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Progress in the field of quantum computing has shown that, should construction of a sufficiently powerful quantum computer become feasible, much of the cryptography used on the Internet today will be rendered insecure. In lieu of this, several approaches to “quantum-safe” cryptography have been proposed, each one becoming a serious field of study. The youngest of these approaches, isogeny based cryptography, is oriented around problems in algebraic geometry involving a particular variety of elliptic curves. Supersingular isogeny Diffie-Hellman (SIDH) is this subfields main contender for quantum-safe key-exchange. Yoo et al. have provided an isogeny-based signature scheme built on top of SIDH. Currently, cryptographic algorithms in this class are hindered by poor performance metrics and, in the case of the Yoo et al. signature scheme, large communication overhead. In this dissertation we explore two different modifications to the implementation of this signature scheme; one with the intent of improving temporal performance, and another with the intent of reducing signature sizes. We show that our first modification, a mechanism for batching together expensive operations, can offer roughly 8% faster signature signing and verification. Our second modification, an adaptation of the SIDH public key compression technique outlined in [CJL + 17], can reduce Yoo et al. signature sizes from roughly 688λ bytes to 544λ bytes at the 128-bit security level on a 64-bit operating system. We also explore the combination of these techniques, and the potential of employing these techniques in different application settings. Our experiments reveal that isogeny based cryptosystems still have much potential for improved performance metrics. While some practitioners may believe isogeny-based cryptosystems impractical, we show that these systems still have room for improvement, and with continued research can be made more efficient - and eventually practical. Achieving more efficient implementations for quantum-safe algorithms will allow us to make them more accessible. With faster and lower-overhead implementations these primitives can be run on low bandwidth, low spec devices; ensuring that more and more machines can be made resistant to quantum cryptanalysis. / Thesis / Master of Science (MSc)

In recent years, there has been a drastic increase in the prevalence of counterfeiting within the electronics supply chain. At the same time, high-end commercial off-the-shelf components like FPGAs and expensive peripherals are making their way onto printed circuit boards. Manufacturers of such PCBs lose billions of dollars as well as their reputation when counterfeiting incidents are revealed within their supply chain. Moreover, there are several safety and security implications of using PCBs with counterfeit components. In this context, it is useful to enable remote integrity checking of these PCBs to identify and mitigate any safety or security concerns when they are deployed. Typical integrity checks look for the presence of an identifier embedded within a secure memory on the PCB. This approach is now being replaced by hardware intrinsic identifiers based on Physical Unclonable Functions or PUFs. Such identifiers can be used to establish trust within any component on a PCB. In this thesis, we present two PUF based protocols for remote integrity checking of PCBs by Manufacturers or end users. We propose one of the protocols for a special case of remote integrity checking - the Third Party Verification. The protocols are demonstrated using prototypes running on two different platforms - Altera DE2-115 and TI MSP430. Finally, we evaluate their performance on these prototypes and determine the feasibility of their use. / Master of Science

Elliptic curve cryptography (ECC) is becoming the algorithm of choice for digital signature generation and authentication in embedded context. However, performance of ECC and the underlying modular arithmetic on embedded processors remains a concern. At the same time, more complex system-on-chip platforms with multiple heterogeneous cores are commonly available in mobile phones and other embedded devices. In this work we investigate the design space for ECC on TI's OMAP 3530 platform, with a focus of utilizing the on-chip DSP core to improve the performance and efficiency of ECC point multiplication on the target platform. We examine multiple aspects of ECC and heterogeneous design such as algorithm-level choices for elliptic curve operations and the effect of interprocessor communication overhead on the design partitioning. We observe how the limitations of the platform constrict the design space of ECC. However, by closely studying the platform and efficiently partitioning the design between the general purpose ARM core and the DSP, we demonstrate a significant speed-up of the resulting ECC implementation. Our system focused approach allows us to accurately measure the performance and power profiles of the resulting implementation. We conclude that heterogeneous multiprocessor design can significantly improve the performance and power consumption of ECC operations, but that the integration cost and the overhead of interprocessor communication cannot be ignored in any actual system. / Master of Science

The Master thesis is an introduction to cryptology. The Thesis describe cryptosystems and selects one ideal cypher for low-power microcontroler. In thesis provides manual for instal development program COde Composer Studio, basic implementation of selected cryptosystem with small numbers and suggestion for implementation selected cyptosystem with big numbers.

The project aims at solving the problem of non-repudiation, integrity and confidentiality of data when digitally exchanging sensitive resources between parties that need to be able to trust each other without the need for a trusted third party. This is done in the framework of answering to what extent digital resources can be shared securely in a decentralized public ledger-based system compared to trust-based alternatives. A background of existing resource sharing solutions is explored which shows an abundance third party trust-based systems, but also an interest in public ledger solutions in the form of the Storj network which uses such technology, but focuses on storage rather than sharing. The proposed solution, called SecuRES, is a communication protocol based on public ledger technology which acts similar to Bitcoin. A prototype based on the protocol has been implemented which proves the ability to share encrypted files with one or several recipients through a decentralized public ledger-based network. It was concluded that the SecuRES solution could do away with the requirement of trust in third parties for all but some optional operations using external authentication services. This is done while still maintaining data integrity of a similar or greater degree to trust-based solutions and offers the additional benefits of non-repudiation, high confidentiality and high transparency from the ability to make source code and protocol documentation openly available without endangering the system. Further research is needed to investigate whether the system can scale up for widespread adoption while maintaining security and reasonable performance requirements. / Projektet ämnar lösa problemen med oförnekbarhet, integritet och konfidentialitet när man delar känsligt data mellan parter som behöver lita på varandra utan inblanding av betrodd tredje part. Detta diskuteras för att besvara till vilken omfattning digitala resurser kan delas säkert i ett decentraliserat system baserat på publika liggare jämfört med existerande tillitsbaserade alternativ. En undersökning av nuvarande resursdelningslösningar visar att det existerar många tillitsbaserade system men även en växande andel lösningar baserade på publika liggare. En intressant lösning som lyfts fram är Storj som använder sådan teknologi men fokuserar på resurslagring mer är delning. Projektets föreslagna lösning, kallad SecuRES, är ett kommunikationsprotokoll baserat på en publik liggare likt Bitcoin. En prototyp baserad på protokollet har tagits fram som visar att det är möjligt att dela krypterade filer med en eller flera mottagare genom ett decentraliserat nätverk baserat på publika liggare. Slutsatsen som dras är att SecuRES klarar sig utan betrodda tredje parter för att dela resurser medan vissa operationer kan göras mer användarvänliga genom externa autentiseringstjänster. Själva lösningen garanterar integritet av data och medför ytterligare fördelar såsom oförnekbarhet, konfidentialitet och hög transparens då man kan göra källkoden och protocoldokumentation fritt läsbar utan att utsätta systemet för fara. Vidare forskning behövs för att undersöka om systemet kan skalas upp för allmän användning och alltjämt bibehålla säkerhets- samt prestandakrav.

Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. Tate pairing is a bilinear map used in identity based cryptography schemes. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. Similarly, Tate pairing is also quite computationally expensive. Therefore, it is more attractive to implement the ECC and Tate pairing using hardware than using software. The bases of both ECC and Tate pairing are Galois field arithmetic units. In this thesis, I propose the FPGA implementations of the elliptic curve point multiplication in GF (2283) as well as Tate pairing computation on supersingular elliptic curve in GF (2283). I have designed and synthesized the elliptic curve point multiplication and Tate pairing module using Xilinx's FPGA, as well as synthesized all the Galois arithmetic units used in the designs. Experimental results demonstrate that the FPGA implementation can speedup the elliptic curve point multiplication by 31.6 times compared to software based implementation. The results also demonstrate that the FPGA implementation can speedup the Tate pairing computation by 152 times compared to software based implementation.