Rethinking Modular Multi-Exponentiation in Real-World Applications

The importance of efficient multi-exponen- tiation algorithms in a large spectrum of cryptographic applications continues to grow. Previous literature on the subject pays attention exclusively on the mini- mization of the number of modular multiplications. However, a small reduction of the multiplicative com- plexity can be easily overshadowed by other figures of merit. In this article, we demonstrate that the most efficient algorithm for computing multi-exponentiation changes if considering execution time instead of number of multi-exponentiations. We focus our work on two al- gorithms that perform best under the number of multi- exponentiation metric and show that some side opera- tions affects their theoretical ranking. We provide this analysis on different hardware, such as Intel Core and ARM CPUs and the two latest generations of Rasp- berry Pis, to show how the machine chosen affects the execution time of multi-exponentiation

Rethinking Modular Multi-Exponentiation in Real-World Applications

The importance of efficient multi-exponen- tiation algorithms in a large spectrum of cryptographic applications continues to grow. Many of the algorithms proposed in the past pay attention exclusively on the minimization of the number of modular multiplications. However, a short reduction of the multiplicative com- plexity can be easily overshadowed by other figures of merit. In this article we demonstrate a large number of practical results aimed at concrete cryptographic tasks requiring multi-exponentiations and provide rec- ommendations on the best possible algorithmic strate- gies for different selection of security parameters

A Study of High Performance Multiple Precision Arithmetic on Graphics Processing Units

Multiple precision (MP) arithmetic is a core building block of a wide variety of algorithms in computational mathematics and computer science. In mathematics MP is used in computational number theory, geometric computation, experimental mathematics, and in some random matrix problems. In computer science, MP arithmetic is primarily used in cryptographic algorithms: securing communications, digital signatures, and code breaking. In most of these application areas, the factor that limits performance is the MP arithmetic. The focus of our research is to build and analyze highly optimized libraries that allow the MP operations to be offloaded from the CPU to the GPU. Our goal is to achieve an order of magnitude improvement over the CPU in three key metrics: operations per second per socket, operations per watt, and operation per second per dollar. What we find is that the SIMD design and balance of compute, cache, and bandwidth resources on the GPU is quite different from the CPU, so libraries such as GMP cannot simply be ported to the GPU. New approaches and algorithms are required to achieve high performance and high utilization of GPU resources. Further, we find that low-level ISA differences between GPU generations means that an approach that works well on one generation might not run well on the next. Here we report on our progress towards MP arithmetic libraries on the GPU in four areas: (1) large integer addition, subtraction, and multiplication; (2) high performance modular multiplication and modular exponentiation (the key operations for cryptographic algorithms) across generations of GPUs; (3) high precision floating point addition, subtraction, multiplication, division, and square root; (4) parallel short division, which we prove is asymptotically optimal on EREW and CREW PRAMs

Elliptical Curve Digital Signatures Algorithm

Elliptical digital signatures algorithm provides security services for resource constrained embedded devices. The ECDSA level security can be enhanced by several parameters as parameter key size and the security level of ECDSA elementary modules such as hash function, elliptic curve point multiplication on koblitz curve which is used to compute public key and a pseudo-random generator which generates key pair generation. This paper describes novel security approach on authentication schemes as a modification of ECDSA scheme. This paper provides a comprehensive survey of recent developments on elliptic curve digital signatures approaches. The survey of ECDSA involves major issues like security of cryptosystem, RFID-tag authentication, Montgomery multiplication over binary fields, Scaling techniques, Signature generation ,signature verification, point addition and point doubling of the different coordinate system and classification. DOI: 10.17762/ijritcc2321-8169.150318

Utilizing the Double-Precision Floating-Point Computing Power of GPUs for RSA Acceleration

Asymmetric cryptographic algorithm (e.g., RSA and Elliptic Curve Cryptography) implementations on Graphics Processing Units (GPUs) have been researched for over a decade. The basic idea of most previous contributions is exploiting the highly parallel GPU architecture and porting the integer-based algorithms from general-purpose CPUs to GPUs, to offer high performance. However, the great potential cryptographic computing power of GPUs, especially by the more powerful floating-point instructions, has not been comprehensively investigated in fact. In this paper, we fully exploit the floating-point computing power of GPUs, by various designs, including the floating-point-based Montgomery multiplication/exponentiation algorithm and Chinese Remainder Theorem (CRT) implementation in GPU. And for practical usage of the proposed algorithm, a new method is performed to convert the input/output between octet strings and floating-point numbers, fully utilizing GPUs and further promoting the overall performance by about 5%. The performance of RSA-2048/3072/4096 decryption on NVIDIA GeForce GTX TITAN reaches 42,211/12,151/5,790 operations per second, respectively, which achieves 13 times the performance of the previous fastest floating-point-based implementation (published in Eurocrypt 2009). The RSA-4096 decryption precedes the existing fastest integer-based result by 23%

Security systems based on Gaussian integers : Analysis of basic operations and time complexity of secret transformations

Many security algorithms currently in use rely heavily on integer arithmetic modulo prime numbers. Gaussian integers can be used with most security algorithms that are formulated for real integers. The aim of this work is to study the benefits of common security protocols with Gaussian integers. Although the main contribution of this work is to analyze and improve the application of Gaussian integers for various public key (PK) algorithms, Gaussian integers were studied in the context of image watermarking as well. The significant benefits of the application of Gaussian integers become apparent when they are used with Discrete Logarithm Problem (DLP) based PK algorithms. In order to quantify the complexity of the Gaussian integer DLP, it is reduced to two other well known problems: DLP for Lucas sequences and the real integer DLP. Additionally, a novel exponentiation algorithm for Gaussian integers, called Lucas sequence Exponentiation of Gaussian integers (LSEG) is introduced and its performance assessed, both analytically and experimentally. The LSEG achieves about 35% theoretical improvement in CPU time over real integer exponentiation. Under an implementation with the GMP 5.0.1 library, it outperformed the GMP\u27s mpz_powm function (the particularly efficient modular exponentiation function that comes with the GMP library) by 40% for bit sizes 1000-4000, because of low overhead associated with LSEG. Further improvements to real execution time can be easily achieved on multiprocessor or multicore platforms. In fact, over 50% improvement is achieved with a parallelized implementation of LSEG. All the mentioned improvements do not require any special hardware or software and are easy to implement. Furthermore, an efficient way for finding generators for DLP based PK algorithms with Gaussian integers is presented. In addition to DLP based PK algorithms, applications of Gaussian integers for factoring-based PK cryptosystems are considered. Unfortunately, the advantages of Gaussian integers for these algorithms are not as clear because the extended order of Gaussian integers does not directly come into play. Nevertheless, this dissertation describes the Extended Square Root algorithm for Gaussian integers used to extend the Rabin Cryptography algorithm into the field of Gaussian integers. The extended Rabin Cryptography algorithm with Gaussian integers allows using fewer preset bits that are required by the algorithm to guard against various attacks. Additionally, the extension of RSA into the domain of Gaussian integers is analyzed. The extended RSA algorithm could add security only if breaking the original RSA is not as hard as factoring. Even in this case, it is not clear whether the extended algorithm would increase security. Finally, the randomness property of the Gaussian integer exponentiation is utilized to derive a novel algorithm to rearrange the image pixels to be used for image watermarking. The new algorithm is more efficient than the one currently used and it provides a degree of cryptoimmunity. The proposed method can be used to enhance most picture watermarking algorithms

A hybrid deep learning forecasting model using GPU disaggregated function evaluations applied for household electricity demand forecasting.

As the new generation of smart sensors is evolving towards high sampling acquisitions systems, the amount of information to be handled by learning algorithms has been increasing. The Graphics Processing Unit (GPU) architectures provide a greener alternative with low energy consumption for mining big-data, harnessing the power of thousands of processing cores in a single chip, opening a widely range of possible applications. Here, we design a novel evolutionary computing GPU parallel function evaluation mechanism, in which different parts of time series are evaluated by different processing threads. By applying a metaheuristics fuzzy model in a low-frequency data for household electricity demand forecasting, results suggested that the proposed GPU learning strategy is scalable as the number of training rounds increases

Efficient Location Privacy In Mobile Applications

Location awareness is an essential part of today\u27s mobile devices. It is a well-established technology that offers significant benefits to mobile users. While location awareness has triggered the exponential growth of mobile computing, it has also introduced new privacy threats due to frequent location disclosures. Movement patterns could be used to identify individuals and also leak sensitive information about them, such as health condition, lifestyle, political/religious affiliations, etc. In this dissertation we address location privacy in the context of mobile applications. First we look into location privacy in the context of Dynamic Spectrum Access (DSA) technology. DSA is a promising framework for mitigating the spectrum shortage caused by fixed spectrum allocation policies. In particular, DSA allows license-exempt users to access the licensed spectrum bands when not in use by their respective owners. Here, we focus on the database-driven DSA model, where mobile users issue location-based queries to a white-space database in order to identify idle channels in their area. We present a number of efficient protocols that allow users to retrieve channel availability information from the white-space database while maintaining their location secret. In the second part of the dissertation we look into location privacy in the context of location-aware mobile advertising. Location-aware mobile advertising is expanding very rapidly and is forecast to grow much faster than any other industry in the digital era. Unfortunately, with the rise and expansion of online behavioral advertising, consumers have grown very skeptical of the vast amount of data that is extracted and mined from advertisers today. As a result, the consensus has shifted towards stricter privacy requirements. Clearly, there exists an innate conflict between privacy and advertisement, yet existing advertising practices rely heavily on non-disclosure agreements and policy enforcement rather than computational privacy guarantees. In the second half of this dissertation, we present a novel privacy-preserving location-aware mobile advertisement framework that is built with privacy in mind from the ground up. The framework consists of several methods which ease the tension that exists between privacy and advertising by guaranteeing, through cryptographic constructions, that (i) mobile users receive advertisements relative to their location and interests in a privacy-preserving manner, and (ii) the advertisement network can only compute aggregate statistics of ad impressions and click-through-rates. Through extensive experimentation, we show that our methods are efficient in terms of both computational and communication cost, especially at the client side

Secret Key Leakage from Public Key Perturbation of DLP-based Cryptosystems

Finding efficient countermeasures for cryptosystems against fault attacks is challenged by a constant discovery of flaws in designs. Even elements, such as public keys, that do not seem critical must be protected. From the attacks against RSA, we develop a new attack of DLP-based cryptosystems, built in addition on a lattice analysis to recover DSA public keys from partially known nonces. Based on a realistic fault model, our attack only requires 16 faulty signatures to recover a 160-bit DSA secret key within a few minutes on a standard PC. These results significantly improves the previous public element fault attack in the context of DLP-based cryptosystems

Power Efficient Fpga Implementation Of Rsa Algortihm

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2010Bu çalışmada Rivest, Shamir, Adleman (RSA) algoritması sahada programlanabilir kapı dizisi üzerinde gerçeklenmekte ve güç tasarruf yöntemlerinden yararlanılarak dinamik güç harcamaları azaltılmaktadır. RSA algoritması en yaygın kullanıma sahip açık anahtarlı şifreleme algoritmalarından biridir. RSA algoritmasını oluşturan matematiksel temel işlemleri iki ana başlıkta toplamak mümkündür: moduler çarpma işlemi ve moduler üs alma, exponent işlemi. RSA algoritmasında kullanılan aritmetik işlem ME mod N işlemidir. Bu işlemdeki N sayısı aralarında asal iki sayının çarpımından oluşan modulo değeri, M mesaj ya da düz metin dediğimiz bilgi, E ise açık anahtar olarak bilinen değerdir. İyi bir RSA gerçeklemesi oluşturmak istenirse; yapılması gereken en önemli şey, iyi bir modular çarpma devresi oluşturmaktır. Bu matematiksel açıklamalardan yola çıkararak anlamalıyız ki; bir RSA gerçeklemesinde en çok güç tüketen blok modular çarpma devresidir. Bu nedenle güç tüketimlerinin karşılaştırılması açısından modular çarpma devresine farklı teknikler uygulanmıştır. Daha sonra çok yaygın bir kullanıma sahip olan ardışıl ikili modular üs alma tekniği ile RSA algoritması gerçeklenmiştir. Bilgisayar benzetim programı ile yapıların test vektörü girişlerine karşılık doğru sonuçlar verdiği gösterilmiştir.In this study, dynamic power consumptions of Field Programmable Gate Array (FPGA) implementations of the Rivest, Shamir, Adleman (RSA) has been reduced by using low power design methods. RSA is one of the most popular public key cryptographic algorithms. The mathematics behind RSA algorithm, are summarized in two operations, modular multiplication and modular exponentiation. In the RSA cryptosystem, the arithmetic operation ME mod N is used, where N is a prime product of two relative prime numbers, M is the message and E is the public key. In order to create an efficient implementation of RSA, one has to design efficiently the multiplication of two modular numbers. So this mathematical background provides a good understanding that Modular Multiplication block dissipates the most of the power, dissipated in RSA. For comparison of power dissipations, different methods are used to implement Modular Multiplication block. Then RSA implemented by using Sequential Binary Modular Exponentiation which has widespread applications. Computer simulations have been used to show that the implementations of the algorithm generate correct outputs against test vectors.Yüksek LisansM.Sc