Phase-shift Fault Analysis of Grain-128

Phase-shift fault attack is a type of fault attack used for cryptanalysis of stream ciphers. It involves clocking a cipher’s feedback shift registers out of phase, in order to generate faulted keystream. Grain-128 cipher is a 128-bit modification of the Grain cipher which is one of the finalists in the eSTREAM project. In this work, we propose a phase-shift fault attack against Grain-128 loaded with key-IV pairs that result in an all-zero LFSR after initialisation. We frame equations in terms of the input and output bits of the cipher and solve them using a SAT solver. By correctly guessing 40 innerstate bits, we are able to recover the entire 128-bit key with just 2 phase-shift faults for keystreams of length 200 bits

Private Multi-party Matrix Multiplication and Trust Computations

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose a protocol with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using ProVerif, a cryptographic protocol verification tool, we are able to check the security of the protocol and provide a countermeasure for each attack found by the tool. We also give a randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.Comment: Pierangela Samarati. SECRYPT 2016 : 13th International Conference on Security and Cryptography, Lisbonne, Portugal, 26--28 Juillet 2016. 201

How to Explain Modern Security Concepts to your Children

International audienceAt the main cryptography conference CRYPTO in 1989, Quisquater et al. published a paper showing how to explain the complex notion of zero-knowledge proof in a simpler way that children can understand. In the same line of work, we present simple and intuitive explanations of various modern security concepts and technologies, including symmetric encryption, public key encryption, homomorphic encryption, intruder models (CPA, CCA1, CCA2) and security properties (OW, IND, NM). The explanations given in this paper may also serve in demystifying such complex security notions for non-expert adults

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

Mixing Additive and Multiplicative Masking for Probing Secure Polynomial Evaluation Methods

International audienceMasking is a sound countermeasure to protect implementations of block-cipher algorithms against Side Channel Analysis (SCA). Currently, the most efficient masking schemes use Lagrange's Interpolation Theorem in order to represent any S-box by a polynomial function over a binary finite field. Masking the processing of an S-box is then achieved by masking every operation involved in the evaluation of its polynomial representation. While the common approach requires to use the well-known Ishai-Sahai-Wagner (ISW) scheme in order to secure this processing, there exist alternatives. In the particular case of power functions, Genelle, Prouff and Quisquater proposed an efficient masking scheme (GPQ). However, no generalization has been suggested for polynomial functions so far. In this paper, we solve the open problem of extending GPQ for polynomials, and we also solve the open problem of proving that both the original scheme and its variants for polynomials satisfy the t-SNI security definition. Our approach to extend GPQ is based on the cyclotomic method and results in an alternate cyclotomic method which is three times faster in practice than the original proposal in almost all scenarios we address. The best-known method for polynomial evaluation is currently CRV which requires to use the cyclotomic method for one of its step. We also show how to plug our alternate cyclo-tomic approach into CRV and again provide an alternate approach that outperforms the original in almost all scenarios. We consider the masking of n-bit S-boxes for n ∈ [4; 8] and we get in practice 35% improvement of efficiency for S-boxes with dimension n ∈ {5, 7, 8} and 25% for 6-bit S-boxes

Cryptanalysis of Some Block Cipher Constructions

When the public-key cryptography was introduced in the 1970s, symmetric-key cryptography was believed to soon become outdated. Nevertheless, we still heavily rely on symmetric-key primitives as they give high-speed performance. They are used to secure mobile communication, e-commerce transactions, communication through virtual private networks and sending electronic tax returns, among many other everyday activities. However, the security of symmetric-key primitives does not depend on a well-known hard mathematical problem such as the factoring problem, which is the basis of the RSA public-key cryptosystem. Instead, the security of symmetric-key primitives is evaluated against known cryptanalytic techniques. Accordingly, the topic of furthering the state-of-the-art of cryptanalysis of symmetric-key primitives is an ever-evolving topic. Therefore, this thesis is dedicated to the cryptanalysis of symmetric-key cryptographic primitives. Our focus is on block ciphers as well as hash functions that are built using block ciphers. Our contributions can be summarized as follows: First, we tackle the limitation of the current Mixed Integer Linear Programming (MILP) approaches to represent the differential propagation through large S-boxes. Indeed, we present a novel approach that can efficiently model the Difference Distribution Table (DDT) of large S-boxes, i.e., 8-bit S-boxes. As a proof of the validity and efficiency of our approach, we apply it on two out of the seven AES-round based constructions that were recently proposed in FSE 2016. Using our approach, we improve the lower bound on the number of active S-boxes of one construction and the upper bound on the best differential characteristic of the other. Then, we propose meet-in-the-middle attacks using the idea of efficient differential enumeration against two Japanese block ciphers, i.e., Hierocrypt-L1 and Hierocrypt-3. Both block ciphers were submitted to the New European Schemes for Signatures, Integrity, and Encryption (NESSIE) project, selected as one of the Japanese e-Government recommended ciphers in 2003 and reselected in the candidate recommended ciphers list in 2013. We construct five S-box layer distinguishers that we use to recover the master keys of reduced 8 S-box layer versions of both block ciphers. In addition, we present another meet-in-the-middle attack on Hierocrypt-3 with slightly higher time and memory complexities but with much less data complexity. Afterwards, we shift focus to another equally important cryptanalytic attack, i.e., impossible differential attack. SPARX-64/128 is selected among the SPARX family that was recently proposed to provide ARX based block cipher whose security against differential and linear cryptanalysis can be proven. We assess the security of SPARX-64/128 against impossible differential attack and show that it can reach the same number of rounds the division-based integral attack, proposed by the designers, can reach. Then, we pick Kiasu-BC as an example of a tweakable block cipher and prove that, on contrary to its designers’ claim, the freedom in choosing the publicly known tweak decreases its security margin. Lastly, we study the impossible differential properties of the underlying block cipher of the Russian hash standard Streebog and point out the potential risk in using it as a MAC scheme in the secret-IV mode

Automated Search Oriented to Key Recovery on Ciphers with Linear Key Schedule

Automatic modelling to search distinguishers with high probability covering as many rounds as possible, such as MILP, SAT/SMT, CP models, has become a very popular cryptanalysis topic today. In those models, the optimizing objective is usually the probability or the number of rounds of the distinguishers. If we want to recover the secret key for a round-reduced block cipher, there are usually two phases, i.e., finding an efficient distinguisher and performing key-recovery attack by extending several rounds before and after the distinguisher. The total number of attacked rounds is not only related to the chosen distinguisher, but also to the extended rounds before and after the distinguisher. In this paper, we try to combine the two phases in a uniform automatic model. Concretely, we apply this idea to automate the related-key rectangle attacks on SKINNY and ForkSkinny. We propose some new distinguishers with advantage to perform key-recovery attacks. Our key-recovery attacks on a few versions of round-reduced SKINNY and ForkSkinny cover 1 to 2 more rounds than the best previous attacks

Cryptanalysis of Block Ciphers with New Design Strategies

Block ciphers are among the mostly widely used symmetric-key cryptographic primitives, which are fundamental building blocks in cryptographic/security systems. Most of the public-key primitives are based on hard mathematical problems such as the integer factorization in the RSA algorithm and discrete logarithm problem in the DiffieHellman. Therefore, their security are mathematically proven. In contrast, symmetric-key primitives are usually not constructed based on well-defined hard mathematical problems. Hence, in order to get some assurance in their claimed security properties, they must be studied against different types of cryptanalytic techniques. Our research is dedicated to the cryptanalysis of block ciphers. In particular, throughout this thesis, we investigate the security of some block ciphers constructed with new design strategies. These new strategies include (i) employing simple round function, and modest key schedule, (ii) using another input called tweak rather than the usual two inputs of the block ciphers, the plaintext and the key, to instantiate different permutations for the same key. This type of block ciphers is called a tweakable block cipher, (iii) employing linear and non-linear components that are energy efficient to provide low energy consumption block ciphers, (iv) employing optimal diffusion linear transformation layer while following the AES-based construction to provide faster diffusion rate, and (v) using rather weak but larger S-boxes in addition to simple linear transformation layers to provide provable security of ARX-based block ciphers against single characteristic differential and linear cryptanalysis. The results presented in this thesis can be summarized as follows: Initially, we analyze the security of two lightweight block ciphers, namely, Khudra and Piccolo against Meet-in-the-Middle (MitM) attack based on the Demirci and Selcuk approach exploiting the simple design of the key schedule and round function. Next, we investigate the security of two tweakable block ciphers, namely, Kiasu-BC and SKINNY. According to the designers, the best attack on Kiasu-BC covers 7 rounds. However, we exploited the tweak to present 8-round attack using MitM with efficient enumeration cryptanalysis. Then, we improve the previous results of the impossible differential cryptanalysis on SKINNY exploiting the tweakey schedule and linear transformation layer. Afterwards, we study the security of new low energy consumption block cipher, namely, Midori128 where we present the longest impossible differential distinguishers that cover complete 7 rounds. Then, we utilized 4 of these distinguishers to launch key recovery attack against 11 rounds of Midori128 to improve the previous results on this cipher using the impossible differential cryptanalysis. Then, using the truncated differential cryptanalysis, we are able to attack 13 rounds of Midori128 utilizing a 10-round differential distinguisher. We also analyze Kuznyechik, the standard Russian federation block cipher, against MitM with efficient enumeration cryptanalysis where we improve the previous results on Kuznyechik, using MitM attack with efficient enumeration, by presenting 6-round attack. Unlike the previous attack, our attack exploits the exact values of the coefficients of the MDS transformation that is used in the cipher. Finally, we present key recovery attacks using the multidimensional zero-correlation cryptanalysis against SPARX-128, which follows the long trail design strategy, to provide provable security of ARX-based block ciphers against single characteristic differential and linear cryptanalysis

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license