Maximizing the Efficiency using Montgomery Multipliers on FPGA in RSA Cryptography for Wireless Sensor Networks

The architecture and modeling of RSA public key encryption/decryption systems are presented in this work. Two different architectures are proposed, mMMM42 (modified Montgomery Modular Multiplier 4 to 2 Carry Save Architecture) and RSACIPHER128 to check the suitability for implementation in Wireless Sensor Nodes to utilize the same in Wireless Sensor Networks. It can easily be fitting into systems that require different levels of security by changing the key size. The processing time is increased and space utilization is reduced in FPGA due to its reusability. VHDL code is synthesized and simulated using Xilinx-ISE for both the architectures. Architectures are compared in terms of area and time. It is verified that this architecture support for a key size of 128bits. The implementation of RSA encryption/decryption algorithm on FPGA using 128 bits data and key size with RSACIPHER128 gives good result with 50% less utilization of hardware. This design is also implemented for ASIC using Mentor Graphics

Novel Area-Efficient and Flexible Architectures for Optimal Ate Pairing on FPGA

While FPGA is a suitable platform for implementing cryptographic algorithms, there are several challenges associated with implementing Optimal Ate pairing on FPGA, such as security, limited computing resources, and high power consumption. To overcome these issues, this study introduces three approaches that can execute the optimal Ate pairing on Barreto-Naehrig curves using Jacobean coordinates with the goal of reaching 128-bit security on the Genesys board. The first approach is a pure software implementation utilizing the MicroBlaze processor. The second involves a combination of software and hardware, with key operations in $F_{p}$ and $F_{p^{2}}$ being transformed into IP cores for the MicroBlaze. The third approach builds on the second by incorporating parallelism to improve the pairing process. The utilization of multiple MicroBlaze processors within a single system offers both versatility and parallelism to speed up pairing calculations. A variety of methods and parameters are used to optimize the pairing computation, including Montgomery modular multiplication, the Karatsuba method, Jacobean coordinates, the Complex squaring method, sparse multiplication, squaring in $G_{\phi 6}F_{p^{12}}$, and the addition chain method. The proposed systems are designed to efficiently utilize limited resources in restricted environments, while still completing tasks in a timely manner.Comment: 13 pages, 8 figures, and 5 table

Generalised Mersenne Numbers Revisited

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property --- and hence the same efficiency ratio --- holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio

Complements and signed digit representations: Analysis of a multi-exponentiation-algorithm of Wu, Lou, Lai and Chang

Wu, Lou, Lai and Chang proposed a multi-exponentiation algorithm using binary complements and the non-adjacent form. The purpose of this paper is to show that neither the analysis of the algorithm given by its original proposers nor that by other authors are correct. In fact it turns out that the complement operation does not have significant influence on the performance of the algorithm and can therefore be omitted

マルチパーティー計算の効率的な構成と実装

電気通信大学201

Privacy Preserving Cryptographic Protocols for Secure Heterogeneous Networks

Disertační práce se zabývá kryptografickými protokoly poskytující ochranu soukromí, které jsou určeny pro zabezpečení komunikačních a informačních systémů tvořících heterogenní sítě. Práce se zaměřuje především na možnosti využití nekonvenčních kryptografických prostředků, které poskytují rozšířené bezpečnostní požadavky, jako je například ochrana soukromí uživatelů komunikačního systému. V práci je stanovena výpočetní náročnost kryptografických a matematických primitiv na různých zařízeních, které se podílí na zabezpečení heterogenní sítě. Hlavní cíle práce se zaměřují na návrh pokročilých kryptografických protokolů poskytujících ochranu soukromí. V práci jsou navrženy celkově tři protokoly, které využívají skupinových podpisů založených na bilineárním párování pro zajištění ochrany soukromí uživatelů. Tyto navržené protokoly zajišťují ochranu soukromí a nepopiratelnost po celou dobu datové komunikace spolu s autentizací a integritou přenášených zpráv. Pro navýšení výkonnosti navržených protokolů je využito optimalizačních technik, např. dávkového ověřování, tak aby protokoly byly praktické i pro heterogenní sítě.The dissertation thesis deals with privacy-preserving cryptographic protocols for secure communication and information systems forming heterogeneous networks. The thesis focuses on the possibilities of using non-conventional cryptographic primitives that provide enhanced security features, such as the protection of user privacy in communication systems. In the dissertation, the performance of cryptographic and mathematic primitives on various devices that participate in the security of heterogeneous networks is evaluated. The main objectives of the thesis focus on the design of advanced privacy-preserving cryptographic protocols. There are three designed protocols which use pairing-based group signatures to ensure user privacy. These proposals ensure the protection of user privacy together with the authentication, integrity and non-repudiation of transmitted messages during communication. The protocols employ the optimization techniques such as batch verification to increase their performance and become more practical in heterogeneous networks.

A Programmable SoC-Based Accelerator for Privacy-Enhancing Technologies and Functional Encryption

A multitude of privacy-enhancing technologies (PETs) has been presented recently to solve the privacy problems of contemporary services utilizing cloud computing. Many of them are based on additively homomorphic encryption (AHE) that allows the computation of additions on encrypted data. The main technical obstacles for adaptation of PETs in practical systems are related to performance overheads compared with current privacy-violating alternatives. In this article, we present a hardware/software (HW/SW) codesign for programmable systems-on-chip (SoCs) that is designed for accelerating applications based on the Paillier encryption. Our implementation is a microcode-based multicore architecture that is suitable for accelerating various PETs using AHE with large integer modular arithmetic. We instantiate the implementation in a Xilinx Zynq-7000 programmable SoC and provide performance evaluations in real hardware. We also investigate its efficiency in a high-end Xilinx UltraScale+ programmable SoC. We evaluate the implementation with two target use cases that have relevance in PETs: privacy-preserving computation of squared Euclidean distances over encrypted data and multi-input functional encryption (FE) for inner products. Both of them represent the first hardware acceleration results for such operations, and in particular, the latter one is among the very first published implementation results of FE on any platform.Peer reviewe