Universal Forgery and Multiple Forgeries of MergeMAC and Generalized Constructions

This article presents universal forgery and multiple forgeries against MergeMAC that has been recently proposed to fit scenarios where bandwidth is limited and where strict time constraints apply. MergeMAC divides an input message into two parts, $m\|\tilde{m}$, and its tag is computed by $\mathcal{F}( \mathcal{P}_1(m) \oplus \mathcal{P}_2(\tilde{m}) )$, where $\mathcal{P}_1$ and $\mathcal{P}_2$ are PRFs and $\mathcal{F}$ is a public function. The tag size is 64 bits. The designers claim $64$-bit security and imply a risk of accepting beyond-birthday-bound queries. This paper first shows that it is inevitable to limit the number of queries up to the birthday bound, because a generic universal forgery against CBC-like MAC can be adopted to MergeMAC. Afterwards another attack is presented that works with a very few number of queries, 3 queries and $2^{58.6}$ computations of $\mathcal{F}$, by applying a preimage attack against weak $\mathcal{F}$, which breaks the claimed security. The analysis is then generalized to a MergeMAC variant where $\mathcal{F}$ is replaced with a one-way function $\mathcal{H}$. Finally, multiple forgeries are discussed in which the attacker\u27s goal is to improve the ratio of the number of queries to the number of forged tags. It is shown that the attacker obtains tags of $q^2$ messages only by making $2q-1$ queries in the sense of existential forgery, and this is tight when $q^2$ messages have a particular structure. For universal forgery, tags for $3q$ arbitrary chosen messages can be obtained by making $5q$ queries

Design and Analysis of Cryptographic Algorithms for Authentication

During the previous decades, the upcoming demand for security in the digital world, e.g., the Internet, lead to numerous groundbreaking research topics in the field of cryptography. This thesis focuses on the design and analysis of cryptographic primitives and schemes to be used for authentication of data and communication endpoints, i.e., users. It is structured into three parts, where we present the first freely scalable multi-block-length block-cipher-based compression function (Counter-bDM) in the first part. The presented design is accompanied by a thorough security analysis regarding its preimage and collision security. The second and major part is devoted to password hashing. It is motivated by the large amount of leaked password during the last years and our discovery of side-channel attacks on scrypt – the first modern password scrambler that allowed to parameterize the amount of memory required to compute a password hash. After summarizing which properties we expect from a modern password scrambler, we (1) describe a cache-timing attack on scrypt based on its password-dependent memory-access pattern and (2) outline an additional attack vector – garbage-collector attacks – that exploits optimization which may disregard to overwrite the internally used memory. Based on our observations, we introduce Catena – the first memory-demanding password-scrambling framework that allows a password-independent memory-access pattern for resistance to the aforementioned attacks. Catena was submitted to the Password Hashing Competition (PHC) and, after two years of rigorous analysis, ended up as a finalist gaining special recognition for its agile framework approach and side-channel resistance. We provide six instances of Catena suitable for a variety of applications. We close the second part of this thesis with an overview of modern password scramblers regarding their functional, security, and general properties; supported by a brief analysis of their resistance to garbage-collector attacks. The third part of this thesis is dedicated to the integrity (authenticity of data) of nonce-based authenticated encryption schemes (NAE). We introduce the so-called j-IV-Collision Attack, allowing to obtain an upper bound for an adversary that is provided with a first successful forgery and tries to efficiently compute j additional forgeries for a particular NAE scheme (in short: reforgeability). Additionally, we introduce the corresponding security notion j-INT-CTXT and provide a comparative analysis (regarding j-INT-CTXT security) of the third-round submission to the CAESAR competition and the four classical and widely used NAE schemes CWC, CCM, EAX, and GCM.Die fortschreitende Digitalisierung in den letzten Jahrzehnten hat dazu geführt, dass sich das Forschungsfeld der Kryptographie bedeutsam weiterentwickelt hat. Diese, im Wesentlichen aus drei Teilen bestehende Dissertation, widmet sich dem Design und der Analyse von kryptographischen Primitiven und Modi zur Authentifizierung von Daten und Kommunikationspartnern. Der erste Teil beschäftigt sich dabei mit blockchiffrenbasierten Kompressionsfunktionen, die in ressourcenbeschränkten Anwendungsbereichen eine wichtige Rolle spielen. Im Rahmen dieser Arbeit präsentieren wir die erste frei skalierbare und sichere blockchiffrenbasierte Kompressionsfunktion Counter-bDM und erweitern somit flexibel die erreichbare Sicherheit solcher Konstruktionen. Der zweite Teil und wichtigste Teil dieser Dissertation widmet sich Passwort-Hashing-Verfahren. Zum einen ist dieser motiviert durch die große Anzahl von Angriffen auf Passwortdatenbanken großer Internet-Unternehmen. Zum anderen bot die Password Hashing Competition (PHC) die Möglichkeit, unter Aufmerksamkeit der Expertengemeinschaft die Sicherheit bestehender Verfahren zu hinterfragen, sowie neue sichere Verfahren zu entwerfen. Im Rahmen des zweiten Teils entwarfen wir Anforderungen an moderne Passwort-Hashing-Verfahren und beschreiben drei Arten von Seitenkanal-Angriffen (Cache-Timing-, Weak Garbage-Collector- und Garbage-Collector-Angriffe) auf scrypt – das erste moderne Password-Hashing-Verfahren welches erlaubte, den benötigten Speicheraufwand zur Berechnung eines Passworthashes frei zu wählen. Basierend auf unseren Beobachtungen und Angriffen, stellen wir das erste moderne PasswordHashing-Framework Catena vor, welches für gewählte Instanzen passwortunabhängige Speicherzugriffe und somit Sicherheit gegen oben genannte Angriffe garantiert. Catena erlangte im Rahmen des PHC-Wettbewerbs besondere Anerkennung für seine Agilität und Resistenz gegen SeitenkanalAngriffe. Wir präsentieren sechs Instanzen des Frameworks, welche für eine Vielzahl von Anwendungen geeignet sind. Abgerundet wird der zweite Teil dieser Arbeit mit einem vergleichenden Überblick von modernen Passwort-Hashing-Verfahren hinsichtlich ihrer funktionalen, sicherheitstechnischen und allgemeinen Eigenschaften. Dieser Vergleich wird unterstützt durch eine kurze Analyse bezüglich ihrer Resistenz gegen (Weak) Garbage-Collector-Angriffe. Der dritte teil dieser Arbeit widmet sich der Integrität von Daten, genauer, der Sicherheit sogenannter Nonce-basierten authentisierten Verschlüsselungsverfahren (NAE-Verfahren), welche ebenso wie Passwort-Hashing-Verfahren in der heutigen Sicherheitsinfrastruktur des Internets eine wichtige Rolle spielen. Während Standard-Definitionen keine Sicherheit nach dem Fund einer ersten erfolgreich gefälschten Nachricht betrachten, erweitern wir die Sicherheitsanforderungen dahingehend wie schwer es ist, weitere Fälschungen zu ermitteln. Wir abstrahieren die Funktionsweise von NAEVerfahren in Klassen, analysieren diese systematisch und klassifizieren die Dritt-Runden-Kandidaten des CAESAR-Wettbewerbs, sowie vier weit verbreitete NAE-Verfahren CWC, CCM, EAX und GCM

Design and Analysis of Cryptographic Algorithms for Authentication

During the previous decades, the upcoming demand for security in the digital world, e.g., the Internet, lead to numerous groundbreaking research topics in the field of cryptography. This thesis focuses on the design and analysis of cryptographic primitives and schemes to be used for authentication of data and communication endpoints, i.e., users. It is structured into three parts, where we present the first freely scalable multi-block-length block-cipher-based compression function (Counter-bDM) in the first part. The presented design is accompanied by a thorough security analysis regarding its preimage and collision security. The second and major part is devoted to password hashing. It is motivated by the large amount of leaked password during the last years and our discovery of side-channel attacks on scrypt – the first modern password scrambler that allowed to parameterize the amount of memory required to compute a password hash. After summarizing which properties we expect from a modern password scrambler, we (1) describe a cache-timing attack on scrypt based on its password-dependent memory-access pattern and (2) outline an additional attack vector – garbage-collector attacks – that exploits optimization which may disregard to overwrite the internally used memory. Based on our observations, we introduce Catena – the first memory-demanding password-scrambling framework that allows a password-independent memory-access pattern for resistance to the aforementioned attacks. Catena was submitted to the Password Hashing Competition (PHC) and, after two years of rigorous analysis, ended up as a finalist gaining special recognition for its agile framework approach and side-channel resistance. We provide six instances of Catena suitable for a variety of applications. We close the second part of this thesis with an overview of modern password scramblers regarding their functional, security, and general properties; supported by a brief analysis of their resistance to garbage-collector attacks. The third part of this thesis is dedicated to the integrity (authenticity of data) of nonce-based authenticated encryption schemes (NAE). We introduce the so-called j-IV-Collision Attack, allowing to obtain an upper bound for an adversary that is provided with a first successful forgery and tries to efficiently compute j additional forgeries for a particular NAE scheme (in short: reforgeability). Additionally, we introduce the corresponding security notion j-INT-CTXT and provide a comparative analysis (regarding j-INT-CTXT security) of the third-round submission to the CAESAR competition and the four classical and widely used NAE schemes CWC, CCM, EAX, and GCM.Die fortschreitende Digitalisierung in den letzten Jahrzehnten hat dazu geführt, dass sich das Forschungsfeld der Kryptographie bedeutsam weiterentwickelt hat. Diese, im Wesentlichen aus drei Teilen bestehende Dissertation, widmet sich dem Design und der Analyse von kryptographischen Primitiven und Modi zur Authentifizierung von Daten und Kommunikationspartnern. Der erste Teil beschäftigt sich dabei mit blockchiffrenbasierten Kompressionsfunktionen, die in ressourcenbeschränkten Anwendungsbereichen eine wichtige Rolle spielen. Im Rahmen dieser Arbeit präsentieren wir die erste frei skalierbare und sichere blockchiffrenbasierte Kompressionsfunktion Counter-bDM und erweitern somit flexibel die erreichbare Sicherheit solcher Konstruktionen. Der zweite Teil und wichtigste Teil dieser Dissertation widmet sich Passwort-Hashing-Verfahren. Zum einen ist dieser motiviert durch die große Anzahl von Angriffen auf Passwortdatenbanken großer Internet-Unternehmen. Zum anderen bot die Password Hashing Competition (PHC) die Möglichkeit, unter Aufmerksamkeit der Expertengemeinschaft die Sicherheit bestehender Verfahren zu hinterfragen, sowie neue sichere Verfahren zu entwerfen. Im Rahmen des zweiten Teils entwarfen wir Anforderungen an moderne Passwort-Hashing-Verfahren und beschreiben drei Arten von Seitenkanal-Angriffen (Cache-Timing-, Weak Garbage-Collector- und Garbage-Collector-Angriffe) auf scrypt – das erste moderne Password-Hashing-Verfahren welches erlaubte, den benötigten Speicheraufwand zur Berechnung eines Passworthashes frei zu wählen. Basierend auf unseren Beobachtungen und Angriffen, stellen wir das erste moderne PasswordHashing-Framework Catena vor, welches für gewählte Instanzen passwortunabhängige Speicherzugriffe und somit Sicherheit gegen oben genannte Angriffe garantiert. Catena erlangte im Rahmen des PHC-Wettbewerbs besondere Anerkennung für seine Agilität und Resistenz gegen SeitenkanalAngriffe. Wir präsentieren sechs Instanzen des Frameworks, welche für eine Vielzahl von Anwendungen geeignet sind. Abgerundet wird der zweite Teil dieser Arbeit mit einem vergleichenden Überblick von modernen Passwort-Hashing-Verfahren hinsichtlich ihrer funktionalen, sicherheitstechnischen und allgemeinen Eigenschaften. Dieser Vergleich wird unterstützt durch eine kurze Analyse bezüglich ihrer Resistenz gegen (Weak) Garbage-Collector-Angriffe. Der dritte teil dieser Arbeit widmet sich der Integrität von Daten, genauer, der Sicherheit sogenannter Nonce-basierten authentisierten Verschlüsselungsverfahren (NAE-Verfahren), welche ebenso wie Passwort-Hashing-Verfahren in der heutigen Sicherheitsinfrastruktur des Internets eine wichtige Rolle spielen. Während Standard-Definitionen keine Sicherheit nach dem Fund einer ersten erfolgreich gefälschten Nachricht betrachten, erweitern wir die Sicherheitsanforderungen dahingehend wie schwer es ist, weitere Fälschungen zu ermitteln. Wir abstrahieren die Funktionsweise von NAEVerfahren in Klassen, analysieren diese systematisch und klassifizieren die Dritt-Runden-Kandidaten des CAESAR-Wettbewerbs, sowie vier weit verbreitete NAE-Verfahren CWC, CCM, EAX und GCM

On Weak Keys and Forgery Attacks Against Polynomial-Based MAC Schemes

Abstract. Universal hash functions are commonly used primitives for fast and secure message authentication in the form of Message Authentication Codes (MACs) or Authenticated Encryption with Associated Data (AEAD) schemes. These schemes are widely used and standardised, the most well known being McGrew and Viega’s Galois/Counter Mode (GCM). In this paper we identify some properties of hash functions based on polynomial evaluation that arise from the underlying algebraic structure. As a result we are able to describe a general forgery attack, of which Saarinen’s cycling attack from FSE 2012 is a special case. Our attack removes the requirement for long messages and applies regardless of the field in which the hash function is evaluated. Furthermore we provide a common description of all published attacks against GCM, by showing that the existing attacks are the result of these algebraic properties of the polynomial-based hash function. We also greatly expand the number of known weak GCM keys and show that almost every subset of the keyspace is a weak key class. Finally, we demonstrate that these algebraic properties and corresponding attacks are highly relevant to GCM/2 +, a variant of GCM designed to increase the efficiency in software

Cryptanalysis of OCB₂:Attacks on Authenticity and Confidentiality

We present practical attacks on OCB2. This mode of operation of a blockcipher was designed with the aim to provide particularly efficient and provably-secure authenticated encryption services, and since its proposal about 15 years ago it belongs to the top performers in this realm. OCB2 was included in an ISO standard in 2009. An internal building block of OCB2 is the tweakable blockcipher obtained by operating a regular blockcipher in XEX$^\ast$ mode. The latter provides security only when evaluated in accordance with certain technical restrictions that, as we note, are not always respected by OCB2. This leads to devastating attacks against OCB2\u27s security promises: We develop a range of very practical attacks that, amongst others, demonstrate universal forgeries and full plaintext recovery. We complete our report with proposals for (provably) repairing OCB2. To our understanding, as a direct consequence of our findings, OCB2 is currently in a process of removal from ISO standards. Our attacks do not apply to OCB1 and OCB3, and our privacy attacks on OCB2 require an active adversary

On the Security Margin of TinyJAMBU with Refined Differential and Linear Cryptanalysis

International audienceThis paper presents the first third-party security analysis of TinyJAMBU, which is one of 32 second-round candidates in NIST’s lightweight cryptography standardization process. TinyJAMBU adopts an NLFSR based keyed-permutation that computes only a single NAND gate as a non-linear component per round. The designers evaluated the minimum number of active AND gates, however such a counting method neglects the dependency between multiple AND gates. There also exist previous works considering such dependencies with stricter models, however those are known to be too slow. In this paper, we present a new model that provides a good balance of efficiency and accuracy by only taking into account the first-order correlation of AND gates that frequently occurs in TinyJAMBU. With the refined model, we show a 338-round differential with probability 2^(−62.68) that leads to a forgery attack breaking 64-bit security. This implies that the security margin of TinyJAMBU with respect to the number of unattacked rounds is approximately 12%. We also show a differential on full 384 rounds with probability 2^(−70.64), thus the security margin of full rounds with respect to the data complexity, namely the gap between the claimed security bits and the attack complexity, is less than 8 bits. Our attacks also point out structural weaknesses of the mode that essentially come from the minimal state size to be lightweight

Cryptanalysis of OCB2

We present practical attacks against OCB2, an ISO-standard authenticated encryption (AE) scheme. OCB2 is a highly-efficient blockcipher mode of operation. It has been extensively studied and widely believed to be secure thanks to the provable security proofs. Our attacks allow the adversary to create forgeries with single encryption query of almost-known plaintext. This attack can be further extended to powerful almost-universal and universal forgeries using more queries. The source of our attacks is the way OCB2 implements AE using a tweakable blockcipher, called XEX*. We have verified our attacks using a reference code of OCB2. Our attacks do not break the privacy of OCB2, and are not applicable to the others, including OCB1 and OCB3

Power Yoga: Variable-Stretch Security of CCM for Energy-Efficient Lightweight IoT

The currently ongoing NIST LWC project aims at identifying new standardization targets for lightweight authenticated encryption with associated data (AEAD) and (optionally) lightweight cryptographic hashing. NIST has deemed it important for performance and cost to be optimized on relevant platforms, especially for short messages. Reyhanitabar, Vaudenay and Vizár (Asiacrypt 2016) gave a formal treatment for security of nonce-based AEAD with variable stretch, i.e., when the length of the authentication tag is changed between encryptions without changing the key. They argued that AEAD supporting variable stretch is of practical interest for constrained applications, especially low-power devices operated by battery, due to the ability to flexibly trade communication overhead and level of integrity. In this work, we investigate this hypothesis with affirmative results. We present vCCM, a variable-stretch variant of the standard CCM and prove it is secure when used with variable stretch. We then experimentally measure the energy consumption of a real-world wireless sensor node when encrypting and sending messages with vCCM and CCM, respectively. Our projections show that the flexible trade of integrity level and ciphertext expansion can lead up to 21% overall energy consumption reduction in certain scenarios. As vCCM is obtained from the widely-used CCM by a black-box transformation, allowing any existing CCM implementations to be reused as-is, our results can be immediately put to use in practice. vCCM is all the more relevant because neither the NIST LWC project, nor any of the candidates give a consideration for the support of variable stretch and the related integrity-overhead trade-off

Lightweight MACs from Universal Hash Functions

International audienceLightweight cryptography is a topic of growing importance, with the goal to secure the communication of low-end devices that are not powerful enough to use conventional cryptography. There have been many recent proposals of lightweight block ciphers, but comparatively few results on lightweight Message Authentication Codes (MACs). Therefore, this paper focuses on lightweight MACs. We review some existing constructions, and revisit the choices made in mainstream MACs with a focus on lightweight cryptography. We consider MACs based on universal hash functions, because they offer information theoretic security , can be implemented efficiently and are widely used in conventional cryptography. However, many constructions used in practice (such as GMAC or Poly1305-AES) follow the Wegman-Carter-Shoup construction , which is only secure up to 2 64 queries with a 128-bit state. We point out that there are simple solutions to reach security beyond the birthday bound, and we propose a concrete instantiation, MAC611, reaching 61-bit security with a 61-bit universal hash function. We wrote an optimized implementation on two ARM micro-controllers, and we obtain very good performances on the Cortex-M4, at only 3.7 c/B for long messages, and less than one thousand cycles for short messages