Pseudo-random sequence generator based on random selection of an elliptic curve

Elliptic curves cryptography was introduced independently by Victor Miller (Miller, 1986) and Neal Koblitz (Koblitz, 1987(Koblitz, ) in 1985. .At that time elliptic curve cryptography was not actually seen as a promising cryptographic technique.As time progress and further research and intensive development done especially on the implementation side, elliptic curve cryptography is now being implemented widely.Elliptic curves cryptography offers smaller key size, bandwidth savings and faster in implementations when compared to the RSA (Rivest-Shamir-Adleman) cryptography which based its security on the integer factorization problem.The most interesting feature of the elliptic curves is the group structure of the points generated by the curves, where points on the elliptic curves form a group.The security of elliptic curves cryptography relies on the elliptic curves discrete logarithm problem.The elliptic curve discrete logarithm problem is analogous to the ordinary algebraic discrete logarithm problem, l = g x , where given the l and g, it is infeasible to compute the x.Elliptic curve discrete logarithm problem deals with solving for n the relation P = nG.Given the point P and the point G, then it is very hard to find the integer n.To implement the discrete logarithm problem in elliptic curve cryptography, the main task is to compute the order of group of the curves or in other words the number of points on the curve.Computation to find the number of points on a curve, has given rise to several point counting algorithms.The Schoof and the SEA (Schoof-Elkies-Atkin) point counting algorithms will be part of the discussion in this chapter.This chapter is organized as follows: Section 2, gives some preliminaries on elliptic curves, and in section 3, elliptic curve discrete logarithm problem is discussed.Some relevant issues on elliptic curve cryptography is discussed in section 4, in which the Diffie-Hellman key exchange scheme, ElGamal elliptic curve cryptosystem and elliptic curve digital signature scheme are discussed here accompanied with some examples.Section 5 discussed the two point counting algorithms, Schoof algorithm and the SEA (Schoof-Elkies-Atkin) algorithm.Following the discussion in section 5, section 6 summaries some similarities and the differences between these two algorithms.Section 7 gives some brief literature on these two point counting algorithms.Finally, section 8 is the concluding remarks for this chapter. Elliptic curvesElliptic curves obtained their name from their relation to elliptic integrals that arise from the computation of the arc length of ellipses (Lawrence & Wade, 2006).Elliptic curves are www.intechopen.com Cryptography and Security in Computing1 1 2 3 4 2 2 4 Fig. 1.1. 2(1 ) (1 ) yx x x   www.intechopen.com

A promising direction for constructing cryptographically stable pseudo-random sequence generators is an application of transformations in a group of points of elliptic and hypereliptic curves. This will allow building evidence-stable crypto algorithms, the problem of finding the private key in which is associated with solving a theoretically complex elliptic curve discrete logarithm problem. This paper proposes a method for generating pseudo-random sequences of the maximal period using transformations on elliptic curves. This method consists in the application of recurrent transformations with sequential formation of elements of points group of elliptic curves. This allows providing the maximum period of pseudo-random sequences with the reduction of the problem of finding the private key to the solution of the theoretically complex elliptic curve discrete logarithm problem. The block diagram of the device for generating pseudo-random sequences and the scheme for generating the internal states of the generator are given. We also present the results of statistical testing of some generators, which show that the generated sequences are indistinguishable in a statistical sense from truly random ones.KeywordsPseudo-random sequencesElliptic curvesMaximum period

There have been many digital signature schemes were developed based on the discrete logarithm problem on a finite field. In this study, we use the elliptic curve discrete logarithm problem to build new collective signature schemes. The cryptosystem on elliptic curve allows to generate digital signatures with the same level of security as other cryptosystems but with smaller keys. To extend practical applicability and enhance the security level of the group signature protocols, we propose two new types of collective digital signature schemes based on the discrete logarithm problem on the elliptic curve: i) the collective digital signature scheme shared by several signing groups and ii) the collective digital signature scheme shared by several signing groups and several individual signers. These two new types of collective signatures have combined the advantages of group digital signatures and collective digital signatures. These signatures have a fixed size and do not depend on the number of members participating in the creation of the final collective signature. One of the advantages of the proposed collective signature protocols is that they can be deployed on top of the available public key infrastructures.

Radio frequency identification (RFID) is the fastest growing technology in the world today. Thus, wireless communication between tags and readers became an integral part of retail products, library books, personal identifications, and healthcare. The RFID system can provide security features to the data transferred along the network to maintain data privacy, integrity, and confidentiality. Elliptic curve cryptography (ECC) is widely used in RFID authentication protocols to improve communication security. Zhao proposed an RFID authentication protocol using ECC where a unique access list for tags is generated with the reader identifier to elevate the security level. Although Zhao's protocol can withstand most of the RFID security attacks, it has a very high computation cost. The authors improve Zhao protocol and propose a new RFID authentication protocol by reducing the computation cost almost to the half of that in Zhao. The proposed protocol shows a significant improvement in the computation cost.

Radio Frequency IDentification (RFID) technology successfully integrates radio transmitter and receiver, small size memory space and control circuitry to remotely store and retrieve data via wireless RF transceiver. As low-cost RFID tag can be massively manufactured by semiconductor industry, new applications associated with RFID technology have emerged rapidly such as inventory tracking, book storage and management, and airport baggage handling. Generally an RFID system is composed of many RFID tags (or tagged objects), at least one RFID reader, and one backend application system with database. An RFID tag gains its operation energy from query signals that are radio waves transmitted by RFID reader. Once a tag responds the query with its stored information to RFID reader, usually a unique identity number or string, the RFID system can recognize the tag carrier and perform required business logic operation. As RFID technique is widely used in supply chain management, the corresponding RFID application systems are expected to process and manage large amount of tagged objects at a predefined period of time regularly. Therefore, for large-scaled RFID applications, tag reading throughput is very critical since it will affect the total data processing time. To measure tag reading throughput of a RFID system, two performance criteria are usually adopted: tag reading delay and reader energy consumption [5]. As RFID reader and tag always communicate over a shared wireless channel, it is very easy to have signal collisions during a normal tag identification process when multiple tags exist in reader’s interrogation area. Signal collision results in query or data retransmission and eventually increases communication overhead and time delay of tag identification. Hence, an efficient tag collision arbitration mechanism is very important and critical for RFID systems to achieve effective performance. Existing RFID tag identification schemes can be classified into aloha-based solutions [3, 10, 12-13, 16, 21, 23-24] and tree-based solutions [1, 2, 4, 6-9, 14-15, 17-20, 22]. In aloha-based schemes, a reader estimates the number of tags in its interrogation area and broadcasts the total number of timeslots to each tag. Then each RFID tag randomly selects its own timeslot to transmit its ID without knowing which timeslots have been selected by other tags. By distributing tag responses to distinct timeslots instead of getting all tag responses at the same time, aloha-based schemes effectively reduce the probability of signal collision. However, aloha-based schemes have tag starvation problem in which certain tags may not

Radio Frequency Identification (RFID) technology has been considered the “next revolution in supply chain management” (Srivastava, 2004, p. 60). Current research and development related to RFID focuses on the manufacturing and retail sectors with the aim of improving supply chain efficiency. After the manufacturing and retail sectors, health care is considered to be the next sector for RFID (Ericson, 2004). RFID technology’s potential to improve asset management in the health sector is considerable, especially with respect to asset management optimization. In fact, health expenses have increased substantially in Organization for Economic Co-operation and Development (OECD) countries in recent years. In Canada, the public health budget amounted to $91.4 billion (CAD) for the year 2005–2006 compared to $79.9 billion in 2003–2004 (CIHI, 2005). Moreover, the health care industry has been the focus of intense public policy attention. In order to curb this upward trend, the public heath sector in Canada is subject to strict budget constraints. Among the different alternatives for reducing expenditures, the improvement of asset management within the different health institutions appears to be worthwhile. RFID technology seems to be a viable alternative to help hospitals effectively manage and locate medical equipment and other assets, track files, capture charges, detect and deter counterfeit products, and maintain and manage materials. In other words, health care organizations would benefit particularly from RFID applications. The main objective of this study is to investigate the potential for RFID technology within one specific supply chain in the health care sector.B ased on a field study conducted in a large nonprofit hospital, this article tests some scenarios for integrating RFID technology in the context of two warehousing activities. We will first introduce the context of the health care sector and the current applications of RFID technology in that sector. The next section presents the methodological approach that was used in the study. The research findings and their implications are then discussed. Finally, some closing remarks are made.

Autonomous mobile robot localization based on RSSI measurements using an RFID sensor and neural network BPANN

This paper examines the cryptographic security of fixed versus random elliptic curves over the field GF(p). Its basic assumption is that a large precomputation to aid in breaking the elliptic curve discrete logarithm problem (ECDLP) can be made for a fixed curve. We take this into account when examining curve security as well as considering a variation of Pollard's rho method where computations from solutions of previous ECDLPs can be used to solve subsequent ECDLPs on the same curve. We present a lower bound on the expected time to solve such ECDLPs using this method, as well as an approximation of the expected time remaining to solve an ECDLP when a given size of precomputation is available. We conclude that adding 5 bits to the size of a fixed curve to avoid general software attacks and an extra 6 bits to avoid attacks on special moduli and a parameters provides an equivalent level of security.

Elliptic curve cryptography is a public key cryptosystem based on the elliptic curve discrete logarithm problem. The reason for the attractiveness of ECC is that there is no sub-exponential algorithm known to solve the elliptic curve discrete logarithm problem. This leads to lower memory requirements, lower computation requirements and higher security than other public key cryptosystems. This project describes an implementation of a micro coded elliptic curve processor using FPGA technology. This processor implements optimal normal basis field operations. The design is generated by a parameterized module generator which can accommodate arbitrary n and also produce field multipliers with different speed/area tradeoffs. The control part of the processor is micro coded, enabling curve operations to be incorporated into the processor hence reducing the chip's I/O requirements. The micro coded approach also facilitates rapid development and algorithmic optimization. for example, projective and affine coordinates were supported using different sets of micro codes. The design was successfully tested on a Xilinx Spartan -II kit device. Elliptic curve processor is particularly suitable for recourse limited devices because of its lower requirements of memory and computation. It is applicable to be implanted into smart cards, cellular phones and other hand-held devices so that secure communication can be provided. For based on implement the FPGA Using Verilog HDL.

RFID technology and its diverse applications: A brief exposition with a proposed Machine Learning approach

Anonymous channel tickets have been proposed as a way to provide user anonymity and to reduce the overhead of re-authentication for authentication in wireless environments. Chen et al. proposed a secure and efficient protocol, based on a protocol proposed by Yang et al., which is resistant to guessing attacks on networks from which users’ secret keys are easy to obtain. However, their scheme is time-consuming in the phases of ticket issuing and authentication. Furthermore, a malicious attacker can utilize the expired time, Texp, to launch a denial of authentication (DoA) attack, which is a type of denial of service attack. Because Texp is exposed to any user, it would be easy to launch a DoA attack that could make the scheme impractical. To resist against DoAs that the scheme of Chen et al. might suffer, we propose an improved scheme based on elliptic curve cryptography in this paper. Our scheme not only reduces time cost but also enhances security. The basis of the proposed scheme is the elliptic curve discrete logarithm problem. The operations of points of an elliptic curve are faster and use fewer bits to achieve the same level of security. Therefore, our scheme is more suitable for mobile devices, which have limited computing power and storage. Copyright © 2012 John Wiley & Sons, Ltd.

Radio-frequency identification (RFID) is an automatic identification method, relying on storing and remotely retrieving data using devices called RFID tags or transponders. RFID stands for Radiofrequency Identification. The acronym refers to small electronic devices that consist of a small chip and an antenna. RFID technology, initially explored in the 1980s, became more accessible and widely implemented by the early 2000s.Libraries Libraries have long served as essential institutions for knowledge preservation and dissemination, traditionally relying on physical resources like books and journals. RFID systems consist of tags, readers, and integrated software. The integration of RFID technology represents a significant advancement in library services, enhancing efficiency and user experience. A notable development in this area is RFID (Radio Frequency Identification) technology, which has significantly enhanced library management and user experience. RFID technology utilizes radio waves to identify and track objects, such as library materials, automatically. The advent of digital technology has revolutionized libraries, transforming them into dynamic hubs of information and community engagement. RFID technology provides several benefits, including improved user experience, operational efficiency, cost-effectiveness, and optimized resource utilization. The evolution of library technology began with mechanical cataloguing systems, progressing to automated systems and Integrated Library Systems (ILS). In a library setting, RFID technology improves inventory control, self-checkout systems, and security. While challenges exist, the benefits of RFID technology in improving library operations and services are substantial. RFID technology in libraries offers significant enhancements across various operational aspects. The adoption of RFID in libraries has led to benefits such as faster inventory checks, reduced checkout times, and enhanced security against theft. This technological evolution encompasses digital cataloguing systems, online databases, e-books, and automated circulation systems, among other advancements. Self-checkout systems improve user convenience by allowing patrons to borrow materials independently. RFID also enhances security through anti-theft measures and enables real-time data collection for operational insights and personalized services.

With the rapid development of the Internet, many users start to take action putting personal or company information on it, and share with everyone. The Internet is public as it were, if we do not control its limit of authority to assure security, it's possible that those attackers do illegal access of important information and destroy them. Not only personal privacy is invaded, but the mass property damage. Therefore, effective access control system has been more and more emphasized these days. To fight against these network attacks, it is necessary to establish an effective and safe access control system; here we proposed a scheme, a key management which called Lagrange interpolation mainly takes access control model as framework, and use Elliptic Curve Cryptography system to enhance security. The fact we choose Lagrange interpolation is the key we use is randomized, no relationship between each key, so is relatively hard. As Elliptic Curve Cryptography system, we want attackers to encounter Elliptic Curve Discrete Logarithm Problem. Once the prime number is big enough, attackers will have trouble deciphering the key. Access control is so comprehensive, such as electronic documents, online television system sand wireless networks and so on, from previous literature; mobile agent technology applied in access control and key management would waste space and do exist some flaws in security, also we still have a lot of works to do on medical application. Hence, we propose these schemes in mobile agent in order to reach improvement, and then analyze of security and try to simulate what attackers will do. We conclude four common attacks: External Collective Attack, Internal Attack, Collusion Attacks and Equation Breaking Attack. As results, attackers are hard to decipher the key because of no relationship between each key and will face Elliptic Curve Discrete Logarithm Problem. We confirm that the proposed schemes can be more efficiently and safety to protect mobile agent.

ABSTRACTIn order to obtain double encryption via elliptic curve cryptography (ECC) and chaotic synchronisation, this study presents a design methodology for neural-network (NN)-based secure communications in multiple time-delay chaotic systems. ECC is an asymmetric encryption and its strength is based on the difficulty of solving the elliptic curve discrete logarithm problem which is a much harder problem than factoring integers. Because it is much harder, we can get away with fewer bits to provide the same level of security. To enhance the strength of the cryptosystem, we conduct double encryption that combines chaotic synchronisation with ECC. According to the improved genetic algorithm, a fuzzy controller is synthesised to realise the exponential synchronisation and achieves optimal H∞ performance by minimising the disturbances attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of the proposed approach.

A pairing over an elliptic curve E(F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pm</sub> ) to an extension field of F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pmk</sub> has begun to be attractive in cryptosystems, where k is called the embedding degree. The cryptosystems using a pairing are called the pairing-based cryptosystems. The embedding degree k is also an indicator of the relationship between the elliptic curve discrete logarithm problem (ECDLP) and the discrete logarithm problem (DLP), where ECDLP over E(F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pm</sub> ) is reduced to DLP over F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pmk</sub> . An elliptic curve is determined by j-invarient or order, however the explicit condition between these parameters and an embedding degree has been described only in some degrees. In this paper, we investigate a new condition of the existence of elliptic curves with pre-determined embedding degrees, and present some examples of the elliptic curves over 160-bit, 192-bit and 224-bit F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pm</sub> .