Key Randomization Countermeasures to Power Analysis Attacks on Elliptic Curve Cryptosystems

It is essential to secure the implementation of cryptosystems in embedded devices agains side-channel attacks. Namely, in order to resist differential (DPA) attacks, randomization techniques should be employed to decorrelate the data processed by the device from secret key parts resulting in the value of this data. Among the countermeasures that appeared in the literature were those that resulted in a random representation of the key known as the binary signed digit representation (BSD). We have discovered some interesting properties related to the number of possible BSD representations for an integer and we have proposed a different randomization algorithm. We have also carried our study to the $\tau$-adic representation of integers which is employed in elliptic curve cryptosystems (ECCs) using Koblitz curves. We have then dealt with another randomization countermeasure which is based on randomly splitting the key. We have investigated the secure employment of this countermeasure in the context of ECCs

Efficient Arithmetic for the Implementation of Elliptic Curve Cryptography

The technology of elliptic curve cryptography is now an important branch in public-key based crypto-system. Cryptographic mechanisms based on elliptic curves depend on the arithmetic of points on the curve. The most important arithmetic is multiplying a point on the curve by an integer. This operation is known as elliptic curve scalar (or point) multiplication operation. A cryptographic device is supposed to perform this operation efficiently and securely. The elliptic curve scalar multiplication operation is performed by combining the elliptic curve point routines that are defined in terms of the underlying finite field arithmetic operations. This thesis focuses on hardware architecture designs of elliptic curve operations. In the first part, we aim at finding new architectures to implement the finite field arithmetic multiplication operation more efficiently. In this regard, we propose novel schemes for the serial-out bit-level (SOBL) arithmetic multiplication operation in the polynomial basis over F_2^m. We show that the smallest SOBL scheme presented here can provide about 26-30\% reduction in area-complexity cost and about 22-24\% reduction in power consumptions for F_2^{163} compared to the current state-of-the-art bit-level multiplier schemes. Then, we employ the proposed SOBL schemes to present new hybrid-double multiplication architectures that perform two multiplications with latency comparable to the latency of a single multiplication. Then, in the second part of this thesis, we investigate the different algorithms for the implementation of elliptic curve scalar multiplication operation. We focus our interest in three aspects, namely, the finite field arithmetic cost, the critical path delay, and the protection strength from side-channel attacks (SCAs) based on simple power analysis. In this regard, we propose a novel scheme for the scalar multiplication operation that is based on processing three bits of the scalar in the exact same sequence of five point arithmetic operations. We analyse the security of our scheme and show that its security holds against both SCAs and safe-error fault attacks. In addition, we show how the properties of the proposed elliptic curve scalar multiplication scheme yields an efficient hardware design for the implementation of a single scalar multiplication on a prime extended twisted Edwards curve incorporating 8 parallel multiplication operations. Our comparison results show that the proposed hardware architecture for the twisted Edwards curve model implemented using the proposed scalar multiplication scheme is the fastest secure SCA protected scalar multiplication scheme over prime field reported in the literature

PARMESAN: Parallel ARithMEticS over ENcrypted data

Fully Homomorphic Encryption enables the evaluation of an arbitrary computable function over encrypted data. Among all such functions, particular interest goes for integer arithmetics. In this paper, we present a bundle of methods for fast arithmetic operations over encrypted data: addition/subtraction, multiplication, and some of their special cases. On top of that, we propose techniques for signum, maximum, and rounding. All methods are specifically tailored for computations with data encrypted with the TFHE scheme (Chillotti et al., Asiacrypt \u2716) and we mainly focus on parallelization of non-linear homomorphic operations, which are the most expensive ones. This way, evaluation times can be reduced significantly, provided that sufficient parallel resources are available. We implement all presented methods in the Parmesan Library and we provide an experimental evaluation. Compared to integer arithmetics of the Concrete Library, we achieve considerable speedups for all comparable operations. Major speedups are achieved for the multiplication of an encrypted integer by a cleartext one, where we employ special addition-subtraction chains, which save a vast amount of homomorphic operations

Side-Channel Analysis and Cryptography Engineering : Getting OpenSSL Closer to Constant-Time

As side-channel attacks reached general purpose PCs and started to be more practical for attackers to exploit, OpenSSL adopted in 2005 a flagging mechanism to protect against SCA. The opt-in mechanism allows to flag secret values, such as keys, with the BN_FLG_CONSTTIME flag. Whenever a flag is checked and detected, the library changes its execution flow to SCA-secure functions that are slower but safer, protecting these secret values from being leaked. This mechanism favors performance over security, it is error-prone, and is obscure for most library developers, increasing the potential for side-channel vulnerabilities. This dissertation presents an extensive side-channel analysis of OpenSSL and criticizes its fragile flagging mechanism. This analysis reveals several flaws affecting the library resulting in multiple side-channel attacks, improved cache-timing attack techniques, and a new side channel vector. The first part of this dissertation introduces the main topic and the necessary related work, including the microarchitecture, the cache hierarchy, and attack techniques; then it presents a brief troubled history of side-channel attacks and defenses in OpenSSL, setting the stage for the related publications. This dissertation includes seven original publications contributing to the area of side-channel analysis, microarchitecture timing attacks, and applied cryptography. From an SCA perspective, the results identify several vulnerabilities and flaws enabling protocol-level attacks on RSA, DSA, and ECDSA, in addition to full SCA of the SM2 cryptosystem. With respect to microarchitecture timing attacks, the dissertation presents a new side-channel vector due to port contention in the CPU execution units. And finally, on the applied cryptography front, OpenSSL now enjoys a revamped code base securing several cryptosystems against SCA, favoring a secure-by-default protection against side-channel attacks, instead of the insecure opt-in flagging mechanism provided by the fragile BN_FLG_CONSTTIME flag

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland

Synthesis of new pyrazolium based tunable aryl alkyl ionic liquids and their use in removal of methylene blue from aqueous solution

In this study, two new pyrazolium based tunable aryl alkyl ionic liquids, 2-ethyl-1-(4-methylphenyl)-3,5- dimethylpyrazolium tetrafluoroborate (3a) and 1-(4-methylphenyl)-2-pentyl-3,5-dimethylpyrazolium tetrafluoroborate (3b), were synthesized via three-step reaction and characterized. The removal of methylene blue (MB) from aqueous solution has been investigated using the synthesized salts as an extractant and methylene chloride as a solvent. The obtained results show that MB was extracted from aqueous solution with high extraction efficiency up to 87 % at room temperature at the natural pH of MB solution. The influence of the alkyl chain length on the properties of the salts and their extraction efficiency of MB was investigated

Epidemiology of Injury in English Women's Super league Football: A Cohort Study

INTRODUCTION: The epidemiology of injury in male professional football has been well documented (Ekstrand, Hägglund, & Waldén, 2011) and used as a basis to understand injury trends for a number of years. The prevalence and incidence of injuries occurring in womens super league football is unknown. The aim of this study is to estimate the prevalence and incidence of injury in an English Super League Women’s Football squad. METHODS: Following ethical approval from Leeds Beckett University, players (n = 25) signed to a Women’s Super League Football club provided written informed consent to complete a self-administered injury survey. Measures of exposure, injury and performance over a 12-month period was gathered. Participants were classified as injured if they reported a football injury that required medical attention or withdrawal from participation for one day or more. Injuries were categorised as either traumatic or overuse and whether the injury was a new injury and/or re-injury of the same anatomical site RESULTS: 43 injuries, including re-injury were reported by the 25 participants providing a clinical incidence of 1.72 injuries per player. Total incidence of injury was 10.8/1000 h (95% CI: 7.5 to 14.03). Participants were at higher risk of injury during a match compared with training (32.4 (95% CI: 15.6 to 48.4) vs 8.0 (95% CI: 5.0 to 10.85)/1000 hours, p 28 days) of which there were three non-contact anterior cruciate ligament (ACL) injuries. The epidemiological incidence proportion was 0.80 (95% CI: 0.64 to 0.95) and the average probability that any player on this team will sustain at least one injury was 80.0% (95% CI: 64.3% to 95.6%) CONCLUSION: This is the first report capturing exposure and injury incidence by anatomical site from a cohort of English players and is comparable to that found in Europe (6.3/1000 h (95% CI 5.4 to 7.36) Larruskain et al 2017). The number of ACL injuries highlights a potential injury burden for a squad of this size. Multi-site prospective investigations into the incidence and prevalence of injury in women’s football are require