IMPROVING SMART GRID SECURITY USING MERKLE TREES

Abstract—Presently nations worldwide are starting to convert their aging electrical power infrastructures into modern, dynamic power grids. Smart Grid offers much in the way of efficiencies and robustness to the electrical power grid, however its heavy reliance on communication networks will leave it more vulnerable to attack than present day grids. This paper looks at the threat to public key cryptography systems from a fully realized quantum computer and how this could impact the Smart Grid. We argue for the use of Merkle Trees in place of public key cryptography for authentication of devices in wireless mesh networks that are used in Smart Grid applications

Theory and Practice of Cryptography and Network Security Protocols and Technologies

In an age of explosive worldwide growth of electronic data storage and communications, effective protection of information has become a critical requirement. When used in coordination with other tools for ensuring information security, cryptography in all of its applications, including data confidentiality, data integrity, and user authentication, is a most powerful tool for protecting information. This book presents a collection of research work in the field of cryptography. It discusses some of the critical challenges that are being faced by the current computing world and also describes some mechanisms to defend against these challenges. It is a valuable source of knowledge for researchers, engineers, graduate and doctoral students working in the field of cryptography. It will also be useful for faculty members of graduate schools and universities

Faster constant-time evaluation of the Kronecker symbol with application to elliptic curve hashing

We generalize the Bernstein-Yang (BY) algorithm for constant-time modular inversion to compute the Kronecker symbol, of which the Jacobi and Legendre symbols are special cases. We start by developing a basic and easy-to-implement divstep version of the algorithm defined in terms of full-precision division steps. We then describe an optimized version due to Hamburg over word-sized inputs, similar to the jumpdivstep version of the BY algorithm, and formally verify its correctness. Along the way, we introduce a number of optimizations for implementing both versions in constant time and at high-speed. The resulting algorithms are particularly suitable for the special case of computing the Legendre symbol with dense prime $p$, where no efficient addition chain is known for the conventional approach by exponentiation to $\frac{p-1}{2}$. This is often the case for the base field of popular pairing-friendly elliptic curves. Our high-speed implementation for a range of parameters shows that the new algorithm is up to 40 times faster than the conventional exponentiation approach, and up to 25.7\% faster than the previous state of the art. We illustrate the performance of the algorithm with an application for hashing to elliptic curves, where the observed savings amount to 14.7\% -- 48.1\% when used for testing quadratic residuosity within the SwiftEC hashing algorithm. We also apply our techniques to the CTIDH isogeny-based key exchange, with savings of 3.5--13.5\%

Weave ElGamal Encryption for Secure Outsourcing Algebraic Computations over Zp

Thispaperaddressesthesecureoutsourcingproblemforlarge-scalematrixcomputationto a public cloud. We propose a novel public-key weave ElGamal encryption (WEE) scheme for encrypting a matrix over the field Zp. The scheme has the echelon transformation property. We can apply a series of elementary row/column operations to transform an encrypted matrix under our WEE scheme into the row/column echelon form. The decrypted result matches the result of the corresponding operations performed on the original matrix. For security, our WEE scheme is shown to be entry irrecoverable for non-zero entries under the computational Diffie-Hellman assumption. By using our WEE scheme, we propose five secure outsourcing protocols of Gaussian elimination, Gaussian-Jordan elimination, matrix determinant, linear system solver, and matrix inversion. Each of these protocols preserves data privacy for clients (data owners). Furthermore, the linear system solver and matrix inversion protocols provide a cheating-resistant mechanism to verify correctness of computation results. Our experimental result shows that our protocols gain efficiency significantly for an outsourcer. Our outsourcing protocol solves a linear system of n = 1, 000 equations and m = 1, 000 unknown variables about 472 times faster than a non-outsourced version. The efficiency gain is more substantial when (n, m) gets larger. For example, when n = 10, 000 and m = 10, 000, the protocol can solve it about 56, 274 times faster. Our protocols can also be easily implemented in parallel computation architecture to get more efficiency improvement

Méthodes logicielles formelles pour la sécurité des implémentations cryptographiques

Implementations of cryptosystems are vulnerable to physical attacks, and thus need to be protected against them.Of course, malfunctioning protections are useless.Formal methods help to develop systems while assessing their conformity to a rigorous specification.The first goal of my thesis, and its innovative aspect, is to show that formal methods can be used to prove not only the principle of the countermeasures according to a model,but also their implementations, as it is where the physical vulnerabilities are exploited.My second goal is the proof and the automation of the protection techniques themselves, because handwritten security code is error-prone.Les implémentations cryptographiques sont vulnérables aux attaques physiques, et ont donc besoin d'en être protégées.Bien sûr, des protections défectueuses sont inutiles.L'utilisation des méthodes formelles permet de développer des systèmes tout en garantissant leur conformité à des spécifications données.Le premier objectif de ma thèse, et son aspect novateur, est de montrer que les méthodes formelles peuvent être utilisées pour prouver non seulement les principes des contre-mesures dans le cadre d'un modèle, mais aussi leurs implémentations, étant donné que c'est là que les vulnérabilités physiques sont exploitées.Mon second objectif est la preuve et l'automatisation des techniques de protection elles-même, car l'écriture manuelle de code est sujette à de nombreuses erreurs, particulièrement lorsqu'il s'agit de code de sécurité

On the Cryptanalysis of Public-Key Cryptography

Nowadays, the most popular public-key cryptosystems are based on either the integer factorization or the discrete logarithm problem. The feasibility of solving these mathematical problems in practice is studied and techniques are presented to speed-up the underlying arithmetic on parallel architectures. The fastest known approach to solve the discrete logarithm problem in groups of elliptic curves over finite fields is the Pollard rho method. The negation map can be used to speed up this calculation by a factor √2. It is well known that the random walks used by Pollard rho when combined with the negation map get trapped in fruitless cycles. We show that previously published approaches to deal with this problem are plagued by recurring cycles, and we propose effective alternative countermeasures. Furthermore, fast modular arithmetic is introduced which can take advantage of prime moduli of a special form using efficient "sloppy reduction." The effectiveness of these techniques is demonstrated by solving a 112-bit elliptic curve discrete logarithm problem using a cluster of PlayStation 3 game consoles: breaking a public-key standard and setting a new world record. The elliptic curve method (ECM) for integer factorization is the asymptotically fastest method to find relatively small factors of large integers. From a cryptanalytic point of view the performance of ECM gives information about secure parameter choices of some cryptographic protocols. We optimize ECM by proposing carry-free arithmetic modulo Mersenne numbers (numbers of the form 2M – 1) especially suitable for parallel architectures. Our implementation of these techniques on a cluster of PlayStation 3 game consoles set a new record by finding a 241-bit prime factor of 21181 – 1. A normal form for elliptic curves introduced by Edwards results in the fastest elliptic curve arithmetic in practice. Techniques to reduce the temporary storage and enhance the performance even further in the setting of ECM are presented. Our results enable one to run ECM efficiently on resource-constrained platforms such as graphics processing units