Optimization of Supersingular Isogeny Cryptography for Deeply Embedded Systems

Public-key cryptography in use today can be broken by a quantum computer with sufficient resources. Microsoft Research has published an open-source library of quantum-secure supersingular isogeny (SI) algorithms including Diffie-Hellman key agreement and key encapsulation in portable C and optimized x86 and x64 implementations. For our research, we modified this library to target a deeply-embedded processor with instruction set extensions and a finite-field coprocessor originally designed to accelerate traditional elliptic curve cryptography (ECC). We observed a 6.3-7.5x improvement over a portable C implementation using instruction set extensions and a further 6.0-6.1x improvement with the addition of the coprocessor. Modification of the coprocessor to a wider datapath further increased performance 2.6-2.9x. Our results show that current traditional ECC implementations can be easily refactored to use supersingular elliptic curve arithmetic and achieve post-quantum security

Hardware-Software Codesign of a Vector Co-processor for Public Key Cryptography

International audienceUntil now, most cryptography implementations on parallel architectures have focused on adapting the software to SIMD architectures initially meant for media applications. In this paper, we review some of the most significant contributions in this area. We then propose a vector architecture to efficiently implement long precision modular multiplications. Having such a data level parallel hardware provides a circuit whose decode and schedule units are at least of the same complexity as those of a scalar processor. The excess transistors are mainly found in the data path. Moreover, the vector approach gives a very modular architecture where resources can be easily redefined. We built a functional simulator onto which we performed a quantitative analysis to study how the resizing of those resources affects the performance of the modular multiplication operation. Hence we not only propose a vector architecture for our Public Key cryptographic operations but also show how we can analyze the impact of design choices on performance. The proposed architecture is also flexible in the sense that the software running on it would offer room for the implementation of counter-measures against side-channel or fault attacks

Reconfigurable elliptic curve cryptography

Elliptic Curve Cryptosystems (ECC) have been proposed as an alternative to other established public key cryptosystems such as RSA (Rivest Shamir Adleman). ECC provide more security per bit than other known public key schemes based on the discrete logarithm problem. Smaller key sizes result in faster computations, lower power consumption and memory and bandwidth savings, thus making ECC a fast, flexible and cost-effective solution for providing security in constrained environments. Implementing ECC on reconfigurable platform combines the speed, security and concurrency of hardware along with the flexibility of the software approach. This work proposes a generic architecture for elliptic curve cryptosystem on a Field Programmable Gate Array (FPGA) that performs an elliptic curve scalar multiplication in 1.16milliseconds for GF (2163), which is considerably faster than most other documented implementations. One of the benefits of the proposed processor architecture is that it is easily reprogrammable to use different algorithms and is adaptable to any field order. Also through reconfiguration the arithmetic unit can be optimized for different area/speed requirements. The mathematics involved uses binary extension field of the form GF (2n) as the underlying field and polynomial basis for the representation of the elements in the field. A significant gain in performance is obtained by using projective coordinates for the points on the curve during the computation process

An analysis of key generation efficiency of RSA cryptosystem in distributed environments

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2005Includes bibliographical references (leaves: 68)Text in English Abstract: Turkish and Englishix, 74 leavesAs the size of the communication through networks and especially through Internet grew, there became a huge need for securing these connections. The symmetric and asymmetric cryptosystems formed a good complementary approach for providing this security. While the asymmetric cryptosystems were a perfect solution for the distribution of the keys used by the communicating parties, they were very slow for the actual encryption and decryption of the data flowing between them. Therefore, the symmetric cryptosystems perfectly filled this space and were used for the encryption and decryption process once the session keys had been exchanged securely. Parallelism is a hot research topic area in many different fields and being used to deal with problems whose solutions take a considerable amount of time. Cryptography is no exception and, computer scientists have discovered that parallelism could certainly be used for making the algorithms for asymmetric cryptosystems go faster and the experimental results have shown a good promise so far. This thesis is based on the parallelization of a famous public-key algorithm, namely RSA

Customisable arithmetic hardware designs

Imperial Users onl

Parallelism and the software-hardware interface in embedded systems

This thesis by publications addresses issues in the architecture and microarchitecture of next generation, high performance streaming Systems-on-Chip through quantifying the most important forms of parallelism in current and emerging embedded system workloads. The work consists of three major research tracks, relating to data level parallelism, thread level parallelism and the software-hardware interface which together reflect the research interests of the author as they have been formed in the last nine years. Published works confirm that parallelism at the data level is widely accepted as the most important performance leverage for the efficient execution of embedded media and telecom applications and has been exploited via a number of approaches the most efficient being vectorlSIMD architectures. A further, complementary and substantial form of parallelism exists at the thread level but this has not been researched to the same extent in the context of embedded workloads. For the efficient execution of such applications, exploitation of both forms of parallelism is of paramount importance. This calls for a new architectural approach in the software-hardware interface as its rigidity, manifested in all desktop-based and the majority of embedded CPU's, directly affects the performance ofvectorized, threaded codes. The author advocates a holistic, mature approach where parallelism is extracted via automatic means while at the same time, the traditionally rigid hardware-software interface is optimized to match the temporal and spatial behaviour of the embedded workload. This ultimate goal calls for the precise study of these forms of parallelism for a number of applications executing on theoretical models such as instruction set simulators and parallel RAM machines as well as the development of highly parametric microarchitectural frameworks to encapSUlate that functionality.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Design of a novel hybrid cryptographic processor

viii, 87 leaves : ill. (some col.) ; 28 cm.A new multiplier that supports fields GF(p) and GF (2n) for the public-key cryptography, and fields GF (28) for the secret-key cryptography is proposed in this thesis. Based on the core multiplier and other extracted common operations, a novel hybrid crypto-processor is built which processes both public-key and secret-key cryptosystems. The corresponding instruction set is also presented. Three cryptographic algorithms: the Elliptic Curve Cryptography (ECC), AES and RC5 are focused to run in the processor. To compute scalar multiplication kP efficiently, a blend of efficient algorthms on elliptic curves and coordinates selections and of hardware architecture that supports arithmetic operations on finite fields is requried. The Nonadjacent Form (NAF) of k is used in Jacobian projective coordinates over GF(p); Montgomery scalar multiplication is utilized in projective coordinates over GF(2n). The dual-field multiplier is used to support multiplications over GF(p) and GF(2n) according to multiple-precision Montgomery multiplications algorithms. The design ideas of AES and RC5 are also described. The proposed hybrid crypto-processor increases the flexibility of security schemes and reduces the total cost of cryptosystems