20 research outputs found
A survey of hardware implementations of elliptic curve cryptographic systems
Elliptic Curve Cryptography (ECC) has gained much recognition over the last decades and has established itself among the well known public-key cryptography schemes, not least due its smaller key size and relatively lower computational effort compared to RSA. The wide employment of Elliptic Curve Cryptography in many different application areas has been leading to a variety of implementation types and domains ranging from pure software approaches over hardware implemenations to hardware/software co-designs. The following review provides an overview of state of the art hardware implemenations of ECC, specifically in regard to their targeted design goals. In this context the suitability of the hardware/software approach in regard to the security challenges opposed by the low-end embedded devices of the Internet of Things is briefly examined. The paper also outlines ECC’s vulnerability against quantum attacks and references one possible solution to that problem
A Survey of Hardware Implementations of Elliptic Curve Cryptographic Systems
Elliptic Curve Cryptography (ECC) has gained
much recognition over the last decades and has established itself
among the well known public-key cryptography schemes, not
least due its smaller key size and relatively lower computational
effort compared to RSA. The wide employment of Elliptic Curve
Cryptography in many different application areas has been
leading to a variety of implementation types and domains ranging
from pure software approaches over hardware implementations
to hardware/software co-designs. The following review provides
an overview of state of the art hardware implementations of ECC,
specifically in regard to their targeted design goals. In this context
the suitability of the hardware/software approach in regard to the
security challenges opposed by the low-end embedded devices of
the Internet of Things is briefly examined. The paper also outlines
ECC’s vulnerability against quantum attacks and references one
possible solution to that problem
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
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FPGA Implementations of Elliptic Curve Cryptography and Tate Pairing over Binary Field
Elliptic curve cryptography (ECC) is an alternative to traditional techniques for public key cryptography. It offers smaller key size without sacrificing security level. Tate pairing is a bilinear map used in identity based cryptography schemes. In a typical elliptic curve cryptosystem, elliptic curve point multiplication is the most computationally expensive component. Similarly, Tate pairing is also quite computationally expensive. Therefore, it is more attractive to implement the ECC and Tate pairing using hardware than using software. The bases of both ECC and Tate pairing are Galois field arithmetic units. In this thesis, I propose the FPGA implementations of the elliptic curve point multiplication in GF (2283) as well as Tate pairing computation on supersingular elliptic curve in GF (2283). I have designed and synthesized the elliptic curve point multiplication and Tate pairing module using Xilinx's FPGA, as well as synthesized all the Galois arithmetic units used in the designs. Experimental results demonstrate that the FPGA implementation can speedup the elliptic curve point multiplication by 31.6 times compared to software based implementation. The results also demonstrate that the FPGA implementation can speedup the Tate pairing computation by 152 times compared to software based implementation
Efficient Implementation of Elliptic Curve Cryptography on FPGAs
This work presents the design strategies of an FPGA-based elliptic curve co-processor. Elliptic curve cryptography is an important topic in cryptography due to its relatively short key length and higher efficiency as compared to other well-known public key crypto-systems like RSA. The most important contributions of this work are: - Analyzing how different representations of finite fields and points on elliptic curves effect the performance of an elliptic curve co-processor and implementing a high performance co-processor. - Proposing a novel dynamic programming approach to find the optimum combination of different recursive polynomial multiplication methods. Here optimum means the method which has the smallest number of bit operations. - Designing a new normal-basis multiplier which is based on polynomial multipliers. The most important part of this multiplier is a circuit of size for changing the representation between polynomial and normal basis
Low Power Elliptic Curve Cryptography
This M.S. thesis introduces new modulus scaling techniques for transforming a class of primes into special forms which enable efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of a scaled modulus. Our inversion algorithm exhibits superior performance to the Euclidean algorithm and lends itself to efficient hardware implementation due to its simplicity. Using the scaled modulus technique and our specialized inversion algorithm we develop an elliptic curve processor architecture. The resulting architecture successfully utilizes redundant representation of elements in GF(p) and provides a low-power, high speed, and small footprint specialized elliptic curve implementation. We also introduce a unified Montgomery multiplier architecture working on the extension fields GF(p), GF(2) and GF(3). With the increasing research activity for identity based encryption schemes, there has been an increasing need for arithmetic operations in field GF(3). Since we based our research on low-power and small footprint applications, we designed a unified architecture rather than having a seperate hardware for GF{3}. To the best of our knowledge, this is the first time a unified architecture was built working on three different extension fields
Efficient and Secure ECDSA Algorithm and its Applications: A Survey
Public-key cryptography algorithms, especially elliptic curve cryptography (ECC)and elliptic curve digital signature algorithm (ECDSA) have been attracting attention frommany researchers in different institutions because these algorithms provide security andhigh performance when being used in many areas such as electronic-healthcare, electronicbanking,electronic-commerce, electronic-vehicular, and electronic-governance. These algorithmsheighten security against various attacks and the same time improve performanceto obtain efficiencies (time, memory, reduced computation complexity, and energy saving)in an environment of constrained source and large systems. This paper presents detailedand a comprehensive survey of an update of the ECDSA algorithm in terms of performance,security, and applications
Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves (Update)
For most of the time since they were proposed, it was widely
believed that hyperelliptic curve cryptosystems (HECC) carry a
substantial performance penalty compared to elliptic curve
cryptosystems (ECC) and are, thus, not too attractive for
practical applications. Only quite recently improvements have been
made, mainly restricted to curves of genus 2. The work at hand
advances the state-of-the-art considerably in several aspects.
First, we generalize and improve the closed formulae for the group
operation of genus 3 for HEC defined over fields of characteristic
two. For certain curves we achieve over 50% complexity improvement
compared to the best previously published results. Second, we
introduce a new complexity metric for ECC and HECC defined over
characteristic two fields which allow performance comparisons of
practical relevance. It can be shown that the HECC performance is
in the range of the performance of an ECC; for specific
parameters HECC can even possess a lower complexity than an ECC at
the same security level. Third, we describe the first
implementation of a HEC cryptosystem on an embedded (ARM7)
processor. Since HEC are particularly attractive for constrained
environments, such a case study should be of relevance