Extended Generalized Feistel Networks using Matrix Representation

International audienceWhile Generalized Feistel Networks have been widely studied in the literature as a building block of a block cipher, we propose in this paper a unified vision to easily represent them through a matrix representation. We then propose a new class of such schemes called Extended Generalized Feistel Networks well suited for cryptographic applications. We instantiate those proposals into two particular constructions and we finally analyze their security

On generalized Feistel networks

We prove beyond-birthday-bound security for the well-known types of generalized Feistel networks, including: (1) unbalanced Feistel networks, where the $n$-bit to $m$-bit round functions may have $n\ne m$; (2) alternating Feistel networks, where the round functions alternate between contracting and expanding; (3) type-1, type-2, and type-3 Feistel networks, where $n$-bit to $n$-bit round functions are used to encipher $kn$-bit strings for some $k\ge2$; and (4) numeric variants of any of the above, where one enciphers numbers in some given range rather than strings of some given size. Using a unified analytic framework we show that, in any of these settings, for any $\varepsilon>0$, with enough rounds, the subject scheme can tolerate CCA attacks of up to $q\sim N^{1-\varepsilon}$ adversarial queries, where $N$ is the size of the round functions\u27 domain (the size of the larger domain for alternating Feistel). This is asymptotically optimal. Prior analyses for generalized Feistel networks established security to only $q\sim N^{0.5}$ adversarial queries

BBB PRP Security of the Lai-Massey Mode

In spite of being a popular technique for designing block ciphers, Lai-Massey networks have received considerably less attention from a security analysis point-of-view than Feistel networks and Substitution-Permutation networks. In this paper we study the beyond-birthday-bound (BBB) security of Lai-Massey networks with independent random round functions against chosen-plaintext adversaries. Concretely, we show that five rounds are necessary and sufficient to achieve BBB security

Related-Key Analysis of Generalized Feistel Networks with Expanding Round Functions

We extend the prior provable related-key security analysis of (generalized) Feistel networks (Barbosa and Farshim, FSE 2014; Yu et al., Inscrypt 2020) to the setting of expanding round functions, i.e., n-bit to m-bit round functions with n < m. This includes Expanding Feistel Networks (EFNs) that purely rely on such expanding round functions, and Alternating Feistel Networks (AFNs) that alternate expanding and contracting round functions. We show that, when two independent keys $K_1,K_2$ are alternatively used in each round, (a) $2\lceil\frac{m}{n}\rceil+2$ rounds are sufficient for related-key security of EFNs, and (b) a constant number of 4 rounds are sufficient for related-key security of AFNs. Our results complete the picture of provable related-key security of GFNs, and provide additional theoretical support for the AFN-based NIST format preserving encryption standards FF1 and FF3

Meet-in-the-Middle Attacks on Classes of Contracting and Expanding Feistel Constructions

We show generic attacks on unbalanced Feistel ciphers based on the meet-in-the-middle technique. We analyze two general classes of unbalanced Feistel structures, namely contracting Feistels and expanding Feistels. In both of the cases, we consider the practical scenario where the round functions are keyless and known to the adversary. In the case of contracting Feistels with 4 branches, we show attacks on 16 rounds when the key length k (in bits) is as large as the block length n (in bits), and up to 24 rounds when k = 2n. In the case of expanding Feistels, we consider two scenarios: one, where different nonlinear functions without particular structures are used in the round function, and a more practical one, where a single nonlinear is used but different linear functions are introduced in the state update. In the former case, we propose generic attacks on 13 rounds when k = n, and up to 21 rounds when k = 2n. In the latter case, 16 rounds can be attacked for k = n, and 24 rounds for k = 2n

Design and Cryptanalysis of Symmetric-Key Algorithms in Black and White-box Models

Cryptography studies secure communications. In symmetric-key cryptography, the communicating parties have a shared secret key which allows both to encrypt and decrypt messages. The encryption schemes used are very efficient but have no rigorous security proof. In order to design a symmetric-key primitive, one has to ensure that the primitive is secure at least against known attacks. During 4 years of my doctoral studies at the University of Luxembourg under the supervision of Prof. Alex Biryukov, I studied symmetric-key cryptography and contributed to several of its topics. Part I is about the structural and decomposition cryptanalysis. This type of cryptanalysis aims to exploit properties of the algorithmic structure of a cryptographic function. The first goal is to distinguish a function with a particular structure from random, structure-less functions. The second goal is to recover components of the structure in order to obtain a decomposition of the function. Decomposition attacks are also used to uncover secret structures of S-Boxes, cryptographic functions over small domains. In this part, I describe structural and decomposition cryptanalysis of the Feistel Network structure, decompositions of the S-Box used in the recent Russian cryptographic standard, and a decomposition of the only known APN permutation in even dimension. Part II is about the invariant-based cryptanalysis. This method became recently an active research topic. It happened mainly due to recent extreme cryptographic designs, which turned out to be vulnerable to this cryptanalysis method. In this part, I describe an invariant-based analysis of NORX, an authenticated cipher. Further, I show a theoretical study of linear layers that preserve low-degree invariants of a particular form used in the recent attacks on block ciphers. Part III is about the white-box cryptography. In the white-box model, an adversary has full access to the cryptographic implementation, which in particular may contain a secret key. The possibility of creating implementations of symmetric-key primitives secure in this model is a long-standing open question. Such implementations have many applications in industry; in particular, in mobile payment systems. In this part, I study the possibility of applying masking, a side-channel countermeasure, to protect white-box implementations. I describe several attacks on direct application of masking and provide a provably-secure countermeasure against a strong class of the attacks. Part IV is about the design of symmetric-key primitives. I contributed to design of the block cipher family SPARX and to the design of a suite of cryptographic algorithms, which includes the cryptographic permutation family SPARKLE, the cryptographic hash function family ESCH, and the authenticated encryption family SCHWAEMM. In this part, I describe the security analysis that I made for these designs

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

Meet-in-the-Middle Attacks on 3-Line Generalized Feistel Networks

In the paper, we study the security of 3-line generalized Feistel network, which is a considerate choice for some special needs, such as designing a 96-bit cipher based on a 32-bit round function. We show key recovery attacks on 3-line generic balanced Feistel-2 and Feistel-3 based on the meet-in-the-middle technique in the chosen ciphertext scenario. In our attacks, we consider the key size is as large as one-third of the block size. For the first network, we construct a 9-round distinguisher and launch a 10-round key-recovery attack. For the second network, we show a 13-round distinguisher and give a 17-round attack based on some common assumptions