Implementing 128-bit Secure MPKC Signatures

Multivariate Public Key Cryptosystems (MPKCs) are often touted as future-proofing against Quantum Computers. In 2009, it was shown that hardware advances do not favor just ``traditional\u27\u27 alternatives such as ECC and RSA, but also makes MPKCs faster and keeps them competitive at 80-bit security when properly implemented. These techniques became outdated due to emergence of new instruction sets and higher requirements on security. In this paper, we review how MPKC signatures changes from 2009 including new parameters (from a newer security level at 128-bit), crypto-safe implementations, and the impact of new AVX2and AESNI instructions. We also present new techniques on evaluating multivariate polynomials, multiplications of large finite fields by additive Fast Fourier Transforms, and constant time linear solvers

Envisioning the Future of Cyber Security in Post-Quantum Era: A Survey on PQ Standardization, Applications, Challenges and Opportunities

The rise of quantum computers exposes vulnerabilities in current public key cryptographic protocols, necessitating the development of secure post-quantum (PQ) schemes. Hence, we conduct a comprehensive study on various PQ approaches, covering the constructional design, structural vulnerabilities, and offer security assessments, implementation evaluations, and a particular focus on side-channel attacks. We analyze global standardization processes, evaluate their metrics in relation to real-world applications, and primarily focus on standardized PQ schemes, selected additional signature competition candidates, and PQ-secure cutting-edge schemes beyond standardization. Finally, we present visions and potential future directions for a seamless transition to the PQ era

CRYSTALS-Dilithium: A lattice-based digital signature scheme

In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes

An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme

Historically, multivariate public key cryptography has been less than successful at offering encryption schemes which are both secure and efficient. At PQCRYPTO \u2713 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over a finite field. We present an attack based on subspace differential invariants inherent to this methodology. The attack is is a structural key recovery attack which is asymptotically optimal among all known attacks (including algebraic attacks) on the original scheme and its generalizations

Secure Hardware Implementation of Post Quantum Cryptosystems

Solving a hard mathematical problem is the security basis of all current cryptographic systems. With the realization of a large scale quantum computer, hard mathematical problems such as integer factorization and discrete logarithmic problems will be easily solved with special algorithms implemented on such a computer. Indeed, only post-quantum cryptosystems which defy quantum attacks will survive in the post-quantum era. Each newly proposed post-quantum cryptosystem has to be scrutinized against all different types of attacks. Attacks can be classified into mathematical cryptanalysis and side channel attacks. In this thesis, we propose secure hardware implementations against side channel attacks for two of the most promising post-quantum algorithms: the lattice-based public key cryptosystem, NTRU, and the multivariate public key cryptosystem, Rainbow, against power analysis attacks and fault analysis attacks, respectively. NTRUEncrypt is a family of public key cryptosystems that uses lattice-based cryptography. It has been accepted as an IEEE P1363 standard and as an X9.98 Standard. In addition to its small footprint compared to other number theory based public key systems, its resistance to quantum attacks makes it a very attractive candidate for post quantum cryptosystems. On the other hand, similar to other cryptographic schemes, unprotected hardware implementations of NTRUEncrypt are susceptible to side channel attacks such as timing and power analysis. In this thesis, we present an FPGA implementation of NTRUEncrypt which is resistant to first order differential power analysis (DPA) attacks. Our countermeasures are implemented at the architecture level. In particular, we split the ciphertext into two randomly generated shares. This guarantees that during the first step of the decryption process, the inputs to the convolution modules, which are convoluted with the secret key polynomial, are uniformly chosen random polynomials which are freshly generated for each convolution operation and are not under the control of the attacker. The two shares are then processed in parallel without explicitly combining them until the final stage of the decryption. Furthermore, during the final stage of the decryption, we also split the used secret key polynomial into two randomly generated shares which provides theoretical resistance against the considered class of power analysis attacks. The proposed architecture is implemented using Altera Cyclone IV FPGA and simulated on Quartus II in order to compare the non-masked architecture with the masked one. For the considered set of parameters, the area overhead of the protected implementation is about 60% while the latency overhead is between 1.4% to 6.9%. Multivariate Public Key Cryptosystems (MPKCs) are cryptographic schemes based on the difficulty of solving a set of multivariate system of nonlinear equations over a finite field. MPKCs are considered to be secure against quantum attacks. Rainbow, an MPKC signature scheme, is among the leading MPKC candidates for post quantum cryptography. In this thesis, we propose and compare two fault analysis-resistant implementations for the Rainbow signature scheme. The hardware platform for our implementations is Xilinx FPGA Virtex 7 family. Our implementation for the Rainbow signature completes in 191 cycles using a 20ns clock period which is an improvement over the previously reported implementations. The verification completes in 141 cycles using the same clock period. The two proposed fault analysis-resistant schemes offer different levels of protections and increase the area overhead by a factor of 33% and 9%, respectively. The first protection scheme acquires a time overhead of about 72%, but the second one does not have any time overhead

Post-quantum cryptosystems for internet-of-things: A survey on lattice-based algorithms

The latest quantum computers have the ability to solve incredibly complex classical cryptography equations particularly to decode the secret encrypted keys and making the network vulnerable to hacking. They can solve complex mathematical problems almost instantaneously compared to the billions of years of computation needed by traditional computing machines. Researchers advocate the development of novel strategies to include data encryption in the post-quantum era. Lattices have been widely used in cryptography, somewhat peculiarly, and these algorithms have been used in both; (a) cryptoanalysis by using lattice approximation to break cryptosystems; and (b) cryptography by using computationally hard lattice problems (non-deterministic polynomial time hardness) to construct stable cryptographic functions. Most of the dominant features of lattice-based cryptography (LBC), which holds it ahead in the post-quantum league, include resistance to quantum attack vectors, high concurrent performance, parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. While these methods offer possible security for classical cryptosytems in theory and experimentation, their implementation in energy-restricted Internet-of-Things (IoT) devices requires careful study of regular lattice-based implantation and its simplification in lightweight lattice-based cryptography (LW-LBC). This streamlined post-quantum algorithm is ideal for levelled IoT device security. The key aim of this survey was to provide the scientific community with comprehensive information on elementary mathematical facts, as well as to address real-time implementation, hardware architecture, open problems, attack vectors, and the significance for the IoT networks

MAYO: Optimized Implementation with Revised Parameters for ARMv7-M

We present an optimized constant-time implementation of the MAYO signature scheme on ARMv7-M. MAYO is a novel multivariate proposal based on the trapdoor function of the Unbalanced Oil and Vinegar scheme. Our implementation builds on existing techniques for UOV-based schemes and introduces a new approach for evaluating the polar forms of quadratic maps. We modify MAYO\u27s original parameters to achieve greater benefits from the proposed optimizations, resulting in slightly larger keys and shorter signatures for the same level of security. We evaluate the optimized implementation with the new parameters on the STM32H753ZIT6 microcontroller and measure its performance for the signing and verification procedures. At NIST security level I, signing requires approximately 43M cycles, and verification requires approximately 6M cycles. Both are 2.6 times faster than the results obtained from the original parameters

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit. Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing. The emergence of quantum computing poses a major threat to the modern cryptosystems based on modular arithmetic, whereby even the computationally hard problems which constitute the strength of the modular arithmetic ciphers could be solved in polynomial time. This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks. This paper provides an overview of the various research directions that have been explored in post-quantum cryptography and, specifically, the various code-based cryptography research dimensions that have been explored. Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper

Authentication and Integrity Protection at Data and Physical layer for Critical Infrastructures

This thesis examines the authentication and the data integrity services in two prominent emerging contexts such as Global Navigation Satellite Systems (GNSS) and the Internet of Things (IoT), analyzing various techniques proposed in the literature and proposing novel methods. GNSS, among which Global Positioning System (GPS) is the most widely used, provide affordable access to accurate positioning and timing with global coverage. There are several motivations to attack GNSS: from personal privacy reasons, to disrupting critical infrastructures for terrorist purposes. The generation and transmission of spoofing signals either for research purpose or for actually mounting attacks has become easier in recent years with the increase of the computational power and with the availability on the market of Software Defined Radios (SDRs), general purpose radio devices that can be programmed to both receive and transmit RF signals. In this thesis a security analysis of the main currently proposed data and signal level authentication mechanisms for GNSS is performed. A novel GNSS data level authentication scheme, SigAm, that combines the security of asymmetric cryptographic primitives with the performance of hash functions or symmetric key cryptographic primitives is proposed. Moreover, a generalization of GNSS signal layer security code estimation attacks and defenses is provided, improving their performance, and an autonomous anti-spoofing technique that exploits semi-codeless tracking techniques is introduced. Finally, physical layer authentication techniques for IoT are discussed, providing a trade-off between the performance of the authentication protocol and energy expenditure of the authentication process

Métodos algebraicos en criptografía multivariable

La criptografía de curva elíptica no es la solución a largo plazo que esperábamos que fuera. Por tanto, nos hemos visto obligados a replantear nuestra estrategia”. Con estas palabras alertaba en el 2015 la Agencia Nacional de Seguridad estadounidense (NSA) sobre la necesidad de encontrar nuevas herramientas criptográficas que permitan mantener la seguridad en Internet. En un comunicado de su web, la agencia ha mostrado su interés en “iniciar una transición a algoritmos potencialmente resistentes a ordenadores cuánticos en un futuro no muy lejano”.Consideran un objetivo principal disponer de herramientas de seguridad ante un posible ordenador cuántico.En las últimas décadas Internet ha adquirido un papel central en la sociedad. Uno de los pilares sobre los que se sostiene la red es la criptografía de clave pública, que permite las comunicaciones privadas, la identificación de los usuarios en un servidor y la firma de documentos. Entre los diferentes métodos que se utilizan para llevar acabo este tipo de algoritmos está el algoritmo RSA, que se basa en la factorización de números enteros muy grandes. Sin embargo, en el año 1994 Peter Shor presentó un algoritmo que permite factorizar números enteros grandes y podría echar abajo este sistema. La única razón por la que aún el algoritmo de Shor no ha puesto en peligro la seguridad de Internet es que para ello necesita un ordenador cuántico de miles de q-bits. Por el momento dicho ordenador no existe, pero los progresos actuales en computación cuántica permiten pensar que dentro de unas décadas se podrá construir un ordenador cuántico con esas características. Por tanto, es necesario enfrentar este nuevo escenario lo antes posible..