The Inverse S-Box, Non-linear Polynomial Relations and Cryptanalysis of Block Ciphers

Abstract. This paper is motivated by the design of AES. We consider a broader question of cryptanalysis of block ciphers having very good non-linearity and diffusion. Can we expect anyway, to attacks such ciphers, clearly designed to render hopeless the main classical attacks? Recently a lot of attention have been drawn to the existence of multivariate algebraic relations for AES (and other) S-boxes. Then, if the XSL-type algebraic attacks on block ciphers [11] are shown to work well, the answer would be positive. In this paper we show that the answer is certainly positive for many other constructions of ciphers. This is not due to an algebraic attack, but to new types of generalised linear cryptanalysis, highly-nonlinear in flavour. We present several constructions of somewhat special practical block ciphers, seemingly satisfying all the design criteria of AES and using similar S-boxes, and yet being extremely weak. They can be generalised, and evolve into general attacks that can be applied- potentially- to any block cipher. Key Words: block ciphers, AES, Rijndael, interpolation attack on block ciphers, fractional transformations, homographic functions, multivariate equations

Multidimensional Zero-Correlation Linear Cryptanalysis of the Block Cipher KASUMI

The block cipher KASUMI is widely used for security in many synchronous wireless standards. It was proposed by ETSI SAGE for usage in 3GPP (3rd Generation Partnership Project) ciphering algorthms in 2001. There are a great deal of cryptanalytic results on KASUMI, however, its security evaluation against the recent zero-correlation linear attacks is still lacking so far. In this paper, we select some special input masks to refine the general 5-round zero-correlation linear approximations combining with some observations on the $FL$ functions and then propose the 6-round zero-correlation linear attack on KASUMI. Moreover, zero-correlation linear attacks on the last 7-round KASUMI are also introduced under some weak keys conditions. These weak keys take $2^{-14}$ of the whole key space. The new zero-correlation linear attack on the 6-round needs about $2^{85}$ encryptions with $2^{62.8}$ known plaintexts. For the attack under weak keys conditions on the last 7 round, the data complexity is about $2^{62.1}$ known plaintexts and the time complexity $2^{110.5}$ encryptions

Survey and Benchmark of Block Ciphers for Wireless Sensor Networks

Cryptographic algorithms play an important role in the security architecture of wireless sensor networks (WSNs). Choosing the most storage- and energy-efficient block cipher is essential, due to the facts that these networks are meant to operate without human intervention for a long period of time with little energy supply, and that available storage is scarce on these sensor nodes. However, to our knowledge, no systematic work has been done in this area so far.We construct an evaluation framework in which we first identify the candidates of block ciphers suitable for WSNs, based on existing literature and authoritative recommendations. For evaluating and assessing these candidates, we not only consider the security properties but also the storage- and energy-efficiency of the candidates. Finally, based on the evaluation results, we select the most suitable ciphers for WSNs, namely Skipjack, MISTY1, and Rijndael, depending on the combination of available memory and required security (energy efficiency being implicit). In terms of operation mode, we recommend Output Feedback Mode for pairwise links but Cipher Block Chaining for group communications

Interpolation Cryptanalysis of Unbalanced Feistel Networks with Low Degree Round Functions

Arithmetisierungs-Orientierte Symmetrische Primitive (AOSPs) sprechen das bestehende Optimierungspotential bei der Auswertung von Blockchiffren und Hashfunktionen als Bestandteil von sicherer Mehrparteienberechnung, voll-homomorpher Verschlüsselung und Zero-Knowledge-Beweisen an. Die Konstruktionsweise von AOSPs unterscheidet sich von traditionellen Primitiven durch die Verwendung von algebraisch simplen Elementen. Zusätzlich sind viele Entwürfe über Primkörpern statt über Bits definiert. Aufgrund der Neuheit der Vorschläge sind eingehendes Verständnis und ausgiebige Analyse erforderlich um ihre Sicherheit zu etablieren. Algebraische Analysetechniken wie zum Beispiel Interpolationsangriffe sind die erfolgreichsten Angriffsvektoren gegen AOSPs. In dieser Arbeit generalisieren wir eine existierende Analyse, die einen Interpolationsangriff mit geringer Speicherkomplexität verwendet, um das Entwurfsmuster der neuen Chiffre GMiMC und ihrer zugehörigen Hashfunktion GMiMCHash zu untersuchen. Wir stellen eine neue Methode zur Berechnung des Schlüssels basierend auf Nullstellen eines Polynoms vor, demonstrieren Verbesserungen für die Komplexität des Angriffs durch Kombinierung mehrere Ausgaben, und wenden manche der entwickelten Techniken in einem algebraischen Korrigierender-Letzter-Block Angriff der Schwamm-Konstruktion an. Wir beantworten die offene Frage einer früheren Arbeit, ob die verwendete Art von Interpolationsangriffen generalisierbar ist, positiv. Wir nennen konkrete empfohlene untere Schranken für Parameter in den betrachteten Szenarien. Außerdem kommen wir zu dem Schluss dass GMiMC und GMiMCHash gegen die in dieser Arbeit betrachteten Interpolationsangriffe sicher sind. Weitere kryptanalytische Anstrengungen sind erforderlich um die Sicherheitsgarantien von AOSPs zu festigen

MiMC:Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity

We explore cryptographic primitives with low multiplicative complexity. This is motivated by recent progress in practical applications of secure multi-party computation (MPC), fully homomorphic encryption (FHE), and zero-knowledge proofs (ZK) where primitives from symmetric cryptography are needed and where linear computations are, compared to non-linear operations, essentially ``free\u27\u27. Starting with the cipher design strategy ``LowMC\u27\u27 from Eurocrypt 2015, a number of bit-oriented proposals have been put forward, focusing on applications where the multiplicative depth of the circuit describing the cipher is the most important optimization goal. Surprisingly, albeit many MPC/FHE/ZK-protocols natively support operations in \GF{p} for large $p$, very few primitives, even considering all of symmetric cryptography, natively work in such fields. To that end, our proposal for both block ciphers and cryptographic hash functions is to reconsider and simplify the round function of the Knudsen-Nyberg cipher from 1995. The mapping $F(x) := x^3$ is used as the main component there and is also the main component of our family of proposals called ``MiMC\u27\u27. We study various attack vectors for this construction and give a new attack vector that outperforms others in relevant settings. Due to its very low number of multiplications, the design lends itself well to a large class of new applications, especially when the depth does not matter but the total number of multiplications in the circuit dominates all aspects of the implementation. With a number of rounds which we deem secure based on our security analysis, we report on significant performance improvements in a representative use-case involving SNARKs

Decorrelation: A Theory for Block Cipher Security

Pseudorandomness is a classical model for the security of block ciphers. In this paper we propose convenient tools in order to study it in connection with the Shannon Theory, the Carter-Wegman universal hash functions paradigm, and the Luby-Rackoff approach. This enables the construction of new ciphers with security proofs under specific models. We show how to ensure security against basic differential and linear cryptanalysis and even more general attacks. We propose practical construction scheme

Improved Algebraic Cryptanalysis of the Reduced-Round Advanced Encryption Standard

As we know Cryptology is divided into two parts: “Cryptography” and “Cryptanalysis”. Since block ciphers can be deployed in many different applications, so we focus on Advanced Encryption Standard (AES) which is the successor of Data Encryption Standard (DES). In cryptography, we purpose new block cipher (NBC08) in order to understand the inner structure and other known properties. NBC08 accepts an variable-length key up to 512 bits, which is an improved security/performance tradeoff over existing block ciphers. It cannot be analyzed by known cryptanalytic attacks. We study AES specifications and also the algebraic structure for AES over Galois Fields GF(2) and GF(28). We describe the most common cryptanalytic techniques on block ciphers, such as Differential, Linear and Integral cryptanalysis. We study the different solving methods for system of equations of AES in both fields, GF(2) and GF(28). The process of performing these methods on AES acts as Algebraic attack. In cryptanalysis, we improve the algebraic cryptanalysis attack on the reduced-round AES. It’s called Ground Algebraic attack. The notable property of Ground attack is that less requirements to any information for analyzing AES. Ground Algebraic attack is the first attack on reduced-round AES which can break 4-round and 5- round AES by respectively 256 and 2113.5 computational complexities. The number of required chosen plaintexts for cryptanalysis 4-round and 5-round AES is 8 and 15,respectively

Non-Symbolic Fragmentation

This paper reports on the use of non-symbolic fragmentation of data for securing communications. Non-symbolic fragmentation, or NSF, relies on breaking up data into non-symbolic fragments, which are (usually irregularly-sized) chunks whose boundaries do not necessarily coincide with the boundaries of the symbols making up the data. For example, ASCII data is broken up into fragments which may include 8-bit fragments but also include many other sized fragments. Fragments are then separated with a form of path diversity. The secrecy of the transmission relies on the secrecy of one or more of a number of things: the ordering of the fragments, the sizes of the fragments, and the use of path diversity. Once NSF is in place, it can help secure many forms of communication, and is useful for exchanging sensitive information, and for commercial transactions. A sample implementation is described with an evaluation of the technology