistance), we still salvage a simple and elegant collision-resistance-preserving domain extender combining the best of the two worlds, namely, maximized (depth one) parallelizability and polynomial shrinkage. In particular, assume $$2^{n^{0.5+\varepsilon }}$$-hard constant-noise LPN or $$2^{n^{0.25+\varepsilon }}$$-hard low-noise LPN, we obtain a collision resistant hash function that evaluates in parallel only a single layer of small-domain random functions (or random permutations) and shrinks polynomially.

2016

CRYPTO

#### Program Committees

- Asiacrypt 2017

#### Coauthors

- Yu Chen (3)
- Sherman S. M. Chow (1)
- Özgür Dagdelen (1)
- Yi Deng (1)
- Jintai Ding (2)
- Shuqin Fan (1)
- Yanfei Guo (1)
- Chun Guo (1)
- Yongfei Han (1)
- Peng-Chor Leong (1)
- Xiangxue Li (1)
- Hanlin Liu (1)
- Phong Q. Nguyen (2)
- Baodong Qin (1)
- Michael Snook (2)
- Peng-Chong Tan (1)
- Jian Weng (1)
- Kang Yang (1)
- Yu Yu (5)
- Zhenfeng Zhang (7)
- Zongyang Zhang (1)
- Shuoyao Zhao (1)