Decoding Generalized Reed-Solomon Codes and Its Application to RLCE Encryption Schemes

This paper compares the efficiency of various algorithms for implementing quantum resistant public key encryption scheme RLCE on 64-bit CPUs. By optimizing various algorithms for polynomial and matrix operations over finite fields, we obtained several interesting (or even surprising) results. For example, it is well known (e.g., Moenck 1976 \cite{moenck1976practical}) that Karatsuba's algorithm outperforms classical polynomial multiplication algorithm from the degree 15 and above (practically, Karatsuba's algorithm only outperforms classical polynomial multiplication algorithm from the degree 35 and above ). Our experiments show that 64-bit optimized Karatsuba's algorithm will only outperform 64-bit optimized classical polynomial multiplication algorithm for polynomials of degree 115 and above over finite field $GF(2^{10})$. The second interesting (surprising) result shows that 64-bit optimized Chien's search algorithm ourperforms all other 64-bit optimized polynomial root finding algorithms such as BTA and FFT for polynomials of all degrees over finite field $GF(2^{10})$. The third interesting (surprising) result shows that 64-bit optimized Strassen matrix multiplication algorithm only outperforms 64-bit optimized classical matrix multiplication algorithm for matrices of dimension 750 and above over finite field $GF(2^{10})$. It should be noted that existing literatures and practices recommend Strassen matrix multiplication algorithm for matrices of dimension 40 and above. All our experiments are done on a 64-bit MacBook Pro with i7 CPU and single thread C codes. It should be noted that the reported results should be appliable to 64 or larger bits CPU architectures. For 32 or smaller bits CPUs, these results may not be applicable. The source code and library for the algorithms covered in this paper are available at http://quantumca.org/

Cryptanalysis of the Fuzzy Vault for Fingerprints: Vulnerabilities and Countermeasures

Das Fuzzy Vault ist ein beliebter Ansatz, um die Minutien eines menschlichen Fingerabdrucks in einer Sicherheitsanwendung geschützt zu speichern. In dieser Arbeit werden verschiedene Implementationen des Fuzzy Vault für Fingerabdrücke in verschiedenen Angriffsszenarien untersucht. Unsere Untersuchungen und Analysen bestätigen deutlich, dass die größte Schwäche von Implementationen des Fingerabdruck Fuzzy Vaults seine hohe Anfälligkeit gegen False-Accept Angriffe ist. Als Gegenmaßnahme könnten mehrere Finger oder sogar mehrere biometrische Merkmale eines Menschen gleichzeitig verwendet werden. Allerdings besitzen traditionelle Fuzzy Vault Konstruktionen eine wesentliche Schwäche: den Korrelationsangriff. Es ist bekannt, dass das Runden von Minutien auf ein starres System, diese Schwäche beheben. Ausgehend davon schlagen wir eine Implementation vor. Würden nun Parameter traditioneller Konstruktionen übernommen, so würden wir einen signifikanten Verlust an Verifikations-Leistung hinnehmen müssen. In einem Training wird daher eine gute Parameterkonfiguration neu bestimmt. Um den Authentifizierungsaufwand praktikabel zu machen, verwenden wir einen randomisierten Dekodierer und zeigen, dass die erreichbaren Raten vergleichbar mit den Raten einer traditionellen Konstruktion sind. Wir folgern, dass das Fuzzy Vault ein denkbarer Ansatz bleibt, um die schwierige Aufgabe ein kryptographisch sicheres biometrisches Kryptosystem in Zukunft zu implementieren.The fuzzy fingerprint vault is a popular approach to protect a fingerprint's minutiae as a building block of a security application. In this thesis simulations of several attack scenarios are conducted against implementations of the fuzzy fingerprint vault from the literature. Our investigations clearly confirm that the weakest link in the fuzzy fingerprint vault is its high vulnerability to false-accept attacks. Therefore, multi-finger or even multi-biometric cryptosystems should be conceived. But there remains a risk that cannot be resolved by using more biometric information of an individual if features are protected using a traditional fuzzy vault construction: The correlation attack remains a weakness of such constructions. It is known that quantizing minutiae to a rigid system while filling the whole space with chaff makes correlation obsolete. Based on this approach, we propose an implementation. If parameters were adopted from a traditional fuzzy fingerprint vault implementation, we would experience a significant loss in authentication performance. Therefore, we perform a training to determine reasonable parameters for our implementation. Furthermore, to make authentication practical, the decoding procedure is proposed to be randomized. By running a performance evaluation on a dataset generally used, we find that achieving resistance against the correlation attack does not have to be at the cost of authentication performance. Finally, we conclude that fuzzy vault remains a possible construction for helping in solving the challenging task of implementing a cryptographically secure multi-biometric cryptosystem in future

Algorithmic Security is Insufficient: A Comprehensive Survey on Implementation Attacks Haunting Post-Quantum Security

This survey is on forward-looking, emerging security concerns in post-quantum era, i.e., the implementation attacks for 2022 winners of NIST post-quantum cryptography (PQC) competition and thus the visions, insights, and discussions can be used as a step forward towards scrutinizing the new standards for applications ranging from Metaverse, Web 3.0 to deeply-embedded systems. The rapid advances in quantum computing have brought immense opportunities for scientific discovery and technological progress; however, it poses a major risk to today's security since advanced quantum computers are believed to break all traditional public-key cryptographic algorithms. This has led to active research on PQC algorithms that are believed to be secure against classical and powerful quantum computers. However, algorithmic security is unfortunately insufficient, and many cryptographic algorithms are vulnerable to side-channel attacks (SCA), where an attacker passively or actively gets side-channel data to compromise the security properties that are assumed to be safe theoretically. In this survey, we explore such imminent threats and their countermeasures with respect to PQC. We provide the respective, latest advancements in PQC research, as well as assessments and providing visions on the different types of SCAs

Efficient ASIC Architectures for Low Latency Niederreiter Decryption

Post-quantum cryptography addresses the increasing threat that quantum computing poses to modern communication systems. Among the available quantum-resistant systems, the Niederreiter cryptosystem is positioned as a conservative choice with strong security guarantees. As a code-based cryptosystem, the Niederreiter system enables high performance operations and is thus ideally suited for applications such as the acceleration of server workloads. However, until now, no ASIC architecture is available for low latency computation of Niederreiter operations. Therefore, the present work targets the design, implementation and optimization of tailored archi- tectures for low latency Niederreiter decryption. Two architectures utilizing different decoding algorithms are proposed and implemented using a 22nm FDSOI CMOS technology node. One of these optimized architectures improves the decryption latency by 27% compared to a state-of-the-art reference and requires at the same time only 25% of the area

New cryptanalysis of LFSR-based stream ciphers and decoders for p-ary QC-MDPC codes

The security of modern cryptography is based on the hardness of solving certain problems. In this context, a problem is considered hard if there is no known polynomial time algorithm to solve it. Initially, the security assessment of cryptographic systems only considered adversaries with classical computational resources, i.e., digital computers. It is now known that there exist polynomial-time quantum algorithms that would render certain cryptosystems insecure if large-scale quantum computers were available. Thus, adversaries with access to such computers should also be considered. In particular, cryptosystems based on the hardness of integer factorisation or the discrete logarithm problem would be broken. For some others such as symmetric-key cryptosystems, the impact seems not to be as serious; it is recommended to at least double the key size of currently used systems to preserve their security level. The potential threat posed by sufficiently powerful quantum computers motivates the continued study and development of post-quantum cryptography, that is, cryptographic systems that are secure against adversaries with access to quantum computations. It is believed that symmetric-key cryptosystems should be secure from quantum attacks. In this manuscript, we study the security of one such family of systems; namely, stream ciphers. They are mainly used in applications where high throughput is required in software or low resource usage is required in hardware. Our focus is on the cryptanalysis of stream ciphers employing linear feedback shift registers (LFSRs). This is modelled as the problem of finding solutions to systems of linear equations with associated probability distributions on the set of right hand sides. To solve this problem, we first present a multivariate version of the correlation attack introduced by Siegenthaler. Building on the ideas of the multivariate attack, we propose a new cryptanalytic method with lower time complexity. Alongside this, we introduce the notion of relations modulo a matrix B, which may be seen as a generalisation of parity-checks used in fast correlation attacks. The latter are among the most important class of attacks against LFSR-based stream ciphers. Our new method is successfully applied to hard instances of the filter generator and requires a lower amount of keystream compared to other attacks in the literature. We also perform a theoretical attack against the Grain-v1 cipher and an experimental attack against a toy Grain-like cipher. Compared to the best previous attack, our technique requires less keystream bits but also has a higher time complexity. This is the result of joint work with Semaev. Public-key cryptosystems based on error-correcting codes are also believed to be secure against quantum attacks. To this end, we develop a new technique in code-based cryptography. Specifically, we propose new decoders for quasi-cyclic moderate density parity-check (QC-MDPC) codes. These codes were proposed by Misoczki et al.\ for use in the McEliece scheme. The use of QC-MDPC codes avoids attacks applicable when using low-density parity-check (LDPC) codes and also allows for keys with short size. Although we focus on decoding for a particular instance of the p-ary QC-MDPC scheme, our new decoding algorithm is also a general decoding method for p-ary MDPC-like schemes. This algorithm is a bit-flipping decoder, and its performance is improved by varying thresholds for the different iterations. Experimental results demonstrate that our decoders enjoy a very low decoding failure rate for the chosen p-ary QC-MDPC instance. This is the result of joint work with Guo and Johansson.Doktorgradsavhandlin