New Insights On Differential And Linear Bounds Using Mixed Integer Linear Programming (Full Version)

Mixed Integer Linear Programming (MILP) is a very common method of modelling differential and linear bounds for ciphers, as it automates the process of finding the best differential trail or linear approximation. The Convex Hull (CH) modelling, introduced by Sun et al. (Eprint 2013/Asiacrypt 2014), is a popular method in this regard, which can convert the conditions corresponding to a small (4-bit) SBox to MILP constraints efficiently. In our work, we study this modelling with CH in more depth and observe a previously unreported problem associated with it. Our analysis shows, there are SBoxes for which the CH modelling can yield incorrect modelling. As such, using the CH modelling may lead to incorrect differential or linear bounds. This arises from the observation that although the CH is generated for a certain set of points, there can be points outside this set which also satisfy all the inequalities of the CH. As apparently no variant of the CH modelling can circumvent this problem, we propose a new modelling for differential and linear bounds. Our modelling makes use of every points of interest individually. This modelling works for an arbitrary SBox, and is able to find the exact bound. Additionally, we also explore the possibility of using redundant constraints, such that the run time for an MILP solver can be reduced while keeping the optimal result unchanged. For this purpose, we revisit the CH modelling and use the CH constraints as redundant constraints (on top of our usual constraints, which ensure the aforementioned problem does not occur). In fact, we choose two heuristics from the convex hull modelling. The first uses all the inequalities of a convex hull, while second uses a reduced number of inequalities. Apart from that, we also propose to use the solutions for the smaller rounds as another heuristic to find the optimal bound for a higher round. With our experiments on round-reduced GIFT-128, we show it is possible to reduce the run time a few folds using a suitable choice of redundant constraints. Further, we observe the necessity to consider separate heuristics for the differential and linear cases. We also present the optimal linear bounds for 11- and 12-rounds of GIFT-128, extending from the best-known result of 10-rounds

The Problem of Half Round Key XOR

In the design of GIFT, half round key XOR is used. This leads to the undesired consequence that the security against the differential/linear attacks are overestimated. This comes from the observation that; in the usual DDT/LAT based analysis of the differential/linear attacks, the inherent assumption is the full round key is XORed at each round

DORCIS: Depth Optimized Quantum Implementation of Substitution Boxes

In this paper, we present the ``DORCIS\u27\u27 tool, which finds depth-optimized quantum circuit implementations for arbitrary 3- and 4-bit S-boxes. It follows up from the previous LIGHTER-R tool (which only works for 4-bit S-boxes) by extending it in multiple ways. LIGHTER-R only deals at the top level (i.e., Toffoli gates), whereas DORCIS takes quantum decomposition (i.e., Clifford + T gates) into account. Further, DORCIS optimizes for quantum depth and T depth. We match, if not surpass, other optimized quantum circuit implementations put forth in the other papers. Similar to LIGHTER-R, our tool is also easy to use, and we provide an extended interface to IBM\u27s Qiskit

To Infect Or Not To Infect: A Critical Analysis Of Infective Countermeasures In Fault Attacks

As fault based cryptanalysis is becoming more and more of a practical threat, it is imperative to make efforts to devise suitable countermeasures. In this regard, the so-called ``infective countermeasures\u27\u27 have garnered particular attention from the community due to its ability in inhibiting differential fault attacks without explicitly detecting the fault. We observe that despite being adopted over a decade ago, a systematic study of infective countermeasures is missing from the literature. Moreover, there seems to be a lack of proper security analysis of the schemes proposed, as quite a few of them have been broken promptly. Our first contribution comes in the form of a generalization of infective schemes which aids us with a better insight into the vulnerabilities, scopes for cost reduction and possible improvements. This way, we are able to propose lightweight alternatives of two existing schemes. Further we analyze shortcomings of LatinCrypt\u2712 and CHES\u2714 schemes and propose a simple patch for the former

Quantum Implementation of ASCON Linear Layer

In this paper, we show an in-place implementation of the ASCON linear layer. An in-place implementation is important in the context of quantum computing, we expect our work will be useful in quantum implementation of ASCON. In order to get the implementation, we first write the ASCON linear layer as a binary matrix; then apply two legacy algorithms (Gauss-Jordan elimination and PLU factorization) as well as our modified version of Xiang et al.\u27s algorithm/source-code (published in ToSC/FSE\u2720). Our in-place implementation takes 1595 CNOT gates and 119 quantum depth; and this is the first in-place implementation of the ASCON linear layer, to the best of our knowledge

An Overview of Hash Based Signatures

Digital signatures are one of the most basic cryptographic building blocks which are utilized to provide attractive security features like authenticity, unforgeability, and undeniability. The security of existing state of the art digital signatures is based on hardness of number theoretic hardness assumptions like discrete logarithm and integer factorization. However, these hard problems are insecure and face a threat in the quantum world. In particular, quantum algorithms like Shor’s algorithm can be used to solve the above mentioned hardness problem in polynomial time. As an alternative, a new direction of research called post-quantum cryptography (PQC) is supposed to provide a new generation of quantum-resistant digital signatures. Hash based signature is one such candidate to provide post quantum secure digital signatures. Hash based signature schemes are a type of digital signature scheme that use hash functions as their central building block. They are efficient, flexible, and can be used in a variety of applications. In this document, we provide an overview of the hash based signatures. Our presentation of the topic covers a wide range of aspects that are not only comprehensible for readers without expertise in the subject matter, but also serve as a valuable resource for experts seeking reference material

Depth-Optimized Implementation of ASCON Quantum Circuit

The development of quantum computers, which employ a different paradigm of computation, is posing a threat to the security of cryptography. Narrowing down the scope to symmetric-key cryptography, the Grover search algorithm is probably the most influential in terms of its impact on security. Recently, there have been efforts to estimate the complexity of the Grover’s key search for symmetric key ciphers and evaluate their post-quantum security. In this paper, we present a depth-optimized implementation of a quantum circuit for ASCON, which is a symmetric key cipher that has recently been standardized in the NIST (National Institute of Standards and Technology) Lightweight Cryptography standardization. As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme. To our understanding, reducing the depth of the quantum circuit for the target cipher is the most effective approach for Grover’s key search. We demonstrate the optimal Grover’s key search cost for ASCON, along with a proposed depth-optimized quantum circuit. Further, based on the estimated cost, we evaluate the post-quantum security strength of ASCON according to relevant evaluation criteria and state-of-the-art research

Machine Learning Assisted Differential Distinguishers For Lightweight Ciphers (Extended Version)

At CRYPTO 2019, Gohr first introduces the deep learning based cryptanalysis on round-reduced SPECK. Using a deep residual network, Gohr trains several neural network based distinguishers on 8-round SPECK-32/64. The analysis follows an `all-in-one\u27 differential cryptanalysis approach, which considers all the output differences effect under the same input difference. Usually, the all-in-one differential cryptanalysis is more effective compared to the one using only one single differential trail. However, when the cipher is non-Markov or its block size is large, it is usually very hard to fully compute. Inspired by Gohr\u27s work, we try to simulate the all-in-one differentials for non-Markov ciphers through machine learning. Our idea here is to reduce a distinguishing problem to a classification problem, so that it can be efficiently managed by machine learning. As a proof of concept, we show several distinguishers for four high profile ciphers, each of which works with trivial complexity. In particular, we show differential distinguishers for 8-round Gimli-Hash, Gimli-Cipher and Gimli-Permutation; 3-round Ascon-Permutation; 10-round Knot-256 permutation and 12-round Knot-512 permutation; and 4-round Chaskey-Permutation. Finally, we explore more on choosing an efficient machine learning model and observe that only a three layer neural network can be used. Our analysis shows the attacker is able to reduce the complexity of finding distinguishers by using machine learning techniques

From Substitution Box To Threshold

With the escalating demand for lightweight ciphers as well as side channel protected implementation of those ciphers in recent times, this work focuses on two aspects. First, we present a tool for automating the task of finding a Threshold Implementation (TI) of a given Substitution Box (SBox). Our tool returns `with decomposition\u27 and `without decomposition\u27 based TI. The `with decomposition\u27 based implementation returns a combinational SBox; whereas we get a sequential SBox from the `without decomposition\u27 based implementation. Despite being high in demand, it appears that this kind of tool has been missing so far. Second, we show an algorithmic approach where a given cipher implementation can be tweaked (without altering the cipher specification) so that its TI cost can be significantly reduced. We take the PRESENT cipher as our case study (our methodology can be applied to other ciphers as well). Indeed, we show over 31 percent reduction in area and over 52 percent reduction in depth compared to the basic threshold implementation

Hardware Implementation of SpoC-128

In this work, we present a hardware implementation of the lightweight Authenticated Encryption with Associated Data (AEAD) SpoC-128. Designed by AlTawy, Gong, He, Jha, Mandal, Nandi and Rohit; SpoC-128 was submitted to the Lightweight Cryptography (LWC) competition being organised by the National Institute of Standards and Technology (NIST) of the United States Department of Commerce. Our implementation follows the Application Programming Interface (API) specified by the cryptographic engineering research group in the George Mason University (GMU). The source codes are available over the public internet as an open-source project