Hardness of Computing Individual Bits for One-way Functions on Elliptic Curves

We prove that if one can predict any of the bits of the input to an elliptic curve based one-way function over a finite field, then we can invert the function. In particular, our result implies that if one can predict any of the bits of the input to a classical pairing-based one-way function with non-negligible advantage over a random guess then one can efficiently invert this function and thus, solve the Fixed Argument Pairing Inversion problem (FAPI-1/FAPI-2). The latter has implications on the security of various pairing-based schemes such as the identity-based encryption scheme of Boneh–Franklin, Hess’ identity-based signature scheme, as well as Joux’s three-party one-round key agreement protocol. Moreover, if one can solve FAPI-1 and FAPI-2 in polynomial time then one can solve the Computational Diffie--Hellman problem (CDH) in polynomial time. Our result implies that all the bits of the functions defined above are hard-to-compute assuming these functions are one-way. The argument is based on a list-decoding technique via discrete Fourier transforms due to Akavia--Goldwasser–Safra as well as an idea due to Boneh–Shparlinski

Cross-core Microarchitectural Attacks and Countermeasures

In the last decade, multi-threaded systems and resource sharing have brought a number of technologies that facilitate our daily tasks in a way we never imagined. Among others, cloud computing has emerged to offer us powerful computational resources without having to physically acquire and install them, while smartphones have almost acquired the same importance desktop computers had a decade ago. This has only been possible thanks to the ever evolving performance optimization improvements made to modern microarchitectures that efficiently manage concurrent usage of hardware resources. One of the aforementioned optimizations is the usage of shared Last Level Caches (LLCs) to balance different CPU core loads and to maintain coherency between shared memory blocks utilized by different cores. The latter for instance has enabled concurrent execution of several processes in low RAM devices such as smartphones. Although efficient hardware resource sharing has become the de-facto model for several modern technologies, it also poses a major concern with respect to security. Some of the concurrently executed co-resident processes might in fact be malicious and try to take advantage of hardware proximity. New technologies usually claim to be secure by implementing sandboxing techniques and executing processes in isolated software environments, called Virtual Machines (VMs). However, the design of these isolated environments aims at preventing pure software- based attacks and usually does not consider hardware leakages. In fact, the malicious utilization of hardware resources as covert channels might have severe consequences to the privacy of the customers. Our work demonstrates that malicious customers of such technologies can utilize the LLC as the covert channel to obtain sensitive information from a co-resident victim. We show that the LLC is an attractive resource to be targeted by attackers, as it offers high resolution and, unlike previous microarchitectural attacks, does not require core-colocation. Particularly concerning are the cases in which cryptography is compromised, as it is the main component of every security solution. In this sense, the presented work does not only introduce three attack variants that can be applicable in different scenarios, but also demonstrates the ability to recover cryptographic keys (e.g. AES and RSA) and TLS session messages across VMs, bypassing sandboxing techniques. Finally, two countermeasures to prevent microarchitectural attacks in general and LLC attacks in particular from retrieving fine- grain information are presented. Unlike previously proposed countermeasures, ours do not add permanent overheads in the system but can be utilized as preemptive defenses. The first identifies leakages in cryptographic software that can potentially lead to key extraction, and thus, can be utilized by cryptographic code designers to ensure the sanity of their libraries before deployment. The second detects microarchitectural attacks embedded into innocent-looking binaries, preventing them from being posted in official application repositories that usually have the full trust of the customer

Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation

We consider a generalisation of the hidden number problem recently introduced by Boneh and Venkatesan. The initial problem can be stated as follows: recover a number a ∈ double-struck F signp such that for many known random t ∈ double-struck F signp approximations to the values of [at]p are known. Here we study a version of the problem where the "multipliers" t are not known but rather certain approximations to them are given. We present a probabilistic polynomial time solution when the error is small enough, and we show that the problem cannot be solved if the error is sufficiently large. We apply the result to the bit security of "timed-release crypto" introduced by Rivest, Shamir and Wagner, to noisy exponentiation black-boxes and to the bit security of the "inverse" exponentiation. We also show that it implies a certain bit security result for Weil Dairine on elliotic curves.13 page(s

Hidden number problem with hidden multipliers, timed-release crypto and noisy exponentiation

Abstract. We consider a generalisation of the hidden number problem recently introduced by Boneh and Venkatesan. The initial problem can be stated as follows: recover a number a ∈ Fp such that for many known random t ∈ Fp approximations to the values of ⌊at ⌋ p areknown.Herewestudyaversionof the problem where the “multipliers ” t are not known but rather certain approximations to them are given. We present a probabilistic polynomial time solution when the error is small enough, and we show that the problem cannot be solved if the error is sufficiently large. We apply the result to the bit security of “timed-release crypto ” introduced by Rivest, Shamir and Wagner, to noisy exponentiation black-boxes and to the bit security of the “inverse” exponentiation. We also show that it implies a certain bit security result for Weil pairing on elliptic curves. 1

Remote Attacks on FPGA Hardware

Immer mehr Computersysteme sind weltweit miteinander verbunden und über das Internet zugänglich, was auch die Sicherheitsanforderungen an diese erhöht. Eine neuere Technologie, die zunehmend als Rechenbeschleuniger sowohl für eingebettete Systeme als auch in der Cloud verwendet wird, sind Field-Programmable Gate Arrays (FPGAs). Sie sind sehr flexible Mikrochips, die per Software konfiguriert und programmiert werden können, um beliebige digitale Schaltungen zu implementieren. Wie auch andere integrierte Schaltkreise basieren FPGAs auf modernen Halbleitertechnologien, die von Fertigungstoleranzen und verschiedenen Laufzeitschwankungen betroffen sind. Es ist bereits bekannt, dass diese Variationen die Zuverlässigkeit eines Systems beeinflussen, aber ihre Auswirkungen auf die Sicherheit wurden nicht umfassend untersucht. Diese Doktorarbeit befasst sich mit einem Querschnitt dieser Themen: Sicherheitsprobleme die dadurch entstehen wenn FPGAs von mehreren Benutzern benutzt werden, oder über das Internet zugänglich sind, in Kombination mit physikalischen Schwankungen in modernen Halbleitertechnologien. Der erste Beitrag in dieser Arbeit identifiziert transiente Spannungsschwankungen als eine der stärksten Auswirkungen auf die FPGA-Leistung und analysiert experimentell wie sich verschiedene Arbeitslasten des FPGAs darauf auswirken. In der restlichen Arbeit werden dann die Auswirkungen dieser Spannungsschwankungen auf die Sicherheit untersucht. Die Arbeit zeigt, dass verschiedene Angriffe möglich sind, von denen früher angenommen wurde, dass sie physischen Zugriff auf den Chip und die Verwendung spezieller und teurer Test- und Messgeräte erfordern. Dies zeigt, dass bekannte Isolationsmaßnahmen innerhalb FPGAs von böswilligen Benutzern umgangen werden können, um andere Benutzer im selben FPGA oder sogar das gesamte System anzugreifen. Unter Verwendung von Schaltkreisen zur Beeinflussung der Spannung innerhalb eines FPGAs zeigt diese Arbeit aktive Angriffe, die Fehler (Faults) in anderen Teilen des Systems verursachen können. Auf diese Weise sind Denial-of-Service Angriffe möglich, als auch Fault-Angriffe um geheime Schlüsselinformationen aus dem System zu extrahieren. Darüber hinaus werden passive Angriffe gezeigt, die indirekt die Spannungsschwankungen auf dem Chip messen. Diese Messungen reichen aus, um geheime Schlüsselinformationen durch Power Analysis Seitenkanalangriffe zu extrahieren. In einer weiteren Eskalationsstufe können sich diese Angriffe auch auf andere Chips auswirken die an dasselbe Netzteil angeschlossen sind wie der FPGA. Um zu beweisen, dass vergleichbare Angriffe nicht nur innerhalb FPGAs möglich sind, wird gezeigt, dass auch kleine IoT-Geräte anfällig für Angriffe sind welche die gemeinsame Spannungsversorgung innerhalb eines Chips ausnutzen. Insgesamt zeigt diese Arbeit, dass grundlegende physikalische Variationen in integrierten Schaltkreisen die Sicherheit eines gesamten Systems untergraben können, selbst wenn der Angreifer keinen direkten Zugriff auf das Gerät hat. Für FPGAs in ihrer aktuellen Form müssen diese Probleme zuerst gelöst werden, bevor man sie mit mehreren Benutzern oder mit Zugriff von Drittanbietern sicher verwenden kann. In Veröffentlichungen die nicht Teil dieser Arbeit sind wurden bereits einige erste Gegenmaßnahmen untersucht

Exploitation of Unintentional Information Leakage from Integrated Circuits

Unintentional electromagnetic emissions are used to recognize or verify the identity of a unique integrated circuit (IC) based on fabrication process-induced variations in a manner analogous to biometric human identification. The effectiveness of the technique is demonstrated through an extensive empirical study, with results presented indicating correct device identification success rates of greater than 99:5%, and average verification equal error rates (EERs) of less than 0:05% for 40 near-identical devices. The proposed approach is suitable for security applications involving commodity commercial ICs, with substantial cost and scalability advantages over existing approaches. A systematic leakage mapping methodology is also proposed to comprehensively assess the information leakage of arbitrary block cipher implementations, and to quantitatively bound an arbitrary implementation\u27s resistance to the general class of differential side channel analysis techniques. The framework is demonstrated using the well-known Hamming Weight and Hamming Distance leakage models, and approach\u27s effectiveness is demonstrated through the empirical assessment of two typical unprotected implementations of the Advanced Encryption Standard. The assessment results are empirically validated against correlation-based differential power and electromagnetic analysis attacks