Cayley Graphs of Semigroups and Applications to Hashing

In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$. In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also discuss its efficiency, pseudorandomness and security features. Furthermore, we generalized the Fit-Florea and Matula\u27s algorithm (2004) that finds the discrete logarithm in the multiplicative group of integers modulo $2^k$ by establishing a connection between semi-primitive roots modulo $2^k$ where $k\geq 3$ and the logarithmic base used in the algorithm

Analysis and Design of Authentication and Encryption Algorithms for Secure Cloud Systems

Along with the fast growth of networks and mobile devices, cloud computing has become one of the most attractive and effective technologies and business solutions nowadays. Increasing numbers of organizations and customers are migrating their businesses and data to the cloud due to the flexibility and cost-efficiency of cloud systems. Preventing unauthorized access of sensitive data in the cloud has been one of the biggest challenges when designing a secure cloud system, and it strongly relies on the chosen authentication and encryption algorithms for providing authenticity and confidentiality, respectively. This thesis investigates various aspects of authentication and encryption algorithms for securing cloud systems, including authenticated encryption modes of operation, block ciphers, password hashing algorithms, and password-less/two-factor authentication mechanisms. Improving Authenticated Encryption Modes. The Galois/Counter Mode (GCM) is an authenticated encryption mode of operation for block ciphers. It has been widely adopted by many network standards and protocols that protect the security of cloud communications, such as TLS v1.2, IEEE 802.1AE and IPsec. Iwata et al. recently found a flaw in GCM's original proofs for non-96-bit nonce cases, and then presented new security bounds for GCM. The new bounds imply that the success probabilities of adversaries for attacking GCM are much larger than the originally expected ones. We propose a simple change to repair GCM. When applied, it will improve the security bounds by a factor of about $2^{20}$ while maintaining most of the original proofs. Analyzing Polynomial-Based Message Authentication Codes. We investigate attacks on polynomial-based message authentication code (MAC) schemes including the one adopted in GCM. We demonstrate that constructing successful forgeries of these MAC schemes does not necessarily require hash collisions. This discovery removes certain restrictions in the attacks previously proposed by Procter and Cid. Moreover, utilizing a special design of GCM for processing non-96-bit nonces, we turn these forgery attacks into birthday attacks, which will significantly increase their success probabilities. Therefore, by considering the birthday attacks and the security proof flaw found by Iwata et al., cloud system designers should avoid using GCM with non-96-bit nonces if they do not revise the design of GCM. Analyzing Block Ciphers. We propose a new framework for analyzing symmetric-key ciphers by guessing intermediate states to divide ciphers into small components. This framework is suitable for lightweight ciphers with simple key schedules and block sizes smaller than key lengths. Using this framework, we design new attacks on the block cipher family KATAN. These attacks can recover the master keys of 175-round KATAN32, 130-round KATAN48 and 112-round KATAN64 faster than exhaustive search, and thus reach many more rounds than the existing attacks. We also provide new attacks on 115-round KATAN32 and 100-round KATAN48 in order to demonstrate that this new kind of attack can be more time-efficient and memory-efficient than the existing ones. Designing Password Hashing Algorithms. Securely storing passwords and deriving cryptographic keys from passwords are also crucial for most secure cloud system designs. However, choices of well-studied password hashing algorithms are extremely limited, as their security requirements and design principles are different from common cryptographic primitives. We propose two practical password hashing algorithms, Pleco and Plectron. They are built upon well-understood cryptographic algorithms, and combine the advantages of symmetric-key and asymmetric-key primitives. By employing the Rabin cryptosystem, we prove that the one-wayness of Pleco is at least as strong as the hard problem of integer factorization. In addition, both password hashing algorithms are designed to be sequential memory-hard, in order to thwart large-scale password searching using parallel hardware, such as GPUs, FPGAs, and ASICs. Designing Password-less/Two-Factor Authentication Mechanisms. Motivated by a number of recent industry initiatives, we propose Loxin, an innovative solution for password-less authentication for cloud systems and web applications. Loxin aims to improve on passwords with respect to both usability and security. It utilizes push message services for mobile devices to initiate authentication transactions based on asymmetric-key cryptography, and enables users to access multiple services by using pre-owned identities, such as email addresses. In particular, the Loxin server cannot generate users' authentication credentials, thereby eliminating the potential risk of credential leakage if the Loxin server gets compromised. Furthermore, Loxin is fully compatible with existing password-based authentication systems, and thus can serve as a two-factor authentication mechanism

Integrated-Key Cryptographic Hash Functions

Cryptographic hash functions have always played a major role in most cryptographic applications. Traditionally, hash functions were designed in the keyless setting, where a hash function accepts a variable-length message and returns a fixed-length fingerprint. Unfortunately, over the years, significant weaknesses were reported on instances of some popular ``keyless" hash functions. This has motivated the research community to start considering the dedicated-key setting, where a hash function is publicly keyed. In this approach, families of hash functions are constructed such that the individual members are indexed by different publicly-known keys. This has, evidently, also allowed for more rigorous security arguments. However, it turns out that converting an existing keyless hash function into a dedicated-key one is usually non-trivial since the underlying keyless compression function of the keyless hash function does not normally accommodate the extra key input. In this thesis we define and formalise a flexible approach to solve this problem. Hash functions adopting our approach are said to be constructed in the integrated-key setting, where keyless hash functions are seamlessly and transparently transformed into keyed variants by introducing an extra component accompanying the (still keyless) compression function to handle the key input separately outside the compression function. We also propose several integrated-key constructions and prove that they are collision resistant, pre-image resistant, 2nd pre-image resistant, indifferentiable from Random Oracle (RO), indistinguishable from Pseudorandom Functions (PRFs) and Unforgeable when instantiated as Message Authentication Codes (MACs) in the private key setting. We further prove that hash functions constructed in the integrated-key setting are indistinguishable from their variants in the conventional dedicated-key setting, which implies that proofs from the dedicated-key setting can be naturally reduced to the integrated-key setting.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Some Notes on Code-Based Cryptography

This thesis presents new cryptanalytic results in several areas of coding-based cryptography. In addition, we also investigate the possibility of using convolutional codes in code-based public-key cryptography. The first algorithm that we present is an information-set decoding algorithm, aiming towards the problem of decoding random linear codes. We apply the generalized birthday technique to information-set decoding, improving the computational complexity over previous approaches. Next, we present a new version of the McEliece public-key cryptosystem based on convolutional codes. The original construction uses Goppa codes, which is an algebraic code family admitting a well-defined code structure. In the two constructions proposed, large parts of randomly generated parity checks are used. By increasing the entropy of the generator matrix, this presumably makes structured attacks more difficult. Following this, we analyze a McEliece variant based on quasi-cylic MDPC codes. We show that when the underlying code construction has an even dimension, the system is susceptible to, what we call, a squaring attack. Our results show that the new squaring attack allows for great complexity improvements over previous attacks on this particular McEliece construction. Then, we introduce two new techniques for finding low-weight polynomial multiples. Firstly, we propose a general technique based on a reduction to the minimum-distance problem in coding, which increases the multiplicity of the low-weight codeword by extending the code. We use this algorithm to break some of the instances used by the TCHo cryptosystem. Secondly, we propose an algorithm for finding weight-4 polynomials. By using the generalized birthday technique in conjunction with increasing the multiplicity of the low-weight polynomial multiple, we obtain a much better complexity than previously known algorithms. Lastly, two new algorithms for the learning parities with noise (LPN) problem are proposed. The first one is a general algorithm, applicable to any instance of LPN. The algorithm performs favorably compared to previously known algorithms, breaking the 80-bit security of the widely used (512,1/8) instance. The second one focuses on LPN instances over a polynomial ring, when the generator polynomial is reducible. Using the algorithm, we break an 80-bit security instance of the Lapin cryptosystem

TEDT, a Leakage-Resilient AEAD mode for High (Physical) Security Applications

We propose TEDT, a new Authenticated Encryption with Associated Data (AEAD) mode leveraging Tweakable Block Ciphers (TBCs). TEDT provides the following features: (i) It offers asymptotically optimal security in the multi-user setting. (ii) It offers nonce misuse-resilience, that is, the repetition of nonces does not impact the security of ciphertexts produced with fresh nonces. (iii) It offers KDM security in the multi-user setting, that is, its security is maintained even if key-dependent messages are encrypted. (iv) It offers full leakage-resilience, that is, it limits the exploitability of physical leakages via side-channel attacks, even if these leakages happen during every message encryption and decryption operation. (v) It can be implemented with a remarkably low energy cost when strong resistance to side-channel attacks is needed, supports online encryption and handles static & incremental associated data efficiently. Concretely, TEDT encourages leveled implementations, in which two TBCs are implemented: one needs strong and energy demanding protections against side-channel attacks but is used in a limited way, while the other only requires weak and energy efficient protections and performs the bulk of the computation. As a result, TEDT leads to considerably more energy efficient implementations compared to traditional AEAD schemes, whose side-channel security requires to uniformly protect every (T)BC execution

Provably Secure Authenticated Encryption

Authenticated Encryption (AE) is a symmetric key cryptographic primitive that ensures confidentiality and authenticity of processed messages at the same time. The research of AE as a primitive in its own right started in 2000. The security goals of AE were captured in formal definitions in the tradition in the tradition of provable security (such as NAE, MRAE, OAE, RAE or the RUP), where the security of a scheme is formally proven assuming the security of an underlying building block. The prevailing syntax moved to nonce-based AE with associated data (which is an additional input that gets authenticated, but not encrypted). Other types of AE schemes appeared as well, e.g. ones that supported stateful sessions. Numerous AE schemes were designed; in the early years, these were almost exclusively blockcipher modes of operation, most notably OCB in 2001, CCM in 2003 and GCM in 2004. At the same time, issues were discovered both with the security and applicability of the most popular AE schemes, and other applications of symmetric key cryptography. As a response, the Competition for Authenticated Encryption: Security, Applicability, and Robustness (CAESAR) was started in 2013. Its goals were to identify a portfolio of new, secure and reliable AE schemes that would satisfy the needs of practical applications, and also to boost the research in the area of AE. Prompted by CAESAR, 57 new schemes were designed, new types of constructions that gained popularity appeared (such as the Sponge-based AE schemes), and new notions of security were proposed (such as RAE). The final portfolio of the CAESAR competition should be announced in 2018. In this thesis, we push the state of the art in the field of AE in several directions. All of them are related to provable security, in one way, or another. We propose OMD, the first provably secure dedicated AE scheme that is based on a compression function. We further modify OMD to achieve nonce misuse-resistant security (MRAE). We also propose another provably secure variant of OMD called pure OMD, which enjoys a great improvement of performance over OMD. Inspired by the modifications that gave rise to pure OMD, we turn to the popular Sponge-based AE schemes and prove that similar measures can also be applied to the keyed Sponge and keyed Duplex (a variant of the Sponge), allowing a substantial increase of performance without an impact on security. We then address definitional aspects of AE. We critically evaluate the security notion of OAE, whose authors claimed that it provides the best possible security for online schemes under nonce reuse. We challenge these claims, and discuss what are the meaningful requirements for online AE schemes. Based on our findings, we formulate a new definition of online AE security under nonce-reuse, and demonstrate its feasibility. We next turn our attention to the security of nonce-based AE schemes under stretch misuse; i.e. when a scheme is used with varying ciphertext expansion under the same key, even though it should not be. We argue that varying the stretch is plausible, and formulate several notions that capture security in presence of variable stretch. We establish their relations to previous notions, and demonstrate the feasibility of security in this setting. We finally depart from provable security, with the intention to complement it. We compose a survey of universal forgeries, decryption attacks and key recovery attacks on 3rd round CAESAR candidates

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