Hard Lattice Research Articles

A new lattice-based password authenticated key exchange scheme with anonymity and reusable key.

In this article, we propose a novel bilateral generalization inhomogenous short integer solution (BiGISIS)-based password-authenticated key exchange (PAKE) scheme for post-quantum era security. The hardness assumption of the constructed PAKE is based on newly proposed hard lattice problem, BiGISIS. The main aim of this article is to provide a solution for the post-quantum secure PAKE scheme, which is one of the open problems in the literature. The proposed PAKE is the first BiGISIS-based PAKE that satisfies anonymity and reusable key features. The bilateral-pasteurization (BiP) approach is used to obtain the reusable key, and anonymity is achieved thanks to the additional identity components and hash functions. The reusable key structure reduces the time in the key generation, and anonymity prevents illegal user login attempts. The security analysis is done by following the real-or-random (RoR) model assumptions. As a result of security examinations, perfect forward secrecy (PFS) and integrity are satisfied, and the resistance against eavesdropping, manipulation-based attack (MBA), hash function simulation, impersonation, signal leakage attack (SLA), man-in-the-middle (MitM), known-key security (KKS), and offline password dictionary attack (PDA) is captured. According to the comparison analysis, the proposed PAKE is the first SLA-resistant lattice-based PAKE with reusable key and anonymity properties.

Polar sampler: A novel Bernoulli sampler using polar codes with application to integer Gaussian sampling

Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post-quantum public-key cryptography. As the standardization process takes place, optimizing specific parts of proposed schemes, e.g., Bernoulli sampling and integer Gaussian sampling, becomes a worthwhile endeavor. In this work, we propose a novel Bernoulli sampler based on polar codes, dubbed “polar sampler”. The polar sampler is information theoretically optimum in the sense that the number of uniformly random bits it consumes approaches the entropy bound asymptotically. It also features quasi-linear complexity and constant-time implementation. An integer Gaussian sampler is developed using multilevel polar samplers. Our algorithm becomes effective when sufficiently many samples are required at each query to the sampler. Security analysis is given based on Kullback–Leibler divergence and Rényi divergence. Experimental and asymptotic comparisons between our integer Gaussian sampler and state-of-the-art samplers verify its efficiency in terms of entropy consumption, running time and memory cost. We envisage that the proposed Bernoulli sampler can find other applications in cryptography in addition to Gaussian sampling.

R-LWE-Based Distributed Key Generation and Threshold Decryption

Ever since the appearance of quantum computers, prime factoring and discrete logarithm-based cryptography have been questioned, giving birth to the so-called post-quantum cryptography. The most prominent field in post-quantum cryptography is lattice-based cryptography, protocols that are proved to be as difficult to break as certain hard lattice problems like Learning with Errors (LWE) or Ring Learning with Errors (R-LWE). Furthermore, the application of cryptographic techniques to different areas, like electronic voting, has also nourished a great interest in distributed cryptography. In this work, we will give two original threshold protocols based in the lattice problem R-LWE: one for key generation and one for decryption. We will prove them both correct and secure under the assumption of hardness of some well-known lattice problems. Finally, we will give a rough implementation of the protocols in C to give some tentative results about their viability, in particular our model generates keys in the order of 103 ms and decrypts and encrypts in the order of 102 ms.

Analysing the potential of transport triggered architecture for lattice-based cryptography algorithms

Lattice-based structures offer numerous possibilities for post-quantum cryptography. Recently, many post-quantum cryptography algorithms have been built on hard lattice problems. The three of the remaining four algorithms in the final round of the NIST Standardization Process rely on lattice-based methods. However, suitable processor architectures for these algorithms have not been sufficiently investigated. This study examines the potential advantages of transport triggered architecture for these algorithms. We compare popular 64-bit RISC-V processors with our conceptual transport triggered architecture processor over reference software implementations. Our processor provides better results than RISC-V competitors, regardless of the algorithm. It seems to be up to 3× faster, 1.6×-2× smaller, and consumes 1.3×-3.6× less energy than the compared RISC-V cores. Thus, an alternative base architecture is proposed for post-quantum cryptography processor development for embedded systems. The most critical shortcoming of the proposed architecture is the lack of compatible intellectual property core support for system-on-chip designs. We share comparative analyses with test results for different core configurations.

Droplet condensation in the lattice gas with density functional theory.

A density functional for the lattice gas with next-neighbor attractions (Ising model) from fundamental measure theory is applied to the problem of droplet states in three-dimensional, finite systems. The density functional is constructed via an auxiliary model with hard lattice gas particles and lattice polymers to incorporate the attractions. Similar to previous simulation studies, the sequence of droplets changing to cylinders and to planar slabs is found upon increasing the average density ρ[over ¯] in the system. Owing to the discreteness of the lattice, additional effects in the state curve for the chemical potential μ(ρ[over ¯]) are seen upon lowering the temperature away from the critical temperature [oscillations in μ(ρ[over ¯]) in the slab portion and spiky undulations in μ(ρ[over ¯]) in the cylinder portion as well as an undulatory behavior of the radius of the surface of tension R_{s} in the droplet region]. This behavior in the cylinder and droplet region is related to washed-out layering transitions at the surface of liquid cylinders and droplets. The analysis of the large-radius behavior of the surface tension γ(R_{s}) gave a dominant contribution ∝1/R_{s}^{2}, although the consistency of γ(R_{s}) with the asymptotic behavior of the radius-dependent Tolman length seems to suggest a weak logarithmic contribution ∝lnR_{s}/R_{s}^{2} in γ(R_{s}). The coefficient of this logarithmic term is smaller than a universal value derived with field-theoretic methods.

Efficient Implementations of Sieving and Enumeration Algorithms for Lattice-Based Cryptography

The security of lattice-based cryptosystems is based on solving hard lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). Various cryptanalysis algorithms such as (Pro)GaussSieve, HashSieve, ENUM, and BKZ have been proposed to solve these hard problems. Several implementations of these algorithms have been developed. On the other hand, the implementations of these algorithms are expected to be efficient in terms of run time and memory space. In this paper, a modular software package/library containing efficient implementations of GaussSieve, ProGaussSieve, HashSieve, and BKZ algorithms is developed. These implementations are considered efficient in terms of run time. While constructing this software library, some modifications to the algorithms are made to increase the performance. Then, the run times of these implementations are compared with the others. According to the experimental results, the proposed GaussSieve, ProGaussSieve, and HashSieve implementations are at least 70%, 75%, and 49% more efficient than previous ones, respectively.

Post-Quantum Cryptosystems for Internet-of-Things: A Survey on Lattice-Based Algorithms

The latest quantum computers have the ability to solve incredibly complex classical cryptography equations particularly to decode the secret encrypted keys and making the network vulnerable to hacking. They can solve complex mathematical problems almost instantaneously compared to the billions of years of computation needed by traditional computing machines. Researchers advocate the development of novel strategies to include data encryption in the post-quantum era. Lattices have been widely used in cryptography, somewhat peculiarly, and these algorithms have been used in both; (a) cryptoanalysis by using lattice approximation to break cryptosystems; and (b) cryptography by using computationally hard lattice problems (non-deterministic polynomial time hardness) to construct stable cryptographic functions. Most of the dominant features of lattice-based cryptography (LBC), which holds it ahead in the post-quantum league, include resistance to quantum attack vectors, high concurrent performance, parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. While these methods offer possible security for classical cryptosytems in theory and experimentation, their implementation in energy-restricted Internet-of-Things (IoT) devices requires careful study of regular lattice-based implantation and its simplification in lightweight lattice-based cryptography (LW-LBC). This streamlined post-quantum algorithm is ideal for levelled IoT device security. The key aim of this survey was to provide the scientific community with comprehensive information on elementary mathematical facts, as well as to address real-time implementation, hardware architecture, open problems, attack vectors, and the significance for the IoT networks.

Three Strategies for Improving Shortest Vector Enumeration Using GPUs

Hard Lattice problems are assumed to be one of the most promising problems for generating cryptosystems that are secure in quantum computing. The shortest vector problem (SVP) is one of the most famous lattice problems. In this paper, we present three improvements on GPU-based parallel algorithms for solving SVP using the classical enumeration and pruned enumeration. There are two improvements for preprocessing: we use a combination of randomization and the Gaussian heuristic to expect a better basis that leads rapidly to a shortest vector and we expect the level on which the exchanging data between CPU and GPU is optimized. In the third improvement, we improve GPU-based implementation by generating some points in GPU rather than in CPU. We used NVIDIA GeForce GPUs of type GTX 1060 6G. We achieved a significant improvement upon Hermans’s improvement. The improvements speed up the pruned enumeration by a factor of almost 2.5 using a single GPU. Additionally, we provided an implementation for multi-GPUs by using two GPUs. The results showed that our algorithm of enumeration is scalable since the speedups achieved using two GPUs are almost faster than Hermans’s improvement by a factor of almost 5. The improvements also provided a high speedup for the classical enumeration. The speedup achieved using our improvements and two GPUs on a challenge of dimension 60 is almost faster by factor 2 than Correia’s parallel implementation using a dual-socket machine with 16 physical cores and simultaneous multithreading technology.

Nano Ball-Milling Using Titania Nanoparticles to Anchor Cesium Lead Bromine Nanocrystals and Energy Transfer Characteristics in TiO2 @CsPbBr3 Architecture.

Recently, all-inorganic halide perovskite (CsPbX3 , (X= Cl, Br, and I)) nanocrystals (NCs) based hybrid architectures have attracted extensive attention owing to their distinct luminescence characteristics. However, due to stress and lattice mismatch, it is still a challenge to construct heterojunctions between perovskite NCs and the nanostructures with different lattice parameters and non-cubic contour. In this work, a room temperature mechanochemical method is presented to construct TiO2 @CsPbBr3 hybrid architectures, in which TiO2 nanoparticles (NPs) with a hard lattice as nano "balls" mill off the angles and anchor to the CsPbBr3 NCs with a soft lattice. On the contrary, to ball-mill without TiO2 or with conventional ceramics balls replacing TiO2 , CsPbBr3 NCs still maintain cubic contour deriving from their cubic crystal structures. Moreover, the TiO2 @CsPbBr3 architectures display distinct improvement of photoluminescence quantum yields and more excellent thermal stability in contrast with pristine CsPbBr3 owing to the passivation of surface defect, small surface area, and energy transfer from CsPbBr3 to TiO2 . Meanwhile, there is distinct luminous decay characteristic under the radiation of UV and visible light due to the "on" and "off" TiO2 response. The method provides an alternative strategy to acquire other anchoring heterojunctions based on perovskite NCs for further regulating their luminescent characteristics.

Fatigue-Resistant elastomers

The resistance of a material to the growth of a crack is characterized by fracture toughness under monotonic load, and by fatigue threshold under cyclic load. The fatigue threshold of engineering elastomers is commonly limited to ∼50 J/m2, much below their toughness (103∼105 J/m2). Here we report fatigue-resistant elastomers with threshold beyond 500 J/m2. Such an elastomer is a composite of two elastomers: a lattice of a hard elastomer embedded in a matrix of soft elastomer. Both the hard and soft elastomers are elastically stretchable, with small hysteresis. At a crack front in the composite, the soft matrix shears greatly, which de-concentrates stress in the hard lattice. When the crack advances in the composite, the energy dissipated scales with the feature size of the lattice. By contrast, when a crack advances in a homogeneous elastomer, the energy dissipated scales with the mesh size of the polymer network. The fatigue-resistant elastomers open new opportunities for applications requiring stretchable materials.

A new method of generating hard random lattices with short bases

This paper first gives a regularity theorem and its corollary. Then, a new construction of generating hard random lattices with short bases is obtained by using this corollary. This construction is from a new perspective and uses a random matrix whose entries obeyed Gaussian sampling which ensures that the corresponding schemes have a wider application future in cryptography area. Moreover, this construction is more specific than the previous constructions, which makes it can be implemented easier in practical applications.

Design of lattice‐based ElGamal encryption and signature schemes using SIS problem

AbstractThe emerging technologies like quantum computing and cloud computing have a complex computing power and can break the security of the classical cryptographic constructions (like ElGamal's cryptosystem). Thus, we were motivated to work on hard lattice problems, which are more complex and can resist these new modern technologies. In this proposal, we present a lattice‐based version of discrete logarithm problem‐based ElGamal public‐key encryption and signature schemes that exhibit strong security features and efficient implementation. The security of these presented schemes is based on the worst‐case hardness of approximating a small integer vector in their corresponding lattice. Furthermore, this proposed work illustrates a security proof of the proposed schemes and shows that the presented schemes are well protected in the modern computing environment. The performance analysis and comparison with classical ElGamal schemes and recent lattice‐based schemes are also made, and it is seen that the proposed schemes achieve better performance.

Identity-based blind signature from lattices

Blind signature allows a user to get a signature of a signer on an arbitrary message, and the verifier can convince that the signature is indeed signed by the signer without leaking any information about the message. This property is necessary when the user’s privacy needs protection, such as a bank bill, a trade secret, etc. As an alternative of public key infrastructure, the identity-based system can simplify the key management procedures in certificate-based public key systems. Inspired by the requirement of identity-based blind signature in the post quantum world, we research on identity-based blind signature based on hard lattice problems under the random Oracle model. We propose a construction built upon the blind signature by Ruckert, and it is proved to be one-more unforgeable against selective identity and chosen message attacks (sID-CMA) and unconditionally blind. The proposed scheme has 2 moves, and its security can be reduced to the small integer solution (SIS) problem.

Short lattice signatures with constant‐size public keys

AbstractA digital signature scheme allows a signer to sign electronic messages using his or her secret key, and any verifier can validate the correctness according to a given verification procedure. Although a variety of lattice‐based signature schemes have been proposed in the past few years, there does not exist a scheme that has short signatures and constant‐size public keys simultaneously. In this paper, we propose a new method for constructing short lattice signatures with constant‐size public keys in the standard model. In our scheme, each signature contains a low‐dimensional lattice vector and the public key only contains three matrices plus a vector. Compared with previous constructions, our scheme is very simple and does not require any complex homomorphic computation. In order for security proof to work, we introduce a new hard lattice problem, called variant small integer solution (Variant‐SIS), and give the security reduction from small integer solution to Variant‐SIS. Then we define a family of hash functions based on the hardness of Variant‐SIS and prove its security properties, including one‐wayness and collision resistance. As a matter of independent interest, the proposed hard problem may be useful in many other lattice‐based cryptographic constructions. Last, the comparison with similar works demonstrates the superiority of our scheme. Copyright © 2016 John Wiley & Sons, Ltd.

A new certificateless signature scheme under enhanced security models

AbstractIn identity‐based signatures, the key generation center (KGC) always knows user private key, and thus, it can always impersonate the user. Certificateless signatures were introduced by Al‐Riyami and Paterson to solve this key escrow problem of identity‐based signatures in 2003. In certificateless signatures, the private key is determined by neither the user nor the KGC. In 2007, Huang et al. revisited the security models of certificateless signatures. They divided potential adversaries according to their attack power into normal, strong and super adversaries. On the other hand, Au et al. introduced a new attack called malicious‐but‐passive KGC attack in the same year. In the new attack, KGC that holds the master secret key is assumed malicious at the very beginning of the setup phase of the system. The previous schemes that can be proven secure against malicious‐but‐passive KGC attack provided only the security against strong adversaries. In this paper, we construct the first certificateless signature scheme that can be proven secure against malicious‐but‐passive KGC attack of super adversaries. Moreover, our scheme is still secure when the adversary is allowed to obtain valid signatures on the target identity and message. Our construction is based on the hard lattice problems in the random oracle model.Copyright © 2014 John Wiley & Sons, Ltd.

Efficient verifiably encrypted signatures from lattices

Verifiably encrypted signature schemes can convince a verifier that a given ciphertext is an encryption of an ordinary signature on a given message and the ordinary signature can be recovered by the third party, called adjudicator. In 2010, Ruckert et al. proposed a general construction for the verifiably encrypted signatures, and then, they also showed that there exist the lattice-based verifiably encrypted signature schemes. Their constructions are very insightful, but their schemes need an extra adjudication setup phase and Merkle trees, so they have large parameters and keys, that is, they are inefficient. Also, their schemes provide only the limited signature capacity because the signing keys should be reissued after generating $$k$$ k th verifiably encrypted signatures. To overcome the weaknesses of Ruckert et al.'s scheme, we construct a verifiably encrypted signature scheme based on the hard lattice problems. Our scheme provides the full functionality, i.e., the signatures can be generated without any limitations and does not need any extra adjudication setup phases. Moreover, the size of the secret keys in our scheme is constant. Our scheme provides unforgeability, opacity, extractability, and abuse-freeness in the random oracle model.

Characteristics of Residual Stress by Water-Jet Peening

The specimen material was austenitic stainless steel, SUS316L. The residual stress was induced by water-jet peening. The residual stress was measured using the 311 diffraction with conventional X-rays. The measured residual stress showed the equi-biaxial stress state. To investigate thermal stability of the residual stress, the specimen was aged thermally at 773 K in air to 1000 h. The residual stress kept the equi-biaxial stress state against the thermal aging. Lattice plane dependency of the residual stress induced by water-jet peening was evaluated using hard synchrotron X-rays. The residual stress measured by the soft lattice plane showed the equi-biaxial stress state, but the residual stress measured by the hard lattice plane did not. In addition, the distributions of the residual stress in the depth direction were measured using a strain scanning method with hard synchrotron X-rays and neutrons.

Hash Proof System Based on Lattice

We present a hash proof systems (HPS)based on hard lattice problems including learning with error (LWE) and inhomogeneous small integer solution (ISIS). Different from the HPS in past, ours is with error. That is to say, the deterministic private evaluation algorithm is not always equivalent to the deterministic public evaluation algorithm. The difference between them is one or zero. We also show how to construct a public-key encryption scheme which is semantically secure against key-leakage attacks in the standard model using our HPS based on lattice. Compared with previous cryptosystem based on lattice, our construction needs bigger public key space but fewer operations during encryption, and can resist quantum attacks because of the assumption on lattice problem.

Phase transition and temperature stability of piezoelectric properties in Mn-modified Pb(Mg1/3Nb2/3)O3-PbZrO3-PbTiO3 ceramics

This study investigates the effect of two different Mn modifiers [MnO2 and Pb(Mn1/3Nb2/3)O3(PMnN)] on the of phase transitions in Pb(Mg1/3Nb2/3)O3-PbZrO3-PbTiO3 ceramics. The temperature dependence of polarization derived from measured pyroelectric current indicated change in nature of phase transition with MnO2 doping. This phenomenon was supported by the temperature evolution of the linear softening of low lying hard lattice mode as revealed by Raman analysis. The grain size was found to increase with MnO2 doping (5X) while decrease with PMnN modification (0.5X). Interestingly, the piezoelectric constant of MnO2 modified composition showed negligible degradation (<1%) even after heat treatment very close to the ferroelectric-paraelectric transition temperature.

Residual Stresses in Austenitic Stainless Steel due to High Strain Rate

Austenitic stainless steel (SUS316L) was used as specimen material, and the plate specimens were deformed plastically with a wide range of strain rates (6.67×10-5~ 6.70×102/s). The residual micro-stress for each lattice plane was measured with hard synchrotron X-rays. The residual macro-stress due to tensile deformation depended on strain rate. The residual micro-stresses varied from tension to compression, depending on the diffraction elastic constant. The soft lattice plane had tensile residual stress, and the hard lattice plane had compressive residual stress. The higher the strain rate, the smaller the difference in residual micro-stresses. The residual micro-stresses of the surfaces peened with the laser-peening or water-jet-peening were examined. Both surfaces had exhibited large compressive residual stress. The residual micro-stress on the peened surfaces showed a tendency opposite to residual micro-stress due to tensile deformation.