Hyperelliptic Curve Coprocessors on a FPGA

This paper presents the design and implementation of a hyperelliptic curve cryptography (HECC) coprocessor over affine and projective coordinates, along with measurements of its performance, hardware complexity, and power consumption. We applied several design techniques, including parallelism, pipelining, and loop unrolling, in designing field arithmetic units, group operation units, and scalar multiplication units to improve the performance and power consumption. Our affine and projective coordinate-based HECC processors execute in 0.436 ms and 0.531 ms, respectively, based on the underlying field GF(2 89 ). These results are about five times faster than those for previous hardware implementations and at least 13 times better in terms of area-time products. Further results suggest that neither case is superior to the other when considering the hardware complexity and performance. The characteristics of our proposed HECC coprocessor show that it is applicable to high-speed network applications as well as resource-constrained environments, such as PDAs, smart cards, and so on.

One of the recent thrust areas in research on hyperelliptic curve cryptography has been to obtain explicit formulae for performing arithmetic in the Jacobian of such curves. We continue this line of research by obtaining parallel versions of such formulae. Our first contribution is to develop a general methodology for obtaining parallel algorithm of any explicit formula. Any parallel algorithm obtained using our methodology is provably optimal in the number of multiplication rounds. We next apply this methodology to Lange’s explicit formula for arithmetic in genus 2 hyperelliptic curve – both for the affine coordinate and inversion free arithmetic versions. Since encapsulated add-and-double algorithm is an important countermeasure against side channel attacks, we develop parallel algorithms for encapsulated add-and-double for both of Lange’s versions of explicit formula. For the case of inversion free arithmetic, we present parallel algorithms using 4, 8 and 12 multipliers. All parallel algorithms described in this paper are optimal in the number of parallel rounds. One of the conclusions from our work is the fact that the parallel version of inversion free arithmetic is more efficient than the parallel version of arithmetic using affine coordinates.Keywordshyperelliptic curve cryptographyexplicit formulaparallel algorithmJacobianencapsulated add-and-double

Hyperelliptic curves (HEC) look promising for cryptographic applications, because of their short operand size compared to other public-key schemes. The operand sizes seem well suited for small processor architectures, where memory and speed are constrained. However, the group operation has been believed to be too complex and, thus, HEC have not been used in this context so far. In recent years, a lot of effort has been made to speed up group operation of genus-2 HEC. In this paper, we increase the efficiency of the genus-2 and genus-3 hyperelliptic curve cryptosystems (HECC). For certain genus-3 curves, we can gain almost 80 percent performance for a group doubling. This work not only improves Gaudry and Harley's algorithm, but also improves the original algorithm introduced by Cantor [1987]. Contrary to common belief, we show that it is also practical for certain curves to use Cantor's algorithm to obtain the highest efficiency for the group operation. In addition, we introduce a general reduction method for polynomials according to Karatsuba. We implemented our most efficient group operations on Pentium and ARM microprocessors.

Due to short operand size, Hyperelliptic Curve Cryptosystem (HECC) of genus 3 is well suited for all kinds of embedded processor architectures, where resources such as storage, time or power are constrained. In the implementation of HECC, a significant step is the selection of secure hyperelliptic curves on which the Jacobian is constructed and speed up the scalar multiplications in the Jacobians of hyperelliptic curves. In this paper, we have explored various possible attacks to the discrete logarithm in the Jacobian of a Hyperelliptic Curve (HEC) that are to be considered to establish a secure HEC, analysed addition and doubling of divisor which are the prime steps of scalar multiplication and then proposed certain improvements in the existing explicit formula that will result in a performance gain for HECC of genus 3.

Recently, considerable research has been performed in cryptography and security to optimize the area, power, timing, and energy needed for the point multiplication operations over binary elliptic curves. In this paper, we propose an efficient implementation of point multiplication on Koblitz curves targeting extremely-constrained, secure applications. We utilize the Gaussian normal basis (GNB) representation of field elements over GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> ) and employ an efficient bit-level GNB multiplier. One advantage of this GNB multiplier is that we are able to reduce the hardware complexity through sharing the addition/accumulation with other field additions. We utilized the special property of normal basis representation and squarings are implemented very efficiently by only rewiring in hardware. We introduce a new technique for point addition in affine coordinate which requires fewer registers. Based on this technique, we propose an extremely small processor architecture for point multiplication. Through application-specific integrated circuit (ASIC) implementations, we evaluate the area, performance, and energy consumption of the proposed crypto-processor. Utilizing two different working frequencies, it is shown that the proposed architecture reaches better results compared to the previous works, making it suitable for extremely-constrained, secure environments.

With the continuous development of the Internet and communication technologies, network communication provides convenience but also brings security problems such as exposure of users' personal privacy information and theft, private tampering, and forgery of false information. Modern cryptography technology is an important safeguard against message eavesdropping and tampering, while the rapidly developing anonymous communication technology in this century makes it difficult for attackers to infer user's personal information and communication relationships. In response to the potential threats of traditional centralized systems such as central nodes being vulnerable to attacks and data storage being tampered with, this paper proposes a blockchain anonymous communication algorithm KDAC based on key derivation, which takes advantage of the decentralization, data immutability, consensus mechanism and anonymity of blockchain and combines the ECC cryptographic derivation algorithm and anonymous communication technology to realize the key-at-a-time, one-address-at-a-time The key derivation scheme ensures the message integrity and tamper-evident while effectively hiding the identity information of both communication parties. In addition, this paper also optimizes the blockchain anonymous communication system with key derivation. Users only need the initial key of blockchain nodes to join the network for communication, and the information transmission is difficult to trace based on the blockchain network, which can effectively guarantee communication security and anonymity. The experimental results show that the efficiency of the derived key algorithm is roughly in the same order of magnitude as that of the 256-bit AES symmetric encryption algorithm, which can play a better role in practical applications. On the other hand, the derived key generated based on the algorithm has complete randomness in association verification, and it is impossible to reverse the initial parameters, which can well guarantee the anonymity of user identity.

Quantitative micro-elastography (QME) is a compression-based optical coherence elastography technique capable of measuring the mechanical properties of tissue on the micro-scale. As QME requires contact between the imaging window and the sample, the presence of friction affects the accuracy of the estimated elasticity. In previous implementations, a lubricant was applied at the contact surfaces, which was assumed to result in negligible friction. However, recently, errors in the estimation of elasticity caused by friction have been reported. This effect has yet to be characterized and is, therefore, not well understood. In this work, we present a systematic analysis of friction in QME using silicone phantoms. We demonstrate that friction, and, therefore, the elasticity accuracy, is influenced by several experimental factors, including the viscosity of the lubricant, the mechanical contrast between the compliant layer and the sample, and the time after the application of a compressive strain. Elasticity errors over an order of magnitude were observed in the absence of appropriate lubrication when compared to uniaxial compression testing. Using an optimized lubrication protocol, we demonstrate accurate elasticity estimation (<10% error) for nonlinear elastic samples with Young's moduli ranging from 3 kPa to 130 kPa. Finally, using a structured phantom, we demonstrate that friction can significantly reduce mechanical contrast in QME. We believe that the framework established in this study will facilitate more robust elasticity estimations in QME, as well as being readily adapted to understand the effects of friction in other contact elastography techniques.

We revisit the Pseudo-Bayesian approach to the problem of estimating density matrix in quantum state tomography in this paper. Pseudo-Bayesian inference has been shown to offer a powerful paradigm for quantum tomography with attractive theoretical and empirical results. However, the computation of (Pseudo-)Bayesian estimators, due to sampling from complex and high-dimensional distribution, pose significant challenges that hamper their usages in practical settings. To overcome this problem, we present an efficient adaptive MCMC sampling method for the Pseudo-Bayesian estimator by exploring an adaptive proposal scheme together with subsampling method. We show in simulations that our approach is substantially computationally faster than the previous implementation by at least two orders of magnitude which is significant for practical quantum tomography.

One of the most important issues in traditional and modern networks architecture is security. Data integrity and authenticity are the most critical points that a network security model should protect and ensure. Authentication, Authorization and Accounting model (AAA Protocol) is one of the most portable security concepts. Authentication acts providing proof of authenticity for stored data and verifying proof of authenticity for received. Authorization acts providing privileges to those clients that present specific credentials. Accounting acts collecting accounting metrics for two reasons; to forward them to the billing server for billing results, and to keep them saved locally for the procedure of trend analysis. In this paper, the generic AAA architecture is introduced, personalized and practically designed for usage in modern networks. The most efficient way, using supported protocols and cryptographic algorithms, for administrating AAA in practice, is proposed for mobile networks or administrative domains. In this work, a Web based application scenario using the AAA protocol is proposed, with the server-side developed in PHP, SQL and Java, implementation platform.

With recent developments in hyperelliptic curve cryptographic system (HECC) processing and the proposed work, the myth that HECC is not suited for practical applications in constrained networks is dispelled. This article proposes dynamic authenticated contributory group key agreement (DACGKA) protocol using HEC‐DH. The DACGKA is less costly and ideally appropriate for resource‐restricted networks such as VANETs, MANETs, and WSNs because of its lesser key sizes and advancements in operational processing. The suggested protocol is implemented across a finite field using an HEC of genus 1 (ECC), genus 2, and genus 3, with promising results, including a significant reduction in key size and exchange overhead, an increase in key safety, and a broader range of applicability. According to a comparison of the proposed approach on different genus curves, HECC over genus 2 with a suitable key length can be applied for memory and power restricted devices to increase data secrecy and system efficiency. Further, HECC can outperform ECC for low‐cost, secure group communication applications. As a part of security analysis, first, we proved that each coordinate of HEC‐DH secret value is as hard as the entire DH value, and then concrete security proofs based on the HEC‐DLP were established.

Cryptographic algorithms are at the core of IT network protection through data confidentiality, integrity, and authentication. This study explores the computational efficiency and complexity of four cryptographic algorithms: Advanced Encryption Standard (AES), Rivest-Shamir-Adleman (RSA), Lattice-Based Cryptography (LBC), and Hyperelliptic Curve Cryptography (HECC). The investigation compares these algorithms using encryption time, decryption time, key generation time, and security strength. Experiment outcome shows that AES has the optimal encryption time of 2.3 ms for real-time applicability and that RSA has the maximum encryption time of 15.7 ms, emphasizing computational overhead. LBC, which is a promising post-quantum cryptographic method, offers strong security with an average encryption time of 8.9 ms, while HECC offers balance between security and efficiency with an encryption time of 5.4 ms. A comparative analysis shows that lattice-based encryption is most fitting for future quantum-resistant security use and that AES is best used for high-speed encryption. The research emphasizes the need for choosing proper cryptographic algorithms in accordance with security needs and computational efficiency. Research in the future should also be aimed at hybrid cryptographic models and AI-based encryption methods to improve security in the future IT infrastructure.

Public key cryptography is the famous cryptography technique used in many corporate sectors for developing software to provide security services. Hyperelliptic Curve Cryptosystem (HECC) is one of the public key cryptographic technique, an expansion of Elliptic Curve Cryptography which offers the similar level of security compared with other cryptosystems such as RSA, ECC and DSA. HECC supervise the ECC due to shorter operand size. This paper will analysis the performance of HECC over genus curve 2, 3, 4, 5, 6 and compares the result with ECC. It also inspects the use of Hyperelliptic Curve Cryptography technique and affords complete survey on its performance for many applications.

Embedded systems assume an increasing importance in several biomedical applications. These applications present dissimilar requirements and characteristics, posing problems at the computing and communication levels. This paper proposes a general network based platform that follows a distributed approach based on a client/server architecture, in order to integrate embedded systems for biomedical applications. This platform makes use of autonomous communication modules, and relies on personal digital assistants to act as Masters, and to interconnect the embedded systems to computer networks. Information is sent to a main server that maintains and provides access to a database. Data security is assured in all systems by using cryptographic algorithms and protocols. Two embedded systems have been developed based on this platform, a simple system for movement monitoring, and another for biomolecular recognition detection. Furthermore, we show that the optimization of the communication module lead to an increase of 70% of the platform's autonomy for the movement monitoring system.

It is widely recognized that data security will play a central role in future IT systems. Providing public-key cryptographic primitives, which are the core tools for security, is often difficult on embedded processor due to computational, memory, and power constraints. This contribution appears to be the first thorough comparison of two public-key families, namely elliptic curve (ECC) and hyperelliptic curve cryptosystems on a wide range of embedded processor types (ARM, ColdFire, PowerPC). We investigated the influence of the processor type, resources, and architecture regarding throughput. Further, we improved previously known HECC algorithms resulting in a more efficient arithmetic.

We present new results on a cryogenic solid-state maser frequency standard, which relies on the excitation of whispering gallery (WG) modes within a doped monocrystalline sapphire resonator (alpha-Al2O3). Included substitutively within the highest purity HEMEX-grade sapphire crystal lattice are Fe2+ impurities at a concentration of parts per million, an unavoidable result of the manufacturing process. Mass conversion of Fe2+ to Fe3+ ions was achieved by thermally annealing the sapphire in air. Above-threshold maser oscillation was then excited in the resonator at zero applied DC magnetic field by pumping high-Q WG modes coincident in frequency with the electron spin resonance (ESR) energy levels of the Fe3+ spin population. A 2 stage annealing process was undertaken for a sapphire resonator with exceptionally low Fe3+ concentration, resulting in an improvement of 6 orders of magnitude in output power for this particular crystal, and exceeding the previous best implementation of our scheme in another crystal by nearly 20 dB. This represents an output signal 7 orders of magnitude more powerful than a typical commercial hydrogen maser. At this power level, we estimate a limit on the frequency stability of order 1 x 10(-17)/square root(tau) due to the Schawlow-Townes fundamental thermal noise limit.