Signing with Codes

Code-based cryptography is an area of classical cryptography in which cryptographic primitives rely on hard problems and trapdoor functions related to linear error-correcting codes. Since its inception in 1978, the area has produced the McEliece and the Niederreiter cryptosystems, multiple digital signature schemes, identification schemes and code-based hash functions. All of these are believed to be resistant to attacks by quantum computers. Hence, code-based cryptography represents a post-quantum alternative to the widespread number-theoretic systems. This thesis summarizes recent developments in the field of code-based cryptography, with a particular emphasis on code-based signature schemes. After a brief introduction and analysis of the McEliece and the Niederreiter cryptosystems, we discuss the currently unresolved issue of constructing a practical, yet provably secure signature scheme. A detailed analysis is provided for the Courtois, Finiasz and Sendrier signature scheme, along with the mCFS and parallel CFS variations. Finally, we discuss a recent proposal by Preetha et al. that attempts to solve the issue of provable security, currently failing in the CFS scheme case, by randomizing the public key construct. We conclude that, while the proposal is not yet practical, it represents an important advancement in the search for an ideal code-based signature scheme

Code-based Identification and Signature Schemes

In an age of explosive growth of digital communications and electronic data storage, cryptography plays an integral role in our society. Some examples of daily use of cryptography are software updates, e-banking, electronic commerce, ATM cards, etc. The security of most currently used cryptosystems relies on the hardness of the factorization and discrete logarithm problems. However, in 1994 Peter Shor discovered polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. Therefore, it is of extreme importance to develop cryptosystems that remain secure even when the adversary has access to a quantum computer; such systems are called post-quantum cryptosystems. One promising candidate is based on codes; in this thesis we focus more specifically on code-based identification and signature schemes. Public key identification schemes are typically applied in cryptography to reach the goal of entity authentication. Their applications include authentication and access control services such as remote login, credit card purchases and many others. One of the most well-known systems of this kind is the zero-knowledge identification scheme introduced in Crypto 1993 by Stern. It is very fast compared to schemes based on number-theoretic problems since it involves only simple and efficiently executable operations. However, its main drawbacks are the high communication complexity and the large public key size, that makes it impractical for many applications. Our first contribution addresses these drawbacks by taking a step towards reducing communication complexity and public key size simultaneously. To this end, we propose a novel zero-knowledge five-pass identification scheme which improves on Stern's scheme. It reduces the communication complexity by a factor of 25 % compared to Stern's one. Moreover, we obtain a public key of size of 4 KB, whereas Stern's scheme requires 15 KB for the same level of security. To the best of our knowledge, there is no code-based identification scheme with better performance than our proposal using random codes. Our second contribution consists of extending one of the most important paradigms in cryptography, namely the one by Fiat and Shamir. In doing so, we enlarge the class of identification schemes to which the Fiat-Shamir transform can be applied. Additionally, we put forward a generic methodology for proving the security of signature schemes derived from this class of identification schemes. We exemplify our extended paradigm and derive a provably secure signature scheme based on our proposed five-pass identification scheme. In order to contribute to the development of post-quantum schemes with additional features, we present an improved code-based threshold ring signature scheme using our two previous results. Our proposal has a shorter signature length and a smaller public-key size compared to Aguilar et al.'s scheme, which is the reference in this area

Cutting the GRASS: Threshold GRoup Action Signature Schemes

Group actions are fundamental mathematical tools, with a long history of use in cryptography. Indeed, the action of finite groups at the basis of the discrete logarithm problem is behind a very large portion of modern cryptographic systems. With the advent of post-quantum cryptography, however, the method for building protocols shifted towards a different paradigm, centered on the difficulty of discerning \u27noisy\u27 objects, as is the case for lattices, codes, and multivariate systems. This method yields promising results for \u27core\u27 primitives such as encryption or signature, but can be less than ideal in the case when more advanced functionalities are required. In this work, we show that isomorphism problems which stem from cryptographic group actions, can be viable building blocks for threshold signature schemes. In particular, we construct a full $N$-out-of-$N$ threshold signature scheme, and discuss the efficiency issues arising from extending it to the generic $T$-out-of-$N$ case. To give a practical outlook on our constructions, we instantiate them with the LESS and MEDS frameworks, which are two flavors of code-based cryptographic group actions. Finally, we highlight some ideas that would allow for a more efficient and compact $(T,N)$ threshold variant of LESS, whose security relies on new hardness assumptions

SYNERGY OF BUILDING CYBERSECURITY SYSTEMS

The development of the modern world community is closely related to advances in computing resources and cyberspace. The formation and expansion of the range of services is based on the achievements of mankind in the field of high technologies. However, the rapid growth of computing resources, the emergence of a full-scale quantum computer tightens the requirements for security systems not only for information and communication systems, but also for cyber-physical systems and technologies. The methodological foundations of building security systems for critical infrastructure facilities based on modeling the processes of behavior of antagonistic agents in security systems are discussed in the first chapter. The concept of information security in social networks, based on mathematical models of data protection, taking into account the influence of specific parameters of the social network, the effects on the network are proposed in second chapter. The nonlinear relationships of the parameters of the defense system, attacks, social networks, as well as the influence of individual characteristics of users and the nature of the relationships between them, takes into account. In the third section, practical aspects of the methodology for constructing post-quantum algorithms for asymmetric McEliece and Niederreiter cryptosystems on algebraic codes (elliptic and modified elliptic codes), their mathematical models and practical algorithms are considered. Hybrid crypto-code constructions of McEliece and Niederreiter on defective codes are proposed. They can significantly reduce the energy costs for implementation, while ensuring the required level of cryptographic strength of the system as a whole. The concept of security of corporate information and educational systems based on the construction of an adaptive information security system is proposed. ISBN 978-617-7319-31-2 (on-line)ISBN 978-617-7319-32-9 (print) ------------------------------------------------------------------------------------------------------------------ How to Cite: Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O., Korol, O., Milevskyi, S. et. al.; Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O. (Eds.) (2021). Synergy of building cybersecurity systems. Kharkiv: РС ТЕСHNOLOGY СЕNTЕR, 188. doi: http://doi.org/10.15587/978-617-7319-31-2 ------------------------------------------------------------------------------------------------------------------ Indexing:                    Розвиток сучасної світової спільноти тісно пов’язаний з досягненнями в області обчислювальних ресурсів і кіберпростору. Формування та розширення асортименту послуг базується на досягненнях людства у галузі високих технологій. Однак стрімке зростання обчислювальних ресурсів, поява повномасштабного квантового комп’ютера посилює вимоги до систем безпеки не тільки інформаційно-комунікаційних, але і до кіберфізичних систем і технологій. У першому розділі обговорюються методологічні основи побудови систем безпеки для об'єктів критичної інфраструктури на основі моделювання процесів поведінки антагоністичних агентів у систем безпеки. У другому розділі пропонується концепція інформаційної безпеки в соціальних мережах, яка заснована на математичних моделях захисту даних, з урахуванням впливу конкретних параметрів соціальної мережі та наслідків для неї. Враховуються нелінійні взаємозв'язки параметрів системи захисту, атак, соціальних мереж, а також вплив індивідуальних характеристик користувачів і характеру взаємовідносин між ними. У третьому розділі розглядаються практичні аспекти методології побудови постквантових алгоритмів для асиметричних криптосистем Мак-Еліса та Нідеррейтера на алгебраїчних кодах (еліптичних та модифікованих еліптичних кодах), їх математичні моделі та практичні алгоритми. Запропоновано гібридні конструкції криптокоду Мак-Еліса та Нідеррейтера на дефектних кодах. Вони дозволяють істотно знизити енергетичні витрати на реалізацію, забезпечуючи при цьому необхідний рівень криптографічної стійкості системи в цілому. Запропоновано концепцію безпеки корпоративних інформаційних та освітніх систем, які засновані на побудові адаптивної системи захисту інформації. ISBN 978-617-7319-31-2 (on-line)ISBN 978-617-7319-32-9 (print) ------------------------------------------------------------------------------------------------------------------ Як цитувати: Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O., Korol, O., Milevskyi, S. et. al.; Yevseiev, S., Ponomarenko, V., Laptiev, O., Milov, O. (Eds.) (2021). Synergy of building cybersecurity systems. Kharkiv: РС ТЕСHNOLOGY СЕNTЕR, 188. doi: http://doi.org/10.15587/978-617-7319-31-2 ------------------------------------------------------------------------------------------------------------------ Індексація:                 &nbsp

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Association of Christians in the Mathematical Sciences Proceedings 2019

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 29-June 1, 2019 at Indiana Wesleyan University

Efficient code-based one-time signature from automorphism groups with syndrome compatibility

978-1-4673-2580-6International audienceIn this paper we propose a new one-time signature algorithm based on coding theory. The algorithm uses properties of automorphism group of certain codes to dramatically decrease the size of the public key of the scheme. By considering the action of cyclic shifts or the action of the group PSL2(p) we obtain public keys of less than 18 kilobits for a signature of 7 kilobits. Overall the scheme we propose is perfectly fitted to be used with Merkle tree and proposes a very good trade-off between size of key and size of signatures compared to other code-based signature schemes, with multi-time signatures of size 28kb