Exclusive Exponent Blinding May Not Suffice to Prevent Timing Attacks on RSA

The references [9,3,1] treat timing attacks on RSA with CRT and Montgomery\u27s multiplication algorithm in unprotected implementations. It has been widely believed that exponent blinding would prevent any timing attack on RSA. At cost of significantly more timing measurements this paper extends the before-mentioned attacks to RSA with CRT when Montgomery\u27s multiplication algorithm and exponent blinding are applied. Simulation experiments are conducted, which confirm the theoretical results. Effective countermeasures exist. In particular, the attack efficiency is higher than in the previous version [12] while large parts of both papers coincide

Estudio exploratorio de la técnicaTimming Attack en el criptosistema RSA

This paper makes an exploratory bibliographic analysis of the Timing Attack (TA) technique on the Side Channel Attacks (SCA) in RSA. The information assets, operation modes and countermeasures of 22 papers were analyzed. Findings show that smartcards are the most attacked information assets (32%), blinding is the most applied countermeasure (33%) and the Chinese Remainder Theorem (CRT) or Montgomery Multiplication (MM) with CRT are the most frequent operation modes (41%). Furthermore, just one attack was executed in telecom unication systems, this opens the possibilty for future work, analyzing the same technique using the tecnologies WiMAX and the SIP VoIP protocol.  El presente trabajo realiza un análisis bibliográfico exploratorio del tipo de ataque Timing Attack (TA) de On The Side Channel Attack (SCA) en RSA. Para lo cual, se analizaron los activos de información, los modos de operación y las contramedidas efectuadas de 22 artículos. Los resultados evidencian que el activo de información que más ataques tuvo son las tarjetas inteligentes (32%), la contramedida mayormente aplicada es el cegamiento (33%) y los modos de operación más utilizados son el Chinese Remainder Theorem (CRT) o Montgomery Multiplication (MM) con CRT (41%). Adicionalmente se evidencia que sólo un ataque fue realizado a los sistemas de telecomunicaciones, lo cual permite plantear trabajos futuros en el análisis de la misma técnica con base en las tecnologías WiMAX y el protocolo SIP de VoIP. &nbsp

Timing attacks and local timing attacks against Barrett’s modular multiplication algorithm

Montgomery’s and Barrett’s modular multiplication algorithms are widely used in modular exponentiation algorithms, e.g. to compute RSA or ECC operations. While Montgomery’s multiplication algorithm has been studied extensively in the literature and many side-channel attacks have been detected, to our best knowledge no thorough analysis exists for Barrett’s multiplication algorithm. This article closes this gap. For both Montgomery’s and Barrett’s multiplication algorithm, differences of the execution times are caused by conditional integer subtractions, so-called extra reductions. Barrett’s multiplication algorithm allows even two extra reductions, and this feature increases the mathematical difficulties significantly. We formulate and analyse a two-dimensional Markov process, from which we deduce relevant stochastic properties of Barrett’s multiplication algorithm within modular exponentiation algorithms. This allows to transfer the timing attacks and local timing attacks (where a second side-channel attack exhibits the execution times of the particular modular squarings and multiplications) on Montgomery’s multiplication algorithm to attacks on Barrett’s algorithm. However, there are also differences. Barrett’s multiplication algorithm requires additional attack substeps, and the attack efficiency is much more sensitive to variations of the parameters. We treat timing attacks on RSA with CRT, on RSA without CRT, and on Diffie-Hellman, as well as local timing attacks against these algorithms in the presence of basis blinding. Experiments confirm our theoretical results

Boolean Exponent Splitting

A typical countermeasure against side-channel attacks consists of masking intermediate values with a random number. In symmetric cryptographic algorithms, Boolean shares of the secret are typically used, whereas in asymmetric algorithms the secret exponent/scalar is typically masked using algebraic properties. This paper presents a new exponent splitting technique with minimal impact on performance based on Boolean shares. More precisely, it is shown how an exponent can be efficiently split into two shares, where the exponent is the XOR sum of the two shares, typically requiring only an extra register and a few register copies per bit. Our novel exponentiation and scalar multiplication algorithms can be randomized for every execution and combined with other blinding techniques. In this way, both the exponent and the intermediate values can be protected against various types of side-channel attacks. We perform a security evaluation of our algorithms using the mutual information framework and provide proofs that they are secure against first-order side-channel attacks. The side-channel resistance of the proposed algorithms is also practically verified with test vector leakage assessment performed on Xilinx\u27s Zynq zc702 evaluation board

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

New Single-Trace Side-Channel Attacks on a Specific Class of Elgamal Cryptosystem

In 2005, Yen et al. proposed the first $N-1$ attack on the modular exponentiation algorithms such as BRIP and square-and-multiply-always methods. This attack makes use of the ciphertext $N-1$ as a distinguisher of low order to obtain a strong relation between side-channel leakages and secret exponent. The so-called $N-1$ attack is one of the most important order-2 element attacks, as it requires a non-adaptive chosen ciphertext which is considered as a more realistic attack model compared to adaptive chosen ciphertext scenario. To protect the implementation against $N-1$ attack, several literatures propose the simplest solution, i.e. \textquotedblleft block the special message $N-1$ . In this paper, we conduct an in-depth research on the $N-1$ attack based on the square-and-multiply-always (SMA) and Montgomery Ladder (ML) algorithms. We show that despite the unaccepted ciphertext $N-1$ countermeasure, other types of $N-1$ attacks is applicable to specific classes of Elgamal cryptosystems. We propose new chosen-message power-analysis attacks with order-4 elements which utilize a chosen ciphertext $c$ such that $c^2= -1 \bmod p$ where $p$ is the prime number used as a modulus in Elgamal. Such a ciphertext can be found simply when $p\equiv 1\mod 4$. We demonstrate that ML and SMA algorithms are subjected to our new $N-1$-type attack by utilizing a different ciphertext. We implement the proposed attacks on the TARGET Board of the ChipWhisperer CW1173 and our experiments validate the feasibility and effectiveness of the attacks by using only a single power trace

Fast Authentication from Aggregate Signatures with Improved Security

An attempt to derive signer-efficient digital signatures from aggregate signatures was made in a signature scheme referred to as Structure-free Compact Rapid Authentication (SCRA) (IEEE TIFS 2017). In this paper, we first mount a practical universal forgery attack against the NTRU instantiation of SCRA by observing only 8161 signatures. Second, we propose a new signature scheme (FAAS), which transforms any single-signer aggregate signature scheme into a signer-efficient scheme. We show two efficient instantiations of FAAS, namely, FAAS-NTRU and FAAS-RSA, both of which achieve high computational efficiency. Our experiments confirmed that FAAS schemes achieve up to 100x faster signature generation compared to their underlying schemes. Moreover, FAAS schemes eliminate some of the costly operations such as Gaussian sampling, rejection sampling, and exponentiation at the signature generation that are shown to be susceptible to side-channel attacks. This enables FAAS schemes to enhance the security and efficiency of their underlying schemes. Finally, we prove that FAAS schemes are secure (in random oracle model), and open-source both our attack and FAAS implementations for public testing purposes

Enhancing the reliability of digital signatures as non-repudiation evidence under a holistic threat model

Traditional sensitive operations, like banking transactions, purchase processes, contract agreements etc. need to tie down the involved parties respecting the commitments made, avoiding a further repudiation of the responsibilities taken. Depending on the context, the commitment is made in one way or another, being handwritten signatures possibly the most common mechanism ever used. With the shift to digital communications, the same guarantees that exist in real world transactions are expected from electronic ones as well. Non-repudiation is thus a desired property of current electronic transactions, like those carried out in Internet banking, e-commerce or, in general, any electronic data interchange scenario. Digital evidence is generated, collected, maintained, made available and verified by non-repudiation services in order to resolve disputes about the occurrence of a certain event, protecting the parties involved in a transaction against the other's false denial about such an event. In particular, a digital signature is considered as non-repudiation evidence which can be used subsequently, by disputing parties or by an adjudicator, to arbitrate in disputes. The reliability of a digital signature should determine its capability to be used as valid evidence. The reliability depends on the trustworthiness of the whole life cycle of the signature, including the generation, transfer, verification and storage phases. Any vulnerability in it would undermine the reliability of the digital signature, making its applicability as non-repudiation evidence dificult to achieve. Unfortunately, technology is subject to vulnerabilities, always with the risk of an occurrence of security threats. Despite that, no rigorous mechanism addressing the reliability of digital signatures technology has been proposed so far. The main goal of this doctoral thesis is to enhance the reliability of digital signatures in order to enforce their non-repudiation property when acting as evidence. In the first instance, we have determined that current technology does not provide an acceptable level of trustworthiness to produce reliable nonrepudiation evidence that is based on digital signatures. The security threats suffered by current technology are suffice to prevent the applicability of digital signatures as non-repudiation evidence. This finding is also aggravated by the fact that digital signatures are granted legal effectiveness under current legislation, acting as evidence in legal proceedings regarding the commitment made by a signatory in the signed document. In our opinion, the security threats that subvert the reliability of digital signatures had to be formalized and categorized. For that purpose, a holistic taxonomy of potential attacks on digital signatures has been devised, allowing their systematic and rigorous classification. In addition, and assuming a realistic security risk, we have built a new approach more robust and trustworthy than the predecessors to enhance the reliability of digital signatures, enforcing their non-repudiation property. This new approach is supported by two novel mechanisms presented in this thesis: the signature environment division paradigm and the extended electronic signature policies. Finally, we have designed a new fair exchange protocol that makes use of our proposal, demonstrating the applicability in a concrete scenario. ----------------------------------------------------------------------------------------------------------------------------------------------------------------Las operaciones sensibles tradicionales, tales como transacciones bancarias, procesos de compra-venta, firma de contratos etc. necesitan que las partes implicadas queden sujetas a los compromisos realizados, evitando así un repudio posterior de las responsabilidades adquiridas. Dependiendo del contexto, el compromiso se llevaría a cabo de una manera u otra, siendo posiblemente la firma manuscrita el mecanismo más comúnmente empleado hasta la actualidad. Con el paso a las comunicaciones digitales, se espera que las mismas garantías que se encuentran en las transacciones tradicionales se proporcionen también en las electrónicas. El no repudio es, por tanto, una propiedad deseada a las actuales transacciones electrónicas, como aquellas que se llevan a cabo en la banca online, en el comercio electrónico o, en general, en cualquier intercambio de datos electrónico. La evidencia digital se genera, recoge, mantiene, publica y verifica mediante los servicios de no repudio con el fin de resolver disputas acerca de la ocurrencia de un determinado evento, protegiendo a las partes implicadas en una transacción frente al rechazo respecto a dicho evento que pudiera realizar cualquiera de las partes. En particular, una firma digital se considera una evidencia de no repudio que puede emplearse posteriormente por las partes enfrentadas o un tercero durante el arbitrio de la disputa. La fiabilidad de una firma digital debería determinar su capacidad para ser usada como evidencia válida. Dicha fiabilidad depende de la seguridad del ciclo de vida completo de la firma, incluyendo las fases de generación, transferencia, verificación, almacenamiento y custodia. Cualquier vulnerabilidad en dicho proceso podría socavar la fiabilidad de la firma digital, haciendo difícil su aplicación como evidencia de no repudio. Desafortunadamente, la tecnología está sujeta a vulnerabilidades, existiendo siempre una probabilidad no nula de ocurrencia de amenazas a su seguridad. A pesar de ello, hasta la fecha no se ha propuesto ningún mecanismo que aborde de manera rigurosa el estudio de la fiabilidad real de la tecnología de firma digital. El principal objetivo de esta tesis doctoral es mejorar la fiabilidad de las firmas digitales para que éstas puedan actuar como evidencia de no repudio con garantías suficientes

Hardware-Assisted Secure Computation

The theory community has worked on Secure Multiparty Computation (SMC) for more than two decades, and has produced many protocols for many settings. One common thread in these works is that the protocols cannot use a Trusted Third Party (TTP), even though this is conceptually the simplest and most general solution. Thus, current protocols involve only the direct players---we call such protocols self-reliant. They often use blinded boolean circuits, which has several sources of overhead, some due to the circuit representation and some due to the blinding. However, secure coprocessors like the IBM 4758 have actual security properties similar to ideal TTPs. They also have little RAM and a slow CPU.We call such devices Tiny TTPs. The availability of real tiny TTPs opens the door for a different approach to SMC problems. One major challenge with this approach is how to execute large programs on large inputs using the small protected memory of a tiny TTP, while preserving the trust properties that an ideal TTP provides. In this thesis we have investigated the use of real TTPs to help with the solution of SMC problems. We start with the use of such TTPs to solve the Private Information Retrieval (PIR) problem, which is one important instance of SMC. Our implementation utilizes a 4758. The rest of the thesis is targeted at general SMC. Our SMC system, Faerieplay, moves some functionality into a tiny TTP, and thus avoids the blinded circuit overhead. Faerieplay consists of a compiler from high-level code to an arithmetic circuit with special gates for efficient indirect array access, and a virtual machine to execute this circuit on a tiny TTP while maintaining the typical SMC trust properties. We report on Faerieplay\u27s security properties, the specification of its components, and our implementation and experiments. These include comparisons with the Fairplay circuit-based two-party system, and an implementation of the Dijkstra graph shortest path algorithm. We also provide an implementation of an oblivious RAM which supports similar tiny TTP-based SMC functionality but using a standard RAM program. Performance comparisons show Faerieplay\u27s circuit approach to be considerably faster, at the expense of a more constrained programming environment when targeting a circuit