MILP-Aided Bit-Based Division Property for Primitives with Non-Bit-Permutation Linear Layers

Division property is a general integral property introduced by Todo at EUROCRYPT 2015. Recently, at ASIACRYPT 2016, Xiang et al. applied the Mixed Integer Linear Programming (MILP) method to search bit-based division property, and handled the complexity which restricted the application of bit-based division property proposed by Todo and Morii at FSE 2016. However, their MILP-aided search was only applied to some lightweight block ciphers whose linear layers were limited to bit-permutations, and the feasibility of MILP-aided bit-based division property for ciphers with non-bit-permutation linear layers was an open problem. This paper comes out with the affirmative answer. First, we transform the complicated linear layers to their primitive representations, which only involves Copy and XOR operations. Then, the original Copy and XOR models are respectively generalized to deal with more output branches and input elements, and these generalized models are adopted to depict the primitive representations. Accordingly, the MILP-aided bit-based division property can be applied to much more primitives with complicated linear layers. As an illustration, we first evaluate the bit-based division propertyies of some word-oriented block ciphers including Midori64, LED, Joltik-BC, and AES. For Midori64, we obtain a 7-round integral distinguisher, which achieves one more round than the previous results. At the same time, the data requirements of some existing distinguishers are also reduced. We decrease the number of required chosen plaintexts of 4-round and 5-round integral distinguishers for LED and Joltik-BC by half. As to AES, our searching experiments show that integral distinguishers, which are based on the bit-based division property, covering more than four rounds probably do not exist. Then, the bit-based division properties of some bit-oriented block ciphers, such as Serpent and Noekeon, are considered. The data complexities of their distinguishers for short rounds are improved. Moreover, we evaluate the bit-based division properties of the internal permutations involved in some hash functions, e.g., SPONGENT and PHOTON. An 18-round zero-sum distinguisher for SPONGENT-88 is proposed, which achieves four more rounds than the previous ones. We also provide 20-round and 21-round zero-sum distinguishers for SPONGENT-128 and SPONGENT-160, respectively. For most PHOTON permutations $P_{t}$ with 4-bit cell, the data requirements for the 4-round distinguishers are reduced by half. Besides, the length of $P_{256}$\u27s distinguisher is extended by one round. Furthermore, for $P_{288}$ using 8-bit S-boxes, we improve the data complexities of their integral distinguishers significantly

Multiple Limited-Birthday Distinguishers and Applications

In this article, we propose a new improvement of the rebound techniques, used for cryptanalyzing AES-like permutations during the past years. Our improvement, that allows to reduce the complexity of the attacks, increases the probability of the outbound part by considering a new type of differential paths. Moreover, we propose a new type of distinguisher, the multiple limited-birthday problem, based on the limited-birthday one, but where differences on the input and on the output might have randomized positions. We also discuss the generic complexity for solving this problem and provide a lower bound of it as well as we propose an efficient and generic algorithm for solving it. Our advances lead to improved distinguishing or collision results for many AES-based functions such as AES, ECHO, Grøstl, LED, PHOTON and Whirlpool

sLiSCP: Simeck-based Permutations for Lightweight Sponge Cryptographic Primitives

In this paper, we propose a family of lightweight cryptographic permutations called sLiSCP, with the sole aim to provide a realistic minimal design}that suits a variety of lightweight device applications. More precisely, we argue that for such devices the chip area dedicated for security purposes should, not only be consumed by an encryption or hashing algorithm, but also provide as many cryptographic functionalities as possible. Our main contribution is the design of a lightweight permutation employing a 4-subblock Type-2 Generalized-like Structure (GFS) and round-reduced unkeyed Simeck with either 48 or 64-bit block length as the two round functions, thus resulting in two lightweight instances of the permutation, sLiSCP-192 and sLiSCP-256. We leverage the extensive security analysis on both Simeck (Simon-like functions) and Type-2 GFSs and present bounds against differential and linear cryptanalysis. In particular, we provide an estimation on the maximum differential probability of the round-reduced Simeck and use it for bounding the maximum expected differential/linear characteristic probability for our permutation. Due to the iterated nature of the Simeck round function and the simple XOR and cyclic shift mixing layer of the GFS that fosters the propagation of long trails, the long trail strategy}is adopted to provide tighter bounds on both characteristics. Moreover, we analyze sLiSCP against a wide range of distinguishing attacks, and accordingly, claim that there exists no structural distinguishers for sLiSCP with a complexity below $2^{b/2}$ where $b$ is the state size. We demonstrate how sLiSCP can be used as a unified round function in the duplex sponge construction to build (authenticated) encryption and hashing functionalities. The parallel hardware implementation area of the unified duplex mode of sLiSCP-192 (resp. sLiSCP-256) in CMOS $65\,nm$ ASIC is 2289 (resp. 3039) GEs with a throughput of 29.62 (resp. 44.44) kbps, and their areas in CMOS $130\, nm$ are 2498 (resp. 3319) GEs

MOIM: a novel design of cryptographic hash function

A hash function usually has two main components: a compression function or permutation function and mode of operation. In this paper, we propose a new concrete novel design of a permutation based hash functions called MOIM. MOIM is based on concatenating two parallel fast wide pipe constructions as a mode of operation designed by Nandi and Paul, and presented at Indocrypt 2010 where the size of the internal state is significantly larger than the size of the output. And the permutations functions used in MOIM are inspired from the SHA-3 finalist Grøstl hash function which is originally inspired from Rijndael design (AES). As a consequence there is a very strong confusion and diffusion in MOIM. Also, we show that MOIM resists all the generic attacks and Joux attack in two defense security levels

Security analysis of NIST-LWC contest finalists

Dissertação de mestrado integrado em Informatics EngineeringTraditional cryptographic standards are designed with a desktop and server environment in mind, so, with the relatively recent proliferation of small, resource constrained devices in the Internet of Things, sensor networks, embedded systems, and more, there has been a call for lightweight cryptographic standards with security, performance and resource requirements tailored for the highly-constrained environments these devices find themselves in. In 2015 the National Institute of Standards and Technology began a Standardization Process in order to select one or more Lightweight Cryptographic algorithms. Out of the original 57 submissions ten finalists remain, with ASCON and Romulus being among the most scrutinized out of them. In this dissertation I will introduce some concepts required for easy understanding of the body of work, do an up-to-date revision on the current situation on the standardization process from a security and performance standpoint, a description of ASCON and Romulus, and new best known analysis, and a comparison of the two, with their advantages, drawbacks, and unique traits.Os padrões criptográficos tradicionais foram elaborados com um ambiente de computador e servidor em mente. Com a proliferação de dispositivos de pequenas dimensões tanto na Internet of Things, redes de sensores e sistemas embutidos, apareceu uma necessidade para se definir padrões para algoritmos de criptografia leve, com prioridades de segurança, performance e gasto de recursos equilibrados para os ambientes altamente limitados em que estes dispositivos operam. Em 2015 o National Institute of Standards and Technology lançou um processo de estandardização com o objectivo de escolher um ou mais algoritmos de criptografia leve. Das cinquenta e sete candidaturas originais sobram apenas dez finalistas, sendo ASCON e Romulus dois desses finalistas mais examinados. Nesta dissertação irei introduzir alguns conceitos necessários para uma fácil compreensão do corpo deste trabalho, assim como uma revisão atualizada da situação atual do processo de estandardização de um ponto de vista tanto de segurança como de performance, uma descrição do ASCON e do Romulus assim como as suas melhores análises recentes e uma comparação entre os dois, frisando as suas vantagens, desvantagens e aspectos únicos

The PHOTON Family of Lightweight Hash Functions

RFID security is currently one of the major challenges cryptography has to face, often solved by protocols assuming that an on-tag hash function is available. In this article we present the PHOTON lightweight hash-function family, available in many different flavors and suitable for extremely constrained devices such as passive RFID tags. Our proposal uses a sponge-like construction as domain extension algorithm and an AES-like primitive as internal unkeyed permutation. This allows us to obtain the most compact hash function known so far (about 1120 GE for 64-bit collision resistance security), reaching areas very close to the theoretical optimum (derived from the minimal internal state memory size). Moreover, the speed achieved by PHOTON also compares quite favorably to its competitors. This is mostly due to the fact that unlike for previously proposed schemes, our proposal is very simple to analyze and one can derive tight AES-like bounds on the number of active Sboxes. This kind of AES-like primitive is usually not well suited for ultra constrained environments, but we describe in this paper a new method for generating the column mixing layer in a serial way, lowering drastically the area required. Finally, we slightly extend the sponge framework in order to offer interesting trade-offs between speed and preimage security for small messages, the classical use-case in hardware

Design and Cryptanalysis of Lightweight Symmetric Key Primitives

The need for lightweight cryptographic primitives to replace the traditional standardized primitives such as AES, SHA-2 and SHA-3, which are unrealistic in constrained environments, has been anticipated by the cryptographic community for over a decade and half. Such an anticipation came to reality by the apparent proliferation of Radio Frequency Identifiers (RFIDs), Internet of Things (IoT), smart devices and sensor networks in our daily lives. All these devices operate in constrained environments and require reasonable efficiency with low implementation costs and sufficient security. Accordingly, designing lightweight symmetric key cryptographic primitives and analyzing the state-of-the-art algorithms is an active area of research for both academia and industry, which is directly followed by the ongoing National Institute of Standards and Technology’s lightweight cryptography (NIST LWC) standardization project. In this thesis, we focus on the design and security analysis of such primitives. First, we present the design of four lightweight cryptographic permutations, namely sLiSCP, sLiSCP-light, ACE and WAGE. At a high level, these permutations adopt a Nonlinear Feedback Shift Register (NLFSR) based design paradigm. sLiSCP, sLiSCP-light and ACE use reduced-round Simeck block cipher, while WAGE employs Welch-Gong (WG) permutation and two 7-bit sboxes over the finite field $F_{2^7}$ as their underlying nonlinear components. We discuss their design rationale and analyze the security with respect to differential and linear, integral and symmetry based distinguishers using automated tools such as Mixed Integer Linear Programming (MILP) and SAT/SMT solvers. Second, we show the applications of these permutations to achieve Authenticated Encryption with Associated Data (AEAD), Message Authentication Code (MAC), Pseudorandom Bit Generator (PRBG) and Hash functionalities. We introduce the idea of the unified round function, which, when combined in a sponge mode can provide all the aforementioned functionalities with the same circuitry. We give concrete instantiations of several AEAD and hash schemes with varying security levels, e.g., 80, 96, 112 and 128 bits. Next, we present Spoc, a new AEAD mode of operation which offers higher security guarantees compared to traditional sponge-based AEAD schemes with smaller states. We instantiate Spoc with sLiSCP-light permutation and propose another two lightweight AEAD algorithms. Notably, 4 of our proposed schemes, namely ACE, Spix, Spoc and WAGE are round 2 candidates of NIST’s LWC project. Finally, we present cryptanalytic results on some lightweight ciphers. We first analyze the nonlinear initialization phase of WG-5 stream cipher using the division property based cube attack, and give a key recovery attack on 24 (out of 64) rounds with data and time complexities $2^{6.32}$ and $2^{76:81}$, respectively. Next, we propose a novel property of block ciphers called correlated sequences and show its applications to meet-in-the-middle attack. Consequently, we give the best key recovery attacks (up to 27 out of 32 rounds in a single key setting) on Simon and Simeck ciphers with block and key sizes 32 and 64 bits, respectively. The attack requires 3 known plaintext-ciphertext pairs and has a time complexity close to average exhaustive search. It is worth noting that variants of WG-5 and Simeck are the core components of aforementioned AEAD and hash schemes. Lastly, we present practical forgery attacks on Limdolen and HERN which are round 1 candidates of NIST LWC project. We show the existence of structural weaknesses which could be exploited to forge any message with success probability of 1. For Limdolen, we require the output of a single encryption query while for HERN we need at most 4 encryption queries for a valid forgery. Following our attack, both designs are eliminated from second round

MILP-aided Cryptanalysis of Some Block Ciphers

Symmetric-key cryptographic primitives, such as block ciphers, play a pivotal role in achieving confidentiality, integrity, and authentication – which are the core services of information security. Since symmetric-key primitives do not rely on well-defined hard mathematical problems, unlike public-key primitives, there are no formal mathematical proofs for the security of symmetric-key primitives. Consequently, their security is guaranteed only by measuring their immunity against a set of predefined cryptanalysis techniques, e.g., differential, linear, impossible differential, and integral cryptanalysis. The attacks based on cryptanalysis techniques usually include searching in an exponential space of patterns, and for a long time, cryptanalysts have performed this task manually. As a result, it has been hard, time-consuming, and an error-prone task. Indeed, the need for automatic tools becomes more pressing. This thesis is dedicated to investigating the security of symmetric-key cryptographic primitives, precisely block ciphers. One of our main goals is to utilize Mixed Integer Linear Programming (MILP) to automate the evaluation and the validation of block cipher security against a wide range of cryptanalysis techniques. Our contributions can be summarized as follows. First, we investigate the security of two recently proposed block ciphers, CRAFT and SPARX-128/256 against two variants of differential cryptanalysis. We utilize the simple key schedule of CRAFT to construct several repeatable 2-round related-key differential characteristics with the maximum differential probability. Consequently, we are able to mount a practical key recovery attack on full-round CRAFT in the related-key setting. In addition, we use impossible differential cryptanalysis to assess SPARX-128/256 that is provable secure against single-trail differential and linear cryptanalysis. As a result, we can attack 24 rounds similar to the internal attack presented by the designers. However, our attack is better than the integral attack regarding the time and memory complexities. Next, we tackle the limitation of the current Mixed Integer Linear Programming (MILP) model to automate the search for differential distinguishers through modular additions. The current model assumes that the inputs to the modular addition and the consecutive rounds are independent. However, we show that this assumption does not necessarily hold and the current model might lead to invalid attacks. Accordingly, we propose a more accurate MILP model that takes into account the dependency between consecutive modular additions. As a proof of the validity and efficiency of our model, we use it to analyze the security of Bel-T cipher—the standard of the Republic of Belarus. Afterwards, we shift focus to another equally important cryptanalysis technique, i.e., integral cryptanalysis using the bit-based division property (BDP). We present MILP models to automate the search for the BDP through modular additions with a constant and modular subtractions. Consequently, we assess the security of Bel-T block cipher against the integral attacks. Next, we analyze the security of the tweakable block cipher T-TWINE. We present key recovery attacks on 27 and 28 rounds of T-TWINE-80 and T-TWINE-128, respectively. Finally, we address the limitation of the current MILP model for the propagation of the bit-based division property through large non-bit-permutation linear layers. The current models are either inaccurate, which might lead to missing some balanced bits, or inefficient in terms of the number of constraints. As a proof of the effectiveness of our approach, we improve the previous 3- and 4-round integral distinguishers of the Russian encryption standard—Kuznyechik, and the 4-round one of PHOTON’s internal permutation (P288). We also report a 4-round integral distinguisher for the Ukrainian standard Kalyna and a 5-round integral distinguisher for PHOTON’s internal permutation (P288)