Securing Deployed Cryptographic Systems

In 2015 more than 150 million records and $400 billion were lost due to publicly-reported criminal and nation-state cyberattacks in the United States alone. The failure of our existing security infrastructure motivates the need for improved technologies, and cryptography provides a powerful tool for doing this. There is a misperception that the cryptography we use today is a "solved problem" and the real security weaknesses are in software or other areas of the system. This is, in fact, not true at all, and over the past several years we have seen a number of serious vulnerabilities in the cryptographic pieces of systems, some with large consequences. This thesis will discuss three aspects of securing deployed cryptographic systems. We will first explore the evaluation of systems in the wild, using the example of how to efficiently and effectively recover user passwords submitted over TLS encrypted with RC4, with applications to many methods of web authentication as well as the popular IMAP protocol for email. We will then address my work on developing tools to design and create cryptographic systems and bridge the often large gap between theory and practice by introducing AutoGroup+, a tool that automatically translates cryptographic schemes from the mathematical setting used in the literature to that typically used in practice, giving both a secure and optimal output. We will conclude with an exploration of how to actually build real world deployable systems by discussing my work on developing decentralized anonymous credentials in order to increase the security and deployability of existing anonymous credentials systems

On Data Complexity of Distinguishing Attacks vs. Message Recovery Attacks on Stream Ciphers

We revisit the different approaches used in the literature to estimate the data complexity of distinguishing attacks on stream ciphers and analyze their inter-relationships. In the process, we formally argue which approach is applicable (or not applicable) in what scenario. To our knowledge, this is the first kind of such an exposition. We also perform a rigorous statistical analysis of the message recovery attack that exploits a distinguisher and show that in practice there is a significant gap between the data complexities of a message recovery attack and the underlying distinguishing attack. This gap is not necessarily determined by a constant factor as a function of the false positive and negative rate, as one would expect. Rather this gap is also a function of the number of samples of the distinguishing attack. We perform a case study on RC4 stream cipher to demonstrate that the typical complexities for message recovery attack inferred in the literature are but under-estimates and the actual estimates are quite larger

Settling the mystery of Zr=rZ_r=r in RC4

In this paper, using probability transition matrix, at first we revisit the work of Mantin on finding the probability distribution of RC4 permutation after the completion of KSA. After that, we extend the same idea to analyse the probabilities during any iteration of Pseudo Random Generation Algorithm. Next, we study the bias $Z_r=r$ (where $Z_r$ is the $r$-th output keystream bit), which is one of the significant biases observed in RC4 output keystream. This bias has played an important role in the plaintext recovery attack proposed by Isobe et al. in FSE 2013. However, the accurate theoretical explanation of the bias of $Z_r=r$ is still a mystery. Though several attempts have been made to prove this bias, none of those provides accurate justification. Here, using the results found with the help of probability transition matrix we justify this bias of $Z_r=r$ accurately and settle this issue. The bias obtained from our proof matches perfectly with the experimental observations

Glimpses are Forever in RC4 amidst the Spectre of Biases

In this paper we exploit elementary combinatorial techniques to settle different cryptanalytic observations on RC4 that remained unproved for more than two decades. At the same time, we present new observations with theoretical proofs. We first prove the biases (non-randomness) presented by Fluhrer and McGrew (FSE 2000) two decades ago. It is surprising that though the biases have been published long back, and there are many applications of them in cryptanalysis till recent days as well, the proofs have never been presented. In this paper, we complete that task and also show that any such bias immediately provides a glimpse of hidden variables in RC4. Further, we take up the biases of two non-consecutive key-stream bytes skipping one byte in between. We show the incompleteness of such a result presented by SenGupta et al (JoC, 2013) and provide new observations and proofs in this direction relating the key-stream bytes and glimpses. Similarly, we streamline certain missed observation in the famous Glimpse theorem presented by Jenkins in 1996. Our results point out how biases of RC4 key-stream and the Glimpses of the RC4 hidden variables are related. It is evident from our results that the biases and glimpses are everywhere in RC4 and it needs further investigation as we provide very high magnitude of glimpses that were not known earlier. The new glimpses and biases that we identify in this paper may be exploited in improving practical attacks against the protocols that use RC4

Cryptography and Its Applications in Information Security

Nowadays, mankind is living in a cyber world. Modern technologies involve fast communication links between potentially billions of devices through complex networks (satellite, mobile phone, Internet, Internet of Things (IoT), etc.). The main concern posed by these entangled complex networks is their protection against passive and active attacks that could compromise public security (sabotage, espionage, cyber-terrorism) and privacy. This Special Issue “Cryptography and Its Applications in Information Security” addresses the range of problems related to the security of information in networks and multimedia communications and to bring together researchers, practitioners, and industrials interested by such questions. It consists of eight peer-reviewed papers, however easily understandable, that cover a range of subjects and applications related security of information

Applications of the Galois Model LFSR in Cryptography

The linear feedback shift-register is a widely used tool for generating cryptographic sequences. The properties of the Galois model discussed here offer many opportunities to improve the implementations that already exist. We explore the overall properties of the phases of the Galois model and conjecture a relation with modular Golomb rulers. This conjecture points to an efficient method for constructing non-linear filtering generators which fulfil Golic s design criteria in order to maximise protection against his inversion attack. We also produce a number of methods which can improve the rate of output of sequences by combining particular distinct phases of smaller elementary sequences

Randomness Generation for Secure Hardware Masking - Unrolled Trivium to the Rescue

Masking is a prominent strategy to protect cryptographic implementations against side-channel analysis. Its popularity arises from the exponential security gains that can be achieved for (approximately) quadratic resource utilization. Many variants of the countermeasure tailored for different optimization goals have been proposed over the past decades. The common denominator among all of them is the implicit demand for robust and high entropy randomness. Simply assuming that uniformly distributed random bits are available, without taking the cost of their generation into account, leads to a poor understanding of the efficiency and performance of secure implementations. This is especially relevant in case of hardware masking schemes which are known to consume large amounts of random bits per cycle due to parallelism. Currently, there seems to be no consensus on how to most efficiently derive many pseudo-random bits per clock cycle from an initial seed and with properties suitable for masked hardware implementations. In this work, we evaluate a number of building blocks for this purpose and find that hardware-oriented stream ciphers like Trivium and its reduced-security variant Bivium B outperform all competitors when implemented in an unrolled fashion. Unrolled implementations of these primitives enable the flexible generation of many bits per cycle while maintaining high performance, which is crucial for satisfying the large randomness demands of state-of-the-art masking schemes. According to our analysis, only Linear Feedback Shift Registers (LFSRs), when also unrolled, are capable of producing long non-repetitive sequences of random-looking bits at a high rate per cycle even more efficiently than Trivium and Bivium B. Yet, these instances do not provide black-box security as they generate only linear outputs. We experimentally demonstrate that using multiple output bits from an LFSR in the same masked implementation can violate probing security and even lead to harmful randomness cancellations. Circumventing these problems, and enabling an independent analysis of randomness generation and masking scheme, requires the use of cryptographically stronger primitives like stream ciphers. As a result of our studies, we provide an evidence-based estimate for the cost of securely generating n fresh random bits per cycle. Depending on the desired level of black-box security and operating frequency, this cost can be as low as 20n to 30n ASIC gate equivalents (GE) or 3n to 4n FPGA look-up tables (LUTs), where n is the number of random bits required. Our results demonstrate that the cost per bit is (sometimes significantly) lower than estimated in previous works, incentivizing parallelism whenever exploitable and potentially moving low randomness usage in hardware masking research from a primary to secondary design goal

Cryptanalysis, Reverse-Engineering and Design of Symmetric Cryptographic Algorithms

In this thesis, I present the research I did with my co-authors on several aspects of symmetric cryptography from May 2013 to December 2016, that is, when I was a PhD student at the university of Luxembourg under the supervision of Alex Biryukov. My research has spanned three different areas of symmetric cryptography. In Part I of this thesis, I present my work on lightweight cryptography. This field of study investigates the cryptographic algorithms that are suitable for very constrained devices with little computing power such as RFID tags and small embedded processors such as those used in sensor networks. Many such algorithms have been proposed recently, as evidenced by the survey I co-authored on this topic. I present this survey along with attacks against three of those algorithms, namely GLUON, PRINCE and TWINE. I also introduce a new lightweight block cipher called SPARX which was designed using a new method to justify its security: the Long Trail Strategy. Part II is devoted to S-Box reverse-engineering, a field of study investigating the methods recovering the hidden structure or the design criteria used to build an S-Box. I co-invented several such methods: a statistical analysis of the differential and linear properties which was applied successfully to the S-Box of the NSA block cipher Skipjack, a structural attack against Feistel networks called the yoyo game and the TU-decomposition. This last technique allowed us to decompose the S-Box of the last Russian standard block cipher and hash function as well as the only known solution to the APN problem, a long-standing open question in mathematics. Finally, Part III presents a unifying view of several fields of symmetric cryptography by interpreting them as purposefully hard. Indeed, several cryptographic algorithms are designed so as to maximize the code size, RAM consumption or time taken by their implementations. By providing a unique framework describing all such design goals, we could design modes of operations for building any symmetric primitive with any form of hardness by combining secure cryptographic building blocks with simple functions with the desired form of hardness called plugs. Alex Biryukov and I also showed that it is possible to build plugs with an asymmetric hardness whereby the knowledge of a secret key allows the privileged user to bypass the hardness of the primitive

Some Theoretical Conditions for Menezes--Qu--Vanstone Key Agreement to Provide Implicit Key Authentication

Menezes--Qu--Vanstone key agreement (MQV) is intended to provide implicit key authentication (IKA) and several other security objectives. MQV is approved and specified in five standards. This report focuses on the IKA of two-pass MQV, without key confirmation. Arguably, implicit key authentication is the most essential security objective in authenticated key agreement. The report examines various necessary or sufficient formal conditions under which MQV may provide IKA. Incidentally, this report defines, relies on, and inter-relates various conditions on the key deriviation function and Diffie--Hellman groups. While it should be expected that most such definitions and results are already well-known, a reader interested in these topics may be interested in this report as a kind of review, even if they have no interest in MQV whatsoever