Boolean Skolem function synthesis concerns synthesizing outputs as Boolean functions of inputs such that a relational specification between inputs and outputs is satisfied. This problem, also known as Boolean functional synthesis, has several applications, including design of safe controllers for autonomous systems, certified QBF solving, cryptanalysis etc. Recently, complexity theoretic hardness results have been shown for the problem, although several algorithms proposed in the literature are known to work well in practice. This dichotomy between theoretical hardness and practical efficacy has motivated the research into normal forms or representations of input specifications that permit efficient synthesis, thus explaining perhaps the efficacy of these algorithms. In this paper we go one step beyond this and ask if there exists a normal form representation that can in fact precisely characterize "efficient" synthesis. We present a normal form called SAUNF that precisely characterizes tractable synthesis in the following sense: a specification is polynomial time synthesizable iff it can be compiled to SAUNF in polynomial time. Additionally, a specification admits a polynomial-sized functional solution iff there exists a semantically equivalent polynomial-sized SAUNF representation. SAUNF is exponentially more succinct than well-established normal forms like BDDs and DNNFs, used in the context of AI problems, and strictly subsumes other more recently proposed forms like SynNNF. It enjoys compositional properties that are similar to those of DNNF. Thus, SAUNF provides the right trade-off in knowledge representation for Boolean functional synthesis.
Cryptanalysis on standard quantum cryptographic systems generally involves finding optimal adversarial attack strategies on the underlying protocols. The core principle of modelling quantum attacks in many cases reduces to the adversary's ability to clone unknown quantum states which facilitates the extraction of some meaningful secret information. Explicit optimal attack strategies typically require high computational resources due to large circuit depths or, in many cases, are unknown. In this work, we propose variational quantum cloning (VQC), a quantum machine learning based cryptanalysis algorithm which allows an adversary to obtain optimal (approximate) cloning strategies with short depth quantum circuits, trained using hybrid classical-quantum techniques. The algorithm contains operationally meaningful cost functions with theoretical guarantees, quantum circuit structure learning and gradient descent based optimisation. Our approach enables the end-to-end discovery of hardware efficient quantum circuits to clone specific families of quantum states, which in turn leads to an improvement in cloning fidelites when implemented on quantum hardware: the Rigetti Aspen chip. Finally, we connect these results to quantum cryptographic primitives, in particular quantum coin flipping. We derive attacks on two protocols as examples, based on quantum cloning and facilitated by VQC. As a result, our algorithm can improve near term attacks on these protocols, using approximate quantum cloning as a resource.
Wireless communication has been a broadcast system since its inception, which violates security and privacy issues at the physical layer between the intended transmit and receive pairs. As we move towards advanced spectrum sharing methodologies involving billions of devices connected over wireless networks, it is essential to secure the wireless signal such that only the intended receiver can realize the properties of the signal. In this paper, we propose Rand-OFDM, a new waveform, secured with a shared secret key, where the signal properties can be recovered only at the expected receiver. We achieve the signal level security by modifying the OFDM signal in time-domain, thus erasing the OFDM properties and in turn obfuscating the signal properties to an eavesdropper. We introduce a key-based secured training signal for channel estimation, which can be used only at the intended receiver with prior knowledge of the key. As a final step for the recovery of the signal, we use a clustering-based technique to correct the phase of the received signal. Our cryptanalysis shows that Rand-OFDM is especially useful in future wideband signals. Extensive simulation and over-the-air experiments show that the performance of Rand-OFDM is comparable to legacy OFDM and SNR penalty due to the secured waveform varies between 1-4dB. In all these scenarios, Rand-OFDM remains unrecognized by the adversary even at the highest possible SNR.
This paper explores a new framework for lossy image encryption and decryption using a simple shallow encoder neural network E for encryption, and a complex deep decoder neural network D for decryption. E is kept simple so that encoding can be done on low power and portable devices and can in principle be any nonlinear function which outputs an encoded vector. D is trained to decode the encodings using the dataset of image - encoded vector pairs obtained from E and happens independently of E. As the encodings come from E which while being a simple neural network, still has thousands of random parameters and therefore the encodings would be practically impossible to crack without D. This approach differs from autoencoders as D is trained completely independently of E, although the structure may seem similar. Therefore, this paper also explores empirically if a deep neural network can learn to reconstruct the original data in any useful form given the output of a neural network or any other nonlinear function, which can have very useful applications in Cryptanalysis. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the decoded images from D along with some limitations.
Cancelable biometric schemes generate secure biometric templates by combining user specific tokens and biometric data. The main objective is to create irreversible, unlinkable, and revocable templates, with high accuracy in matching. In this paper, we cryptanalyze two recent cancelable biometric schemes based on a particular locality sensitive hashing function, index-of-max (IoM): Gaussian Random Projection-IoM (GRP-IoM) and Uniformly Random Permutation-IoM (URP-IoM). As originally proposed, these schemes were claimed to be resistant against reversibility, authentication, and linkability attacks under the stolen token scenario. We propose several attacks against GRP-IoM and URP-IoM, and argue that both schemes are severely vulnerable against authentication and linkability attacks. We also propose better, but not yet practical, reversibility attacks against GRP-IoM. The correctness and practical impact of our attacks are verified over the same dataset provided by the authors of these two schemes.
In many previous works, a single-pixel imaging (SPI) system is constructed as an optical image encryption system. Unauthorized users are not able to reconstruct the plaintext image from the ciphertext intensity sequence without knowing the illumination pattern key. However, little cryptanalysis about encrypted SPI has been investigated in the past. In this work, we propose a known-plaintext attack scheme and a ciphertext-only attack scheme to an encrypted SPI system for the first time. The known-plaintext attack is implemented by interchanging the roles of illumination patterns and object images in the SPI model. The ciphertext-only attack is implemented based on the statistical features of single-pixel intensity values. The two schemes can crack encrypted SPI systems and successfully recover the key containing correct illumination patterns.
Random number generators (RNGs) that are crucial for cryptographic applications have been the subject of adversarial attacks. These attacks exploit environmental information to predict generated random numbers that are supposed to be truly random and unpredictable. Though quantum random number generators (QRNGs) are based on the intrinsic indeterministic nature of quantum properties, the presence of classical noise in the measurement process compromises the integrity of a QRNG. In this paper, we develop a predictive machine learning (ML) analysis to investigate the impact of deterministic classical noise in different stages of an optical continuous variable QRNG. Our ML model successfully detects inherent correlations when the deterministic noise sources are prominent. After appropriate filtering and randomness extraction processes are introduced, our QRNG system, in turn, demonstrates its robustness against ML. We further demonstrate the robustness of our ML approach by applying it to uniformly distributed random numbers from the QRNG and a congruential RNG. Hence, our result shows that ML has potentials in benchmarking the quality of RNG devices.
This paper proposes a method to estimate the total time required to solve SAT in distributed environments via partitioning approach. It is based on the observation that for some simple forms of problem partitioning one can use the Monte Carlo approach to estimate the time required to solve an original problem. The method proposed is based on an algorithm for searching for partitioning with an optimal solving time estimation. We applied this method to estimate the time required to perform logical cryptanalysis of the widely known stream ciphers A5/1 and Bivium. The paper also describes a volunteer computing project SAT@home aimed at solving hard combinatorial problems reduced to SAT. In this project during several months there were solved 10 problems of logical cryptanalysis of the A5/1 cipher thatcould not be solved using known rainbow tables.
This thesis aims to use intelligent systems to extend and improve performance and security of cryptographic techniques. Genetic algorithms framework for cryptanalysis problem is addressed. A novel extension to the differential cryptanalysis using genetic algorithm is proposed and a fitness measure based on the differential characteristics of the cipher being attacked is also proposed. The complexity of the proposed attack is shown to be less than quarter of normal differential cryptanalysis of the same cipher by applying the proposed attack to both the basic Substitution Permutation Network and the Feistel Network. The basic models of modern block ciphers are attacked instead of actual cipher to prove that the attack is applicable to other ciphers vulnerable to differential cryptanalysis. A new attack for block cipher based on the ability of neural networks to perform an approximation of mapping is proposed. A complete problem formulation is explained and implementation of the attack on some hypothetical Feistel cipher not vulnerable to differential or linear attacks is presented. A new block cipher based on the neural networks is proposed. A complete cipher structure is given and a key scheduling is also shown. The main properties of neural network being able to perform mapping between large dimension domains in a very fast and a very small memory compared to S-Boxes is used as a base for the cipher.
In this paper we analyze the cryptanalysis of the simplified data encryption standard algorithm using meta-heuristics and in particular genetic algorithms. The classic fitness function when using such an algorithm is to compare n-gram statistics of a the decrypted message with those of the target message. We show that using such a function is irrelevant in case of Genetic Algorithm, simply because there is no correlation between the distance to the real key (the optimum) and the value of the fitness, in other words, there is no hidden gradient. In order to emphasize this assumption we experimentally show that a genetic algorithm perform worse than a random search on the cryptanalysis of the simplified data encryption standard algorithm.
Cryptanalysis of knapsack cipher is a fascinating problem which has eluded the computing fraternity for decades. However, in most of the cases either the time complexity of the proposed algorithm is colossal or an insufficient number of samples have been taken for verification. The present work proposes a Genetic Algorithm based technique for cryptanalysis of knapsack cipher. The experiments conducted prove the validity of the technique. The results prove that the technique is better than the existing techniques. An extensive review has been carried out in order to find the gaps in the existing techniques. The work paves the way of the application of computational intelligence techniques to the discipline of cryptanalysis.
In this paper we propose the technology for constructing propositional encodings of discrete functions. It is aimed at solving inversion problems of considered functions using state-of-the-art SAT solvers. We implemented this technology in the form of the software system called Transalg, and used it to construct SAT encodings for a number of cryptanalysis problems. By applying SAT solvers to these encodings we managed to invert several cryptographic functions. In particular, we used the SAT encodings produced by Transalg to construct the family of two-block MD5 collisions in which the first 10 bytes are zeros. Also we used Transalg encoding for the widely known A5/1 keystream generator to solve several dozen of its cryptanalysis instances in a distributed computing environment. In the paper we compare in detail the functionality of Transalg with that of similar software systems.
Recurrent neural networks (RNNs) represent the state of the art in translation, image captioning, and speech recognition. They are also capable of learning algorithmic tasks such as long addition, copying, and sorting from a set of training examples. We demonstrate that RNNs can learn decryption algorithms -- the mappings from plaintext to ciphertext -- for three polyalphabetic ciphers (Vigen\`ere, Autokey, and Enigma). Most notably, we demonstrate that an RNN with a 3000-unit Long Short-Term Memory (LSTM) cell can learn the decryption function of the Enigma machine. We argue that our model learns efficient internal representations of these ciphers 1) by exploring activations of individual memory neurons and 2) by comparing memory usage across the three ciphers. To be clear, our work is not aimed at 'cracking' the Enigma cipher. However, we do show that our model can perform elementary cryptanalysis by running known-plaintext attacks on the Vigen\`ere and Autokey ciphers. Our results indicate that RNNs can learn algorithmic representations of black box polyalphabetic ciphers and that these representations are useful for cryptanalysis.
Propositional satisfiability (SAT) is at the nucleus of state-of-the-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled efficiently by identifying and exploiting a subset of formula's variables called backdoor set (or simply backdoors). This paper proposes a new class of backdoor sets for SAT used in the context of cryptographic attacks, namely guess-and-determine attacks. The idea is to identify the best set of backdoor variables subject to a statistically estimated hardness of the guess-and-determine attack using a SAT solver. Experimental results on weakened variants of the renowned encryption algorithms exhibit advantage of the proposed approach compared to the state of the art in terms of the estimated hardness of the resulting guess-and-determine attacks.
In the present paper, we propose a technology for translating algorithmic descriptions of discrete functions to SAT. The proposed technology is aimed at applications in algebraic cryptanalysis. We describe how cryptanalysis problems are reduced to SAT in such a way that it should be perceived as natural by the cryptographic community. In~the theoretical part of the paper we justify the main principles of general reduction to SAT for discrete functions from a class containing the majority of functions employed in cryptography. Then, we describe the Transalg software tool developed based on these principles with SAT-based cryptanalysis specifics in mind. We demonstrate the results of applications of Transalg to construction of a number of attacks on various cryptographic functions. Some of the corresponding attacks are state of the art. We compare the functional capabilities of the proposed tool with that of other domain-specific software tools which can be used to reduce cryptanalysis problems to SAT, and also with the CBMC system widely employed in symbolic verification. The paper also presents vast experimental data, obtained using the SAT solvers that took first places at the SAT competitions in the recent several years.