Efficient lattice (H)IBE in the standard model

We construct an efficient identity based encryption system based on the standard learning with errors (LWE) problem. Our security proof holds in the standard model. The key step in the construction is a family of lattices for which there are two distinct trapdoors for finding short vectors. One trapdoor enables the real system to generate short vectors in all lattices in the family. The other trapdoor enables the simulator to generate short vectors for all lattices in the family except for one. We extend this basic technique to an adaptively-secure IBE and a Hierarchical IBE.

Lattice mixing and vanishing trapdoors : a framework for fully secure short signatures and more

We propose a framework for adaptive security from hard random lattices in the standard model. Our approach borrows from the recent Agrawal-Boneh-Boyen families of lattices, which can admit reliable and punctured trapdoors, respectively used in reality and in simulation. We extend this idea to make the simulation trapdoors cancel not for a specific forgery but on a non-negligible subset of the possible challenges. Conceptually, we build a compactly representable, large family of input-dependent “mixture” lattices, set up with trapdoors that “vanish” for a secret subset which we hope the forger will target. Technically, we tweak the lattice structure to achieve “naturally nice” distributions for arbitrary choices of subset size. The framework is very general. Here we obtain fully secure signatures, and also IBE, that are compact, simple, and elegant.

Lattice-based certificateless public-key encryption in the standard model

The notion of certificateless public-key encryption (CL-PKE) was introduced by Al-Riyami and Paterson in 2003 that avoids the drawbacks of both traditional PKI-based public-key encryption (i.e., establishing public-key infrastructure) and identity-based encryption (i.e., key escrow). So CL-PKE like identity-based encryption is certificate-free, and unlike identity-based encryption is key escrow-free. In this paper, we introduce simple and efficient CCA-secure CL-PKE based on (hierarchical) identity-based encryption. Our construction has both theoretical and practical interests. First, our generic transformation gives a new way of constructing CCA-secure CL-PKE. Second, instantiating our transformation using lattice-based primitives results in a more efficient CCA-secure CL-PKE than its counterpart introduced by Dent in 2008.

Lattice-based completely non-malleable public-key encryption in the standard model

An encryption scheme is non-malleable if giving an encryption of a message to an adversary does not increase its chances of producing an encryption of a related message (under a given public key). Fischlin introduced a stronger notion, known as complete non-malleability, which requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti later proposed a comparison-based definition of this security notion, which is more in line with the well-studied definitions proposed by Bellare et al. The authors also provide additional feasibility results by proposing two constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Therefore, the only previously known completely non-malleable (and non-interactive) scheme in the standard model, is quite inefficient as it relies on generic NIZK approach. They left the existence of efficient schemes in the common reference string model as an open problem. Recently, two efficient public-key encryption schemes have been proposed by Libert and Yung, and Barbosa and Farshim, both of them are based on pairing identity-based encryption. At ACISP 2011, Sepahi et al. proposed a method to achieve completely non-malleable encryption in the public-key setting using lattices but there is no security proof for the proposed scheme. In this paper we review the mentioned scheme and provide its security proof in the standard model. Our study shows that Sepahi’s scheme will remain secure even for post-quantum world since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best known classical (i.e., non-quantum) algorithms.

Lattice-based threshold changeability for standard shamir sectret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a nonstandard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the standard Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. Our method is a new positive cryptographic application for lattice reduction algorithms, inspired by recent work on lattice-based list decoding of Reed-Solomon codes with noise bounded in the Lee norm. We use fundamental results from the theory of lattices (geometry of numbers) to prove quantitative statements about the information-theoretic security of our construction. These lattice-based security proof techniques may be of independent interest.

Expressive cryptography : lattice perspectives

The invention of asymmetric encryption back in the seventies was a conceptual leap that vastly increased the expressive power of encryption of the times. For the first time, it allowed the sender of a message to designate the intended recipient in an cryptographic way, expressed as a “public key” that was related to but distinct from the “private key” that, alone, embodied the ability to decrypt. This made large-scale encryption a practical and scalable endeavour, and more than anything else—save the internet itself—led to the advent of electronic commerce as we know and practice it today.

Lattice-based completely non-malleable PKE in the standard model

This paper presents ongoing work toward constructing efficient completely non-malleable public-key encryption scheme based on lattices in the standard (common reference string) model. An encryption scheme is completely non-malleable if it requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti proposed two inefficient constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Recently, two efficient public-key encryption schemes have been proposed, both of them are based on pairing identity-based encryption.

Lattice-based threshold-changeability for standard CRT secret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have secure channels between shareholders. In contrast, we show how to increase the threshold parameter of the standard CRT secret-sharing scheme without secure channels between the shareholders. Our method can thus be applied to existing CRT schemes even if they were set up without consideration to future threshold increases. Our method is a positive cryptographic application for lattice reduction algorithms, and we also use techniques from lattice theory (geometry of numbers) to prove statements about the correctness and information-theoretic security of our constructions.

Lattice-based threshold-changeability for standard Shamir secret-sharing schemes

We consider the problem of increasing the threshold parameter of a secret-sharing scheme after the setup (share distribution) phase, without further communication between the dealer and the shareholders. Previous solutions to this problem require one to start off with a non-standard scheme designed specifically for this purpose, or to have communication between shareholders. In contrast, we show how to increase the threshold parameter of the standard Shamir secret-sharing scheme without communication between the shareholders. Our technique can thus be applied to existing Shamir schemes even if they were set up without consideration to future threshold increases. Our method is a new positive cryptographic application for lattice reduction algorithms, inspired by recent work on lattice-based list decoding of Reed-Solomon codes with noise bounded in the Lee norm. We use fundamental results from the theory of lattices (Geometry of Numbers) to prove quantitative statements about the information-theoretic security of our construction. These lattice-based security proof techniques may be of independent interest.

Phonon modes of MgB2 : Super-lattice structures and spectral response

Micrometre-sized MgB2 crystals of varying quality, synthesized at low temperature and autogeneous pressure, are compared using a combination of Raman and Infra-Red (IR) spectroscopy. These data, which include new peak positions in both spectroscopies for high quality MgB2, are interpreted using DFT calculations on phonon behaviour for symmetry-related structures. Raman and IR activity additional to that predicted by point group analyses of the P6/mmm symmetry are detected. These additional peaks, as well as the overall shapes of calculated phonon dispersion (PD) models are explained by assuming a double super-lattice, consistent with a lower symmetry structure for MgB2. A 2x super-lattice in the c-direction allows a simple correlation of the pair breaking energy and the superconducting gap by activation of corresponding acoustic frequencies. A consistent physical interpretation of these spectra is obtained when the position of a phonon anomaly defines a super-lattice modulation in the a-b plane.

Mismatch negativity in recent-onset and chronic schizophrenia : a current source density analysis

Mismatch negativity (MMN) is a component of the event-related potential elicited by deviant auditory stimuli. It is presumed to index pre-attentive monitoring of changes in the auditory environment. MMN amplitude is smaller in groups of individuals with schizophrenia compared to healthy controls. We compared duration-deviant MMN in 16 recent-onset and 19 chronic schizophrenia patients versus age- and sex-matched controls. Reduced frontal MMN was found in both patient groups, involved reduced hemispheric asymmetry, and was correlated with Global Assessment of Functioning (GAF) and negative symptom ratings. A cortically-constrained LORETA analysis, incorporating anatomical data from each individual's MRI, was performed to generate a current source density model of the MMN response over time. This model suggested MMN generation within a temporal, parietal and frontal network, which was right hemisphere dominant only in controls. An exploratory analysis revealed reduced CSD in patients in superior and middle temporal cortex, inferior and superior parietal cortex, precuneus, anterior cingulate, and superior and middle frontal cortex. A region of interest (ROI) analysis was performed. For the early phase of the MMN, patients had reduced bilateral temporal and parietal response and no lateralisation in frontal ROIs. For late MMN, patients had reduced bilateral parietal response and no lateralisation in temporal ROIs. In patients, correlations revealed a link between GAF and the MMN response in parietal cortex. In controls, the frontal response onset was 17 ms later than the temporal and parietal response. In patients, onset latency of the MMN response was delayed in secondary, but not primary, auditory cortex. However amplitude reductions were observed in both primary and secondary auditory cortex. These latency delays may indicate relatively intact information processing upstream of the primary auditory cortex, but impaired primary auditory cortex or cortico-cortical or thalamo-cortical communication with higher auditory cortices as a core deficit in schizophrenia.

Gray matter deficits, mismatch negativity, and outcomes in schizophrenia

Reduced mismatch negativity (MMN) in response to auditory change is a well-established finding in schizophrenia and has been shown to be correlated with impaired daily functioning, rather than with hallmark signs and symptoms of the disorder. In this study, we investigated (1) whether the relationship between reduced MMN and impaired daily functioning is mediated by cortical volume loss in temporal and frontal brain regions in schizophrenia and (2) whether this relationship varies with the type of auditory deviant generating MMN. MMN in response to duration, frequency, and intensity deviants was recorded from 18 schizophrenia subjects and 18 pairwise age- and gender-matched healthy subjects. Patients’ levels of global functioning were rated on the Social and Occupational Functioning Assessment Scale. High-resolution structural magnetic resonance scans were acquired to generate average cerebral cortex and temporal lobe models using cortical pattern matching. This technique allows accurate statistical comparison and averaging of cortical measures across subjects, despite wide variations in gyral patterns. MMN amplitude was reduced in schizophrenia patients and correlated with their impaired day-to-day function level. Only in patients, bilateral gray matter reduction in Heschl’s gyrus, as well as motor and executive regions of the frontal cortex, correlated with reduced MMN amplitude in response to frequency deviants, while reduced gray matter in right Heschl’s gyrus also correlated with reduced MMN to duration deviants. Our findings further support the importance of MMN reduction in schizophrenia by linking frontotemporal cerebral gray matter pathology to an automatically generated event-related potential index of daily functioning.

Functional neuroanatomy of auditory mismatch processing : an event-related fMRI study of duration-deviant oddballs

This study was designed to identify the neural networks underlying automatic auditory deviance detection in 10 healthy subjects using functional magnetic resonance imaging. We measured blood oxygenation level-dependent contrasts derived from the comparison of blocks of stimuli presented as a series of standard tones (50 ms duration) alone versus blocks that contained rare duration-deviant tones (100 ms) that were interspersed among a series of frequent standard tones while subjects were watching a silent movie. Possible effects of scanner noise were assessed by a “no tone” condition. In line with previous positron emission tomography and EEG source modeling studies, we found temporal lobe and prefrontal cortical activation that was associated with auditory duration mismatch processing. Data were also analyzed employing an event-related hemodynamic response model, which confirmed activation in response to duration-deviant tones bilaterally in the superior temporal gyrus and prefrontally in the right inferior and middle frontal gyri. In line with previous electrophysiological reports, mismatch activation of these brain regions was significantly correlated with age. These findings suggest a close relationship of the event-related hemodynamic response pattern with the corresponding electrophysiological activity underlying the event-related “mismatch negativity” potential, a putative measure of auditory sensory memory.

Predicting tours and probabilistic simulation for BKZ lattice reduction algorithm

We investigate the terminating concept of BKZ reduction first introduced by Hanrot et al. [Crypto'11] and make extensive experiments to predict the number of tours necessary to obtain the best possible trade off between reduction time and quality. Then, we improve Buchmann and Lindner's result [Indocrypt'09] to find sub-lattice collision in SWIFFT. We illustrate that further improvement in time is possible through special setting of SWIFFT parameters and also through the combination of different reduction parameters adaptively. Our contribution also include a probabilistic simulation approach top-up deterministic simulation described by Chen and Nguyen [Asiacrypt'11] that can able to predict the Gram-Schmidt norms more accurately for large block sizes.

Orientational relaxation in a random dipolar lattice: Wave-number and frequency dependence

In order to understand the role of translational modes in the orientational relaxation in dense dipolar liquids, we have carried out a computer ''experiment'' where a random dipolar lattice was generated by quenching only the translational motion of the molecules of an equilibrated dipolar liquid. The lattice so generated was orientationally disordered and positionally random. The detailed study of orientational relaxation in this random dipolar lattice revealed interesting differences from those of the corresponding dipolar liquid. In particular, we found that the relaxation of the collective orientational correlation functions at the intermediate wave numbers was markedly slower at the long times for the random lattice than that of the liquid. This verified the important role of the translational modes in this regime, as predicted recently by the molecular theories. The single-particle orientational correlation functions of the random lattice also decayed significantly slowly at long times, compared to those of the dipolar liquid.