Elliptic Curve Cryptography (ecc)

5 Conclusions We explore the deployment of elliptic curve cryptography (ECC) in practice by investigating its usage in Bitcoin, SSH, TLS, and the Austrian citizen card. More than a decade after the first ECC standardization we find that this instantiation of public key cryptography is gaining in popularity. Although ECC is still far from the dominant choice for cryptography, the elliptic curve cryptographic landscape shows considerable deployment in 2013. Of the 12 million scanned hosts which support SSH, we found that 10.3% supported ECDSA for authentication and 13.8% supported a form of ECDH for key exchange. We scanned 30.2 million TLS servers and found that 7.2% support a form of ECDH. In the Austrian citizen card database, 58% of the 829 000 use ECDSA to create digital signatures. All asymmetric cryptography in Bitcoin is based on ECC.

Boston, MA 02115, USA deligiannidisl@wit.edu Abstract—The strength of public key cryptography utilizing Elliptic Curves relies on the difficulty of computing discrete logarithms in a finite field. Diffie-Hellman key exchange algorithm also relies on the same fact. There are two flavors of this algorithm, one using Elliptic Curves and another without using Elliptic Curves. Both flavors of the algorithm rely on the difficulty of computing discrete logarithms in a finite field. Other public key cryptographic algorithms, such as RSA, rely on the difficulty of integer factorization. Both flavors of Diffie-Hellman key exchange algorithm will be discussed in this paper, and we will show implementation details of both of them. Additionally, we will describe what Elliptic Curve Cryptography (ECC) is, and how we can implement different cryptographic algorithms in java, such as digital signatures, encryption / decryption and Key exchange. We will not utilize the java built-in implementations of ECC. Instead, we will use the java programming language as a platform to implement several cryptographic algorithms from the ground up, thus revealing the details of each algorithm and the proofs and reasons these algorithms work. We will describe the theory of ECC and show implementation details that would help students, practitioners, and researchers understand, implement and experiment with such algorithms.

Ms. B. Lavanya Department of Computer Science Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore-641043 --------------------------------------------------------------- ABSTRACT ----------------------------------------------------------- A mobile ad hoc network is a special type of wireless network in which a collection of mobile hosts with wireless network interfaces may form a temporary network. Without the aid of proper fixed infrastructure, providing secure communications is a big challenge. The strength of the security solutions very much depends on the cryptographic keys used for communication. Efficient key management is an important requirement of such networks. For networks like MANET which are basically constrained networks with minimum resources, identification of suitable asymmetric cryptosystem is a vital one. Hence an attempt has been made in this paper to identity a suitable asymmetric-threshold based cryptosystems for small MANETs. The study focuses on the comparison of Rivest Shamir Adelman-Threshold Cryptography and Elliptic Curve Cryptography Threshold Cryptography in terms of the performance parameters like key generation time, Encryption time, Decryption time and communication cost. Different small network scenarios with variable node sizes and key sizes are experimented and the results show that ECC-TC is the most desirable asymmetric-threshold cryptosystem for small MANET.

There is a trend that conventional public key cryptographic systems are gradually replaced with ECC systems. In Sep’2000 Daniel V. Bailey and Christof Paar [11] showed efficient arithmetic in finite field extensions with application in elliptic curve cryptography. In May 2002, M. Bednara, M. Daldrup, J. Shokrollahi, J. Teich, and J. von zur Gathen[12] , showed how an elliptic curve coprocessor based on the Montgomery algorithm for curve multiplication can be implemented using our generic coprocessor architecture.

Elliptical curve cryptography (ECC) is based on a public key cryptosystem based system that is on elliptic curve theory. Elliptic Curve Cryptography can be used to create smaller, faster, and more efficient cryptographic keys. ECC authentication scheme is more suited for wireless communications, like mobile phones and smart cards, personal information like financial transaction or some secret medical reports, confidential data where main consideration is to provide secure data.

Email: {zshi, hai.yan}@engr.uconn.edu Abstract Elliptic Curve Cryptography (ECC) is a promising alternative for public-key algorithms in resource-constrained systems because it provides a similar level of security with much shorter keys than conventional integer-based public-key algorithms. ECC over binary field is of special interest because the operations in binary field are thought more space and time efficient.

6 Conclusions and Future Work We have presented a new, faster implementation of elliptic-curve cryptography. In partic- ular, we have demonstrated faster fields, a new point compression algorithm and a new algorithm for scalar multiplication with precomputation. Our system is faster than previous software implementations of ECC signatures at comparable security levels. It does not use the NEON vector unit found in some smartphones, but it is competitive with software that does. It does not use curves with endomorphisms, but for side-channel-resistant operations it is competitive with software that does.

Department of VLSI Design and Embedded Systems, UTL Technologies, VTU Extension Centre, (India) ABSTRACT The rising growth of data communication and electronic transactions over the internet has made security to become the most important issue over the network. The widely used algorithms for public-key cryptosystems are RSA, Diffie- Hellman key agreement, the digital signature algorithm and systems based on elliptic curve cryptography (ECC).

Data security is an important requirement for many appli- cations in our daily life. Especially internet applications such as e-commerce need to transmit secret data via inse- cure communication channels. Therefore, various crypto- graphical methods exist that allow to protect sensitive data. Asymmetric cryptography, which is also known as public- key cryptography, does not only provide algorithms for en- cryption and decryption of data, but also for digital signa- tures and authentication. Recently asymmetric cryptography based on elliptic curves is gaining interest. Compared to traditional asymmetric techniques, e.g. the RSA algorithm, the elliptic curve cryptography (ECC) achieves an equivalent level of security with smaller key sizes. Using elliptic curve cryptography therefore results in memory as well as band- width savings.

Elliptic Curve Cryptography (ECC) is a promising alter- native for public-key algorithms in resource-constrained systems because it provides a similar level of security with much shorter keys than conventional integer-based public- key algorithms. ECC over binary field is of special interest because the operations in binary field are thought more space and time efficient. However, the software imple- mentations of ECC over binary field are still slow, es- pecially on low-end processors used in small computing devices such as sensor nodes. In this paper, we studied software implementations of ECC. We first investigated whether some architectural parameters such as word size may affect the choice of algorithms when implementing ECC with software. We identified a set of algorithms for ECC implementation for low-end processors. We also examined several improvements to the instruction set ar- chitecture of an 8-bit processor and studied their impact on the performance of ECC.

Chapter 7 Future Work There are a number of possible directions for further research. Our schemes admit effi- cient implementations in the sense that the running time is polynomial. However, they are still much slower than traditional schemes such as ECC (which are safe only against classical adversaries), as well as certain high-performance quantum-resistant schemes such as NTRU. There is always a security vs. efficiency trade-off, but we are nevertheless inter- ested in speeding up implementations to the extent that we can. Some low-hanging fruit may be available in this regard thanks to the existing literature of known optimizations for elliptic curve cryptography and elliptic curve arithmetic. For example, existing results on addition chains could be used to speed up isogeny evaluation.

1. Introduction A lot of information is perceived when we observe an image. Images have become an inevitable source of information. Everyday we come across various image from various sources. When images are confidential and we want the image to be transferred safe and securely, cryptography comes into play. The cryptographic technique which we have implemented in this paper is the Elliptic Curve Cryptography (ECC). Various study on ECC has concluded that the difficultly to solve an Elliptic Curve Discrete Logarithmic Problem is exponentially hard with respect to the key size used. This property makes ECC a very good choice for encryption/decryption process compared to other cryptographic techniques which are linearly difficult or sub exponentially difficult. ECC is a public key cryptography which was developed by Neal Koblitz and Victor S. Miller independently in the year 1985. ECC gains wide acceptance around 2004.

1, 2,3 Department of computer Science & Engineering, Sikkim Manipal Institute Of Technology, Majhitar, Sikkim, India 1 ajitkarki4@gmail.com, 2 gurung_sandeep@yahoo.co.in, 3 kiran.gautam.cse@gmail.com Abstract- Cryptography is an important part of preventing private data from being stolen. Even if an attacker were to break into your computer or intercept your messages they still will not be able to read the data if it is protected by cryptography or encrypted. In addition to concealing the meaning of data, cryptography performs other critical security requirements for data including authentication, repudiation, confidentiality, and integrity. Cryptography comes from Greek words meaning “hidden writing”. Cryptography converts readable data or clear text into encoded data called cipher text. By definition cryptography is the science of hiding information so that unauthorized users cannot read it. It involves Encryption and decryption of messages. Encryption is the process of converting a Plain text into cipher text and decryption is the process of getting back the original Message from the encrypted text. The Crux of cryptography lies in the key involved and the secrecy of the keys used to Encrypt or decrypt. Another important factor is the key strength, i.e. the size of the Key so that it is difficult to perform a brute force on the plain and cipher text and retrieve the key. There have been various cryptographic algorithms suggested. Elliptic curve cryptography (ECC) is a kind of public key cryptosystem like RSA. But it differs from RSA in its quicker evolving capacity and by providing attractive and alternative way to researchers of cryptographic algorithm. The security level which is given by RSA can be provided even by smaller keys of ECC (for example, a 160 bit ECC has roughly the same security strength as 1024 bit RSA). In this paper, we will present some ECC algorithms and also gives mathematical explanations on the working of these algorithms.

email: sdixit_dr@rediffmail.com Abstract - The true impact of any public-key cryptosystem can only be evaluated in the context of a security protocol. Secure communication is an intrinsic requirement in any transaction. It is very important to implement cryptosystems securely against the attacks. Elliptic Curve Cryptography (ECC) is coming forth as an attractive public key cryptosystem for mobile/wireless environments compared to traditional cryptosystems like RSA and DSA. ECC fits well for an efficient and secure encryption scheme because it provides better security with smaller key sizes, which results in faster computations, lower power consumption, as well as memory and bandwidth savings. However, the digital signature is the indispensable way to ensure the security of web services and has great significance in practical applications. By using a digital signature algorithm we can provide authenticity and validation to the electronic document. ECDSA and ECDH use the concept of ECC. In this article we present ECC and most popular algorithms such as RSA, ECDH, ECDSA and ECPP and a comparative study of all these algorithms have been done.

Elliptic curve cryptosystem (ECC) have recently received significant attention by research due to their low computational and communicational overhead. Elliptic curve cryptography (ECC) is the hardest computational problems, the elliptic curve discrete logarithm problem and elliptic curve Deffie-Hellman problem are the most reliable cryptographic technique in ECC. The advantages of ECC that it requires shorter key length compared to other public-key algorithms. So, that its use in low-end systems such as smart cards because of its efficiency and limited computational and communicational overhead.

7. V ARIOUS IMPLEMENTATIONS OF ECC After selecting a suitable set of algorithms, ECC is implemented on either hardware or software platform. Hardware implementation is considered as the most suitable option looking into the large key sizes and slow speed of point multiplication, when come together with limited resources of embedded platform. However, for application specific systems, embedding a separate piece of hardware for cryptography increases the manufacturing cost drastically. Also, various recent researches show that a careful selection of efficient algorithms and proper ECC parameters, ECC can be successfully implemented on software platforms. But, software implementations cannot match up to the speed of hardware implementations. Therefore research in the field of Elliptic curve cryptography has been propagated into both directions of hardware and software solutions.

Transmission of private information over the public channels requires security or data protection against unauthorized access. Elliptic Curve Cryptography (ECC) is one of the efficient encryption technique can be used to secure the private data. High level security requirement of Restricted Services of Indian Regional Navigation Satellite System (IRNSS) to transmit the navigation data through wireless channel, can be achieved by ECC with minimum key size.ECC is based on Elliptic Curve Scalar Multiplication (ECSM) which is the process of multiplying a point on elliptic curve by a scalar value. The operations has been performed on National Institute of Standards and Technology (NIST) recommended elliptic curves over binary field E (2 233 ).The performance of ECC algorithm is influenced by the implementation of elliptic

Vol. 3, Issue 3, March 2015 VII. C ONCLUSION AND F UTURE W ORK In this project, we are concluding a new way, that increases security considerations of the network using AODV algorithm for transfer of data and to increment the efficiency of AODV algorithm using ECC(Elliptic Curve Cryptography). Efficiency, and reliability will be increased for each transmission of data, While enclosing the proposed method by using the ECC algorithm which allow itself to encrypt and decrypt the data that is to be transferred and performs the active classification, we are concluding that the Secured data transmission using elliptic curve cryptography provide a efficiency higher than DSDV when compared with AODV. Any node in between source and destination can try to view the information. So the data which is transmitted has to be encrypted and decrypted so that the security issues will be eliminated and with the usage of the resources and effective delivery to the user, hence the proposed method will provide a effective solution that may help the source and destination to transfer data in a secured manner using encryption and decryption and to detect the efficiency of Aodv protocol.

1 Introduction Koblitz (1987) and Miller (1986) introduced Elliptic curve cryptography (ECC) as a new type of public-key cryptography. Another well-known type of public-key cryptography is Rivest, Shamir and Adleman (RSA) (Rivest, Shamir, & Adleman, 1978). The main advantage of ECC is that it is more efficient than RSA. For example, 283-bit integer in ECC is considered as secure as 3072-bit integer in RSA (Lenstra & Verheul, 2001). Public-key cryptography is also known as asymmetric-key cryptography, and it uses two different keys for data encryption and decryption. The first key is called a public key, and it is accessible to the public. The second key is called a private key because it is kept a secret by the owner. In contrast, symmetric-key cryptography uses one shared secret key for data encryption and decryption. As a result, public-key cryptography has the advantage of eliminating the need to share a secret key with others. Another advantage of public-key cryptography is that it provides the digital signature schemes. With this scheme, we guarantee that the message is sent by the owner and is not been modified by an attacker.

In fact, nobody knows exactly how difficult this problem is to solve, because no one has come up with an efficient algorithm to solve it. It is, however, believed to be more difficult to solve than the general discrete logarithm problem, and the various factorization problems that are used in other cryptosystems (and the best methods for cracking these problems do not seem to adapt easily to elliptic curve problems), which suggests that elliptic curve cryptography is the strongest of all the available cryptographic systems. Looking at the required key sizes for multiple given levels of security (where “more secure” means “takes longer to break”) of elliptic curve cryptosystems as compared to other traditional cryptosys- tems, the required key sizes of other systems rise exponentially as difficulty increases, while the increase in required key size for elliptic curve systems is relatively miniscule.