Post-Quantum Provably-Secure Authentication and MAC from Mersenne Primes

This paper presents a novel, yet efficient secret-key authentication and MAC, which provide post-quantum security promise, whose security is reduced to the quantum-safe conjectured hardness of Mersenne Low Hamming Combination (MERS) assumption recently introduced by Aggarwal, Joux, Prakash, and Santha (CRYPTO 2018). Our protocols are very suitable to weak devices like smart card and RFID tags

New Classes of Binary Random Sequences for Cryptography

In the vision for the 5G wireless communications advancement that yield new security prerequisites and challenges we propose a catalog of three new classes of pseudorandom random sequence generators. This dissertation starts with a review on the requirements of 5G wireless networking systems and the most recent development of the wireless security services applied to 5G, such as private-keys generation, key protection, and flexible authentication. This dissertation proposes new complexity theory-based, number-theoretic approaches to generate lightweight pseudorandom sequences, which protect the private information using spread spectrum techniques. For the class of new pseudorandom sequences, we obtain the generalization. Authentication issues of communicating parties in the basic model of Piggy Bank cryptography is considered and a flexible authentication using a certified authority is proposed

High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA

In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms of execution time. Our approach employs the combination of the schoolbook long and Karatsuba multiplication algorithm for the elliptic curve point multiplication (ECPM) to achieve better parallelization while retaining low complexity. In the hardware implementation, the substantial gain in speed is also contributed by our n-bit pipelined Montgomery Modular Multiplier (pMMM), which is constructed from our n-bit pipelined multiplier-accumulators that utilizes digital signal processor (DSP) primitives as digit multipliers. Additionally, we also introduce our unified, pipelined modular adder-subtractor (pMAS) for the underlying field arithmetic, and leverage a more efficient yet compact scheduling of the Montgomery ladder algorithm. The implementation for 256-bit modulus size on the 7-series FPGA: Virtex-7, Kintex-7, and XC7Z020 yields 0.139, 0.138, and 0.206 ms of execution time, respectively. Furthermore, since our pMMM module is generic for any curve in Weierstrass form, we support multi-curve parameters, resulting in a unified ECC architecture. Lastly, our method also works in constant time, making it suitable for applications requiring high speed and SCA-resistant characteristics

End-to-End Encrypted Group Messaging with Insider Security

Our society has become heavily dependent on electronic communication, and preserving the integrity of this communication has never been more important. Cryptography is a tool that can help to protect the security and privacy of these communications. Secure messaging protocols like OTR and Signal typically employ end-to-end encryption technology to mitigate some of the most egregious adversarial attacks, such as mass surveillance. However, the secure messaging protocols deployed today suffer from two major omissions: they do not natively support group conversations with three or more participants, and they do not fully defend against participants that behave maliciously. Secure messaging tools typically implement group conversations by establishing pairwise instances of a two-party secure messaging protocol, which limits their scalability and makes them vulnerable to insider attacks by malicious members of the group. Insiders can often perform attacks such as rendering the group permanently unusable, causing the state of the group to diverge for the other participants, or covertly remaining in the group after appearing to leave. It is increasingly important to prevent these insider attacks as group conversations become larger, because there are more potentially malicious participants. This dissertation introduces several new protocols that can be used to build modern communication tools with strong security and privacy properties, including resistance to insider attacks. Firstly, the dissertation addresses a weakness in current two-party secure messaging tools: malicious participants can leak portions of a conversation alongside cryptographic proof of authorship, undermining confidentiality. The dissertation introduces two new authenticated key exchange protocols, DAKEZ and XZDH, with deniability properties that can prevent this type of attack when integrated into a secure messaging protocol. DAKEZ provides strong deniability in interactive settings such as instant messaging, while XZDH provides deniability for non-interactive settings such as mobile messaging. These protocols are accompanied by composable security proofs. Secondly, the dissertation introduces Safehouse, a new protocol that can be used to implement secure group messaging tools for a wide range of applications. Safehouse solves the difficult cryptographic problems at the core of secure group messaging protocol design: it securely establishes and manages a shared encryption key for the group and ephemeral signing keys for the participants. These keys can be used to build chat rooms, team communication servers, video conferencing tools, and more. Safehouse enables a server to detect and reject protocol deviations, while still providing end-to-end encryption. This allows an honest server to completely prevent insider attacks launched by malicious participants. A malicious server can still perform a denial-of-service attack that renders the group unavailable or "forks" the group into subgroups that can never communicate again, but other attacks are prevented, even if the server colludes with a malicious participant. In particular, an adversary controlling the server and one or more participants cannot cause honest participants' group states to diverge (even in subtle ways) without also permanently preventing them from communicating, nor can the adversary arrange to covertly remain in the group after all of the malicious participants under its control are removed from the group. Safehouse supports non-interactive communication, dynamic group membership, mass membership changes, an invitation system, and secure property storage, while offering a variety of configurable security properties including forward secrecy, post-compromise security, long-term identity authentication, strong deniability, and anonymity preservation. The dissertation includes a complete proof-of-concept implementation of Safehouse and a sample application with a graphical client. Two sub-protocols of independent interest are also introduced: a new cryptographic primitive that can encrypt multiple private keys to several sets of recipients in a publicly verifiable and repeatable manner, and a round-efficient interactive group key exchange protocol that can instantiate multiple shared key pairs with a configurable knowledge relationship

Побудова модифікацій та криптоаналіз постквантових примітивів сімейства AJPS

Кваліфікаційна робота обсягом 135 сторінок містить 45 рисунків, 3 таблиці та 60 джерел. Протягом останніх років стрімко почала розвиватись постквантова криптографія, метою якої є розробка криптографічних примітивів, що були б стійкі до атак з використанням як квантового, так і класичного комп’ютерів. Починаючи з 2017 року триває конкурс постквантових асиметричних криптопримітивів під егідою Національного інституту стандартів та технологій США (NIST). Одним з учасників першого раунду конкурсу є механізм інкапсуляції ключів Mersenne-756839, основою якого є криптосистема AJPS. Метою роботи є дослідження особливостей перетворення інформації в криптографічних примітивах сімейства AJPS, та їх модифікація задля збільшення рівня захищеності. Об’єктом дослідження є процеси перетворення інформації у постквантових системах криптографічного захисту. Предметом дослідження є моделі постквантових криптографічних примітивів сімейства AJPS. У роботі сформовано рекомендації для алгоритмів генерації ключів криптосистем AJPS-1 і AJPS-2 та побудовано атаку підміни на криптосистему AJPS-2. Доведено нові властивості арифметики за модулем числа Мерсенна, узагальненого числа Мерсенна та числа Кренделла. Побудовано модифікацію криптосистеми AJPS-1 шляхом зміни метрики, а також модифікації AJPS-1 та AJPS-2 шляхом зміни класу чисел, що використовуються в криптосистемах у якості модуля. Виконано порівняльний аналіз усіх побудованих модифікацій і криптосистем AJPS-1 та AJPS-2.The volume of the qualitative work is 135 pages and it contains 45 figures, 3 tables and 60 sources. In recent years, quantum-resistant cryptography has been steadily developing. Its aim is to develop the cryptographic primitives that would be resistant to attacks using both quantum and classical computers. In 2017, the National Institute of Standards and Technology (NIST) has launched the competition for quantum-resistant asymmetric cryptographic primitives, which is ongoing. One of the participants of the first round of the competition is the Mersenne-756839 key encapsulation mechanism, which is based on the AJPS cryptosystem. The purpose of the research is to investigate the peculiarities of conversion of information in cryptographic primitives of the AJPS family, and modification of it in order to increase the security level. The object of the research is the pro cessesofconversionofinformationinquantum-resistantcryptographicsecuritysystems.The subject of the research is the models of quantum-resistant cryptographic primitives of the AJPS family. The recommendations for key generation algorithms of the AJPS-1 and the AJPS-2 cryptosystems are represented in the work and the substitution attack on the AJPS-2 cryptosystem is constructed. The new properties of the arithmetic modulo Mersenne number, generalized Mersenne number and Crandall number are proved. The modification of the AJPS-1 cryptosystem by changing the metric, and also the modification of the AJPS-1 and the AJPS-2 by changing the class of numbers, which is used in the cryptosystems as a module, are created. The comparative analysis of all the modifications, which were created, and the cryptosystems AJPS-1 and AJPS-2 was done

Key Encapsulation from Noisy Key Agreement in the Quantum Random Oracle Model

A multitude of post-quantum key encapsulation mechanisms (KEMs) and public key encryption (PKE) schemes implicitly rely on a protocol by which Alice and Bob exchange public messages and converge on secret values that are identical up to some small noise. By our count, 24 out of 49 KEM or PKE submissions to the NIST Post-Quantum Cryptography Standardization project follow this strategy. Yet the notion of a noisy key agreement (NKA) protocol lacks a formal definition as a primitive in its own right. We provide such a formalization by defining the syntax and security for an NKA protocol. This formalization brings out four generic problems, called A and B State Recovery, Noisy Key Search and Noisy Key Distinguishing, whose solutions must be hard in the quantum computing model. Informally speaking, these can be viewed as noisy, quantum-resistant counterparts of the problems arising from the classical Diffie-Hellman type protocols. We show that many existing proposals contain an NKA component that fits our formalization and we reveal the induced concrete hardness assumptions. The question arises whether considering NKA as an independent primitive can help provide modular designs with improved efficiency and/or proofs. As the second contribution of this paper, we answer this question positively by presenting a generic transform from a secure NKA protocol to an IND-CCA secure KEM in the quantum random oracle model, with a security bound tightly related to the NKD problem. This transformation is essentially the same as that of the NIST candidate Ramstake. While establishing the security of Ramstake was our initial objective, the collection of tools that came about as a result of this journey is of independent interest

Efficient and Side-Channel Resistant Implementations of Next-Generation Cryptography

The rapid development of emerging information technologies, such as quantum computing and the Internet of Things (IoT), will have or have already had a huge impact on the world. These technologies can not only improve industrial productivity but they could also bring more convenience to people’s daily lives. However, these techniques have “side effects” in the world of cryptography – they pose new difficulties and challenges from theory to practice. Specifically, when quantum computing capability (i.e., logical qubits) reaches a certain level, Shor’s algorithm will be able to break almost all public-key cryptosystems currently in use. On the other hand, a great number of devices deployed in IoT environments have very constrained computing and storage resources, so the current widely-used cryptographic algorithms may not run efficiently on those devices. A new generation of cryptography has thus emerged, including Post-Quantum Cryptography (PQC), which remains secure under both classical and quantum attacks, and LightWeight Cryptography (LWC), which is tailored for resource-constrained devices. Research on next-generation cryptography is of importance and utmost urgency, and the US National Institute of Standards and Technology in particular has initiated the standardization process for PQC and LWC in 2016 and in 2018 respectively. Since next-generation cryptography is in a premature state and has developed rapidly in recent years, its theoretical security and practical deployment are not very well explored and are in significant need of evaluation. This thesis aims to look into the engineering aspects of next-generation cryptography, i.e., the problems concerning implementation efficiency (e.g., execution time and memory consumption) and security (e.g., countermeasures against timing attacks and power side-channel attacks). In more detail, we first explore efficient software implementation approaches for lattice-based PQC on constrained devices. Then, we study how to speed up isogeny-based PQC on modern high-performance processors especially by using their powerful vector units. Moreover, we research how to design sophisticated yet low-area instruction set extensions to further accelerate software implementations of LWC and long-integer-arithmetic-based PQC. Finally, to address the threats from potential power side-channel attacks, we present a concept of using special leakage-aware instructions to eliminate overwriting leakage for masked software implementations (of next-generation cryptography)

Secure covert communications over streaming media using dynamic steganography

Streaming technologies such as VoIP are widely embedded into commercial and industrial applications, so it is imperative to address data security issues before the problems get really serious. This thesis describes a theoretical and experimental investigation of secure covert communications over streaming media using dynamic steganography. A covert VoIP communications system was developed in C++ to enable the implementation of the work being carried out. A new information theoretical model of secure covert communications over streaming media was constructed to depict the security scenarios in streaming media-based steganographic systems with passive attacks. The model involves a stochastic process that models an information source for covert VoIP communications and the theory of hypothesis testing that analyses the adversary‘s detection performance. The potential of hardware-based true random key generation and chaotic interval selection for innovative applications in covert VoIP communications was explored. Using the read time stamp counter of CPU as an entropy source was designed to generate true random numbers as secret keys for streaming media steganography. A novel interval selection algorithm was devised to choose randomly data embedding locations in VoIP streams using random sequences generated from achaotic process. A dynamic key updating and transmission based steganographic algorithm that includes a one-way cryptographical accumulator integrated into dynamic key exchange for covert VoIP communications, was devised to provide secure key exchange for covert communications over streaming media. The discrete logarithm problem in mathematics and steganalysis using t-test revealed the algorithm has the advantage of being the most solid method of key distribution over a public channel. The effectiveness of the new steganographic algorithm for covert communications over streaming media was examined by means of security analysis, steganalysis using non parameter Mann-Whitney-Wilcoxon statistical testing, and performance and robustness measurements. The algorithm achieved the average data embedding rate of 800 bps, comparable to other related algorithms. The results indicated that the algorithm has no or little impact on real-time VoIP communications in terms of speech quality (< 5% change in PESQ with hidden data), signal distortion (6% change in SNR after steganography) and imperceptibility, and it is more secure and effective in addressing the security problems than other related algorithms

On the Analysis of Public-Key Cryptologic Algorithms

The RSA cryptosystem introduced in 1977 by Ron Rivest, Adi Shamir and Len Adleman is the most commonly deployed public-key cryptosystem. Elliptic curve cryptography (ECC) introduced in the mid 80's by Neal Koblitz and Victor Miller is becoming an increasingly popular alternative to RSA offering competitive performance due the use of smaller key sizes. Most recently hyperelliptic curve cryptography (HECC) has been demonstrated to have comparable and in some cases better performance than ECC. The security of RSA relies on the integer factorization problem whereas the security of (H)ECC is based on the (hyper)elliptic curve discrete logarithm problem ((H)ECDLP). In this thesis the practical performance of the best methods to solve these problems is analyzed and a method to generate secure ephemeral ECC parameters is presented. The best publicly known algorithm to solve the integer factorization problem is the number field sieve (NFS). Its most time consuming step is the relation collection step. We investigate the use of graphics processing units (GPUs) as accelerators for this step. In this context, methods to efficiently implement modular arithmetic and several factoring algorithms on GPUs are presented and their performance is analyzed in practice. In conclusion, it is shown that integrating state-of-the-art NFS software packages with our GPU software can lead to a speed-up of 50%. In the case of elliptic and hyperelliptic curves for cryptographic use, the best published method to solve the (H)ECDLP is the Pollard rho algorithm. This method can be made faster using classes of equivalence induced by curve automorphisms like the negation map. We present a practical analysis of their use to speed up Pollard rho for elliptic curves and genus 2 hyperelliptic curves defined over prime fields. As a case study, 4 curves at the 128-bit theoretical security level are analyzed in our software framework for Pollard rho to estimate their practical security level. In addition, we present a novel many-core architecture to solve the ECDLP using the Pollard rho algorithm with the negation map on FPGAs. This architecture is used to estimate the cost of solving the Certicom ECCp-131 challenge with a cluster of FPGAs. Our design achieves a speed-up factor of about 4 compared to the state-of-the-art. Finally, we present an efficient method to generate unique, secure and unpredictable ephemeral ECC parameters to be shared by a pair of authenticated users for a single communication. It provides an alternative to the customary use of fixed ECC parameters obtained from publicly available standards designed by untrusted third parties. The effectiveness of our method is demonstrated with a portable implementation for regular PCs and Android smartphones. On a Samsung Galaxy S4 smartphone our implementation generates unique 128-bit secure ECC parameters in 50 milliseconds on average

Democracy Enhancing Technologies: Toward deployable and incoercible E2E elections

End-to-end verifiable election systems (E2E systems) provide a provably correct tally while maintaining the secrecy of each voter's ballot, even if the voter is complicit in demonstrating how they voted. Providing voter incoercibility is one of the main challenges of designing E2E systems, particularly in the case of internet voting. A second challenge is building deployable, human-voteable E2E systems that conform to election laws and conventions. This dissertation examines deployability, coercion-resistance, and their intersection in election systems. In the course of this study, we introduce three new election systems, (Scantegrity, Eperio, and Selections), report on two real-world elections using E2E systems (Punchscan and Scantegrity), and study incoercibility issues in one deployed system (Punchscan). In addition, we propose and study new practical primitives for random beacons, secret printing, and panic passwords. These are tools that can be used in an election to, respectively, generate publicly verifiable random numbers, distribute the printing of secrets between non-colluding printers, and to covertly signal duress during authentication. While developed to solve specific problems in deployable and incoercible E2E systems, these techniques may be of independent interest