A Classification of Differential Invariants for Multivariate Post-quantum Cryptosystems

Multivariate public key cryptography is a set of cryptographic schemes built from the NP-hardness of solving quadratic equations over finite fields, amongst which the hidden field equations (HFE) family of schemes remain the most famous. However, the original HFE scheme was insecure, and the follow-up modifications were shown to be still vulnerable to attacks. In this paper, we propose a new variant of the HFE scheme by considering the special equation x2=x defined over the finite field F3 when x=0,1. We observe that the equation can be used to further destroy the special structure of the underlying central map of the HFE scheme. It is shown that the proposed public key encryption scheme is secure against known attacks including the MinRank attack, the algebraic attacks, and the linearization equations attacks. The proposal gains some advantages over the original HFE scheme with respect to the encryption speed and public key size.

Authentication of public keys in asymmetric cryptography is an important objective to fulfil. Identity-based schemes are an efficient solution for this scenario. There are various identity-based schemes that are based on either factoring problem or DLP problem, but these problems can be solved in polynomial time using quantum computers. Multivariate cryptography is one of the main alternatives for the construction of post-quantum digital signature schemes. Digital signature construction needs modest computations in multivariate public key cryptography, so these schemes are considered quite efficient. In this paper, we present a new identity-based signature scheme in which the signature size and user key size are relatively small. The design of our proposed signature scheme is based on MQDSS construction.KeywordsMultivariate public key cryptographyMQ problemIdentity-based signature scheme

Post-Quantum Secure Inner Product Functional Encryption Using Multivariate Public Key Cryptography

Multivariate public key cryptography is one of the main candidates for post‐quantum cryptography. Rainbow, an improved (multi‐layer) version of unbalanced oil and vinegar (UOV), is one of the most famous multivariate signature schemes that is a promising candidate for NIST standardisation. At INDOCRYPT 2017, Beullens and Preneel introduced a new variant LUOV of UOV. Their idea is to generate a UOV scheme over the binary field and then lift it into a bigger field and hence dramatically reduce the public key size. In this study, the authors first theoretically deduce the choice for the subfield L (which is different from ) which results in smaller signature sizes (up to 40%). Moreover, they extend the idea to Rainbow and theoretically yield the optimal choice for the subfield L over which a Rainbow is generated before being lifted to K . As a result, they can reduce the public key size of the obtained Rainbow scheme up to at least 36%.

This paper presents an algebraic theory for analysis and design of linear multivariable feedback systems. The theory is developed in an algebraic setting sufficiently general to include, as special cases, continuous and discrete time systems, both lumped and distributed. Designs are implemented by construction of a controller with two vector inputs and one vector output. Use of controllers of this type is shown to generate convenient stability results, and convenient global parametrizations of all I/O maps and all disturbance-to-output maps achievable, for a given plant, by a stabilizing compensator. These parametrizations are then used to show that any such I/O map and any such disturbance-to-output map may be simultaneously realized by choice of an appropriate controller. In the special case of lumped systems, it is shown that the design theory. can be reduced to manipulations involving polynomial matrices only. The resulting design procedure is thus shown to be more efficient computationally. Finally, the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting. It is shown that the classical results on asymptotic tracking can be generalized to this setting. Additionally, sufficient conditions for robustness of asymptotic tracking, and robustness of stability are developed.

Background:Brief contact interventions such as telephone-based contacts appear to be useful in individuals who attempted suicide. Most studies of telephone-based contacts in such individuals typically consisted of frequent phone reminders for adherence to treatment and seeking help for mental health issues. Telephone-based psychosocial interventions that incorporate elements of supportive and problem-solving strategies are of interest in Indian settings due to their potential application in mitigating the wide mental health gap. Feasibility studies of telephone-based psychosocial interventions could help ascertain the difficulties that arise in the implementation of such treatments.Methods:A multicentric randomized controlled trial (RCT) is currently underway in general hospital settings in two Indian cities to study the efficacy of telephone-based psychosocial interventions in individuals with a recent suicide attempt, with routine telephone contacts (TCs) serving as the comparator. Prior to that RCT, this feasibility study was conducted to assess the acceptability of the telephone-based intervention and telephone contacts. Feasibility was assessed using dropout rates. Acceptability was assessed using participant-rated Likert-based visual analog scores from 0 to 10, with higher scores indicating greater acceptability.Results:Dropout rates and mean acceptability scores for telephone-based psychosocial interventions were 38.5% and 8.63, while those for TCs were 41.7% and 7.57, respectively.Conclusions:Telephone-based psychosocial interventions are feasible and acceptable in individuals with a recent suicide attempt.

ℳultivariate uadratic public key schemes have been suggested as early as 1985 by Matsumoto and Imai as an alternative for the RSA scheme. Since then, several schemes have been proposed, for example hidden field equations, unbalanced oil and vinegar schemes, and stepwise triangular schemes. All these schemes have a rather large key space for a secure choice of parameters. Surprisingly, the question of equivalent keys has not been discussed in the open literature until recently. In this article, we show that for all basic classes mentioned above, it is possible to reduce the private – and hence the public – key space by several orders of magnitude, i.e. the size of the set of possible private and hence public keys can be reduced. For the Matsumoto–Imai scheme, we are even able to show that the reductions we found are the only ones possible, i.e. that these reductions are tight. While the theorems developed in this article are of independent interest themselves as they broaden our understanding of ℳultivariate uadratic public key systems, we see applications of our results both in cryptanalysis and in memory efficient implementations of -schemes.

5G-based V2V broadcast communications: A security perspective

In this paper we propose a novel cryptanalytic method against multivariate schemes, which adapts differential cryptanalysis to this setting. In multivariate quadratic systems, the differential of the public key is a linear map and has invariants such as the dimension of the kernel. Using linear algebra, the study of this invariant can be used to gain information on the secret key. We successfully apply this new method to break the original Matsumoto-Imai cryptosystem using properties of the differential, thus providing an alternative attack against this scheme besides the attack devised by Patarin. Next, we present an attack against a randomised variant of the Matsumoto-Imai cryptosystem, called PMI. This scheme has recently been proposed by Ding, and according to the author, it resists all previously known attacks. We believe that differential cryptanalysis is a general and powerful method that can give additional insight on most multivariate schemes proposed so far.

We investigate public key encryption that allows the originator of a ciphertext to retrieve a forgotten plaintext from the ciphertext. This type of public key encryption with contrasts more widely analyzed public key encryption with forward secrecy. We advocate that together they form the two sides of a whole coin, whereby offering complementary roles in data security, especially in cloud computing, 3G/4G communications and other emerging computing and communication platforms. We formalize the notion of public key encryption with backward recovery, and present two construction methods together with formal analyses of their security. The first method embodies a generic public key encryption scheme with backward recovery using the encrypt then sign paradigm, whereas the second method provides a more efficient scheme that is built on Hofheinz and Kiltz's public key encryption in conjunction with target collision resistant hashing. Security of the first method is proved in a two-user setting, whereas the second is in a more general multi-user setting.

During its 25 years of existence, the Inorganic Analysis Working Group of the Consultative Committee for Amount of Substance: Metrology in Chemistry and Biology (CCQM IAWG) has achieved much in establishing comparability of measurement results. Impressive work has been done on comparison exercises related to real-world problems in fields such as ecology, food, or health. In more recent attempts, measurements and comparisons were focused on calibration solutions which are the basis of most inorganic chemical measurements. This contribution deals with the question of how to achieve full and transparent SI traceability for the values carried by such solutions. Within this framework, the use of classical primary methods (CPMs) is compared to the use of a primary difference method (PDM). PDM is a method with a dual character, namely a metrological method with a primary character, based on the bundling of many measurement methods for individual impurities, which lead to materials with certified content of the main component. As in classical methods, where small corrections for interferences are accepted, in PDM, many small corrections are bundled. In contrast to classical methods, the PDM is universally applicable to all elements in principle. Both approaches can be used to certify the purity (expressed as mass fraction of the main element) of a high-purity material. This is where the metrological need of National Metrology Institutes (NMIs) for analytical methods meet the challenges of analytical methods. In terms of methods, glow discharge mass spectrometry (GMDS) with sufficient uncertainties for sufficiently small impurity contents is particularly noteworthy for the certification of primary transfer standards (PTS), and isotope dilution mass spectrometry (IDMS), which particularly benefits from PTS (back-spikes) with small uncertainties, is particularly noteworthy for the application. The corresponding relative uncertainty which can be achieved using the PDM is very low (< 10−4). Acting as PTS, they represent the link between the material aspect of the primary calibration solutions and the immaterial world of the International System of Units (SI). The underlying concepts are discussed, the current status of implementation is summarised, and a roadmap of the necessary future activities in inorganic analytical chemistry is sketched. It has to be noted that smaller measurement uncertainties of the purity of high-purity materials not only have a positive effect on chemical measurements, but also trigger new developments and findings in other disciplines such as thermometry or materials science.Graphical Primary Transfer Standards (PTSs) are the link between the immaterial world of the International System of Units (SI) and the material aspects of the primary calibration solutions.

The rarity of prion diseases in this country makes it difficult to remember and put into practice specific preventive measures in suspected and diagnosed cases. In this article we update and review aspects of hospital transmission, and establish the measures of prevention and security which should be used in a general setting, including aspects of the care of these patients, cleaning, disinfecting and sterilizing the material used, and disposal of any residues. We suggest specific preventive measures for Units/Departments in which these patients are most often attended, including aspects of the workplace as dealt with by European and Spanish regulations, establishing the rights and obligations of both employers and employees, and the measures to be taken in the case of an accident at work.

The invention of public-key cryptography was of central importance to the field of cryptography and provided answers to many key management problems for large scale networks. For all its benefits, however, public-key cryptography did not provide a comprehensive solution to the key management problem. Indeed, the possibilities brought forth by public-key cryptography heightened the need for sophisticated key management systems to answer questions such as the following:"How can I easily encrypt a file once for a number of different people using public-key cryptography?""If I lose my keys, how can I decrypt all of my files that were encrypted with those keys?""How do I know that I really have Alice’s public key and not the public key of someone pretending to be Alice?""How can I know that a public key is still trustworthy?"The paper discusses public key cryptography and its use in applications such as Key Agreement, Data Encryption and Digital Signature. The paper discusses some public key algorithms such as DH, RSA, and DSA and also gives working explanations of these algorithms.KeywordsShared SecretCertificate AuthorityCipher TextHash CodeDigital CertificateThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Post-quantum cryptography aims to find quantum-resistant public-key cryptographic schemes, that is, schemes which remain secure against both quantum and standard computers. In fact in 1994, Shor published an algorithm [85] breaking the nowadays used public-key cryptoschemes in polynomial time on a quantum computer. The security of public-key algorithms is based on computationally hard mathematical problems. Among the post-quantum proposals there is the Multivariate Problem: Solving a multivariate polynomial system over a finite field. The general and the most computationally efficient method for solving such systems is computing a Groöbner basis of the ideal they generate. In 2021, Beullens [22] used a strategy involving the MinRank Problem for breaching the most promising multivariate scheme at the time. All the details regarding public-key schemes and in particular the multivariate one can be found within the Introduction. The thesis is divided into three blocks. The goal of Chapter 1 is twofold. It is a collection of algebraic concepts and classical facts that are used through these pages, in particular, Section 1.1 serves this scope. In addition, the problem of solving polynomial systems via Gr¨bner basis is fully explained in Section 1.2. In Chapter 2 and Chapter 3, I present the two main works of my PhD, during which I mainly focused on the analysis of multivariate cryptoschemes twofolds. Firstly, together with my advisor Elisa Gorla, we propose a new definition of ‘random system’ using the concept of generality mutued from algebraic geometry. The details of this work are given in Chapter 2. On the other hand, with the help of Daniel Cabarcas (Universidad Nacional de Colombia), we investigated the SupportMinors Modeling, which is a method for modeling the MinRank Problem used by Beullens in his attack. The specifics of this work can be found in Chapter 3.

The Public Key Cryptosystem is considered as new direction of cryptography since 1976. It contains two main problems; factorization Problem and One-way function problem. In 1984, there was a new approach under the umbrella of public key cryptography, which is called Elliptic Curve cryptography. The RSA Cryptosystem is one candidate on the Factorization problem, that is widely used in the special secure commercial communication systems. Although these systems have higher security, but they are attacked with many attacking methods. One of the new attacking methods is the genetic algorithm. Such attack had success against the knapsack public key cryptosystem (a candidate on the one-way problem), but till know, there are no publications about using such attack against RSA Type Public Key cryptosystem.This paper provides a proposed investigation of applying genetic algorithm in cryptanalysis of RSA public key cryptosystem using cipher text only attack in order to enhance the attack overall performance. The method provides good results. Experimental results show that G.A. enhanced the overall performance & memory consumption.