2008, ISBN 9783540740780

Web Resource

2008, ISBN 9783540740780

Web Resource

2008, ISBN 3540740775

Web Resource

2008, ISBN 3540740775

Web Resource

IEEE Transactions on Circuits and Systems I: Regular Papers, ISSN 1549-8328, 01/2018, Volume 65, Issue 1, pp. 154 - 162

The conversion from an integer scalar to a short and sparse \tau -adic nonadjacent form...

lazy reduction | field programmable gate array | Koblitz curves | Elliptic curve cryptography | scalar multiplication | Hardware | Registers | Acceleration | Field programmable gate arrays | τ NAF conversion">integer toτ NAF conversion | Pipeline processing | ELLIPTIC-CURVES | integer to tau NAF conversion | MULTIPLICATION | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Algorithms | Cryptography | Digital integrated circuits | Converters | Reduction | Division | Conversion | Curves

lazy reduction | field programmable gate array | Koblitz curves | Elliptic curve cryptography | scalar multiplication | Hardware | Registers | Acceleration | Field programmable gate arrays | τ NAF conversion">integer to

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 03/2018, Volume 87, Issue 310, pp. 821 - 854

This article deals with redundant digit expansions with an imaginary quadratic algebraic integer with trace \pm 1 as base and a minimal norm representatives...

MATHEMATICS, APPLIED | continued fractions | tau-adic expansions | linear forms in logarithms | Baker-Davenport method | COMBINATION | Hamming weight | Koblitz curves | geometry of numbers | scalar multiplication | redundant digit sets | Frobenius endomorphism | WEIGHT | elliptic curve cryptography

MATHEMATICS, APPLIED | continued fractions | tau-adic expansions | linear forms in logarithms | Baker-Davenport method | COMBINATION | Hamming weight | Koblitz curves | geometry of numbers | scalar multiplication | redundant digit sets | Frobenius endomorphism | WEIGHT | elliptic curve cryptography

Journal Article

IEEE Transactions on Circuits and Systems II: Express Briefs, ISSN 1549-7747, 11/2018, Volume 65, Issue 11, pp. 1723 - 1727

Point multiplication is the key operation that dominates the speed and area of each elliptic curve cryptosystem. In this brief, we propose a highly efficient...

point multiplication | Elliptic curves | Koblitz curves | Computer architecture | Elliptic curve cryptography (ECC) | Elliptic curve cryptography | pipelining | field-programmable gate array (FPGA) | Clocks | Pipeline processing | PROCESSOR | FPGA | ALGORITHM | IMPLEMENTATION | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | PARALLELIZATION | HIGH-SPEED | Multiplication | Accumulators | Parallel processing | Converters | Rescheduling | Multiplication & division | Elliptic functions

point multiplication | Elliptic curves | Koblitz curves | Computer architecture | Elliptic curve cryptography (ECC) | Elliptic curve cryptography | pipelining | field-programmable gate array (FPGA) | Clocks | Pipeline processing | PROCESSOR | FPGA | ALGORITHM | IMPLEMENTATION | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | PARALLELIZATION | HIGH-SPEED | Multiplication | Accumulators | Parallel processing | Converters | Rescheduling | Multiplication & division | Elliptic functions

Journal Article

ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING, ISSN 0925-1030, 10/2015, Volume 85, Issue 1, pp. 129 - 138

Efficient computation of the finite field arithmetic is required for elliptic curve cryptography over . In order to achieve the above, this paper presents the...

COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | Digit-level multiplier | FPGA IMPLEMENTATION | PARALLELIZATION | Koblitz curves | POINT MULTIPLICATION | Gaussian normal basis | Cryptography | Scalar point multiplication | ENGINEERING, ELECTRICAL & ELECTRONIC

COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | Digit-level multiplier | FPGA IMPLEMENTATION | PARALLELIZATION | Koblitz curves | POINT MULTIPLICATION | Gaussian normal basis | Cryptography | Scalar point multiplication | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

IEEE Transactions on Circuits and Systems II: Express Briefs, ISSN 1549-7747, 01/2013, Volume 60, Issue 1, pp. 41 - 45

Fast and high-performance computation of finite-field arithmetic is crucial for elliptic curve cryptography (ECC) over binary extension fields. In this brief,...

point multiplication | Elliptic curves | Koblitz curves | Gaussian processes | Computer architecture | Elliptic curve cryptography | field-programmable gate array (FPGA) | parallel processing | Field programmable gate arrays | Cryptoprocessor | Clocks | elliptic curve cryptography (ECC) | ELLIPTIC-CURVES | ALGORITHM | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | SCALAR MULTIPLICATION | PARALLELIZATION | NORMAL BASES | Finite fields | Usage | Microprocessors | Digital integrated circuits | Innovations | Central processing units | Design and construction

point multiplication | Elliptic curves | Koblitz curves | Gaussian processes | Computer architecture | Elliptic curve cryptography | field-programmable gate array (FPGA) | parallel processing | Field programmable gate arrays | Cryptoprocessor | Clocks | elliptic curve cryptography (ECC) | ELLIPTIC-CURVES | ALGORITHM | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | SCALAR MULTIPLICATION | PARALLELIZATION | NORMAL BASES | Finite fields | Usage | Microprocessors | Digital integrated circuits | Innovations | Central processing units | Design and construction

Journal Article

Microprocessors and Microsystems, ISSN 0141-9331, 06/2013, Volume 37, Issue 4-5, pp. 394 - 406

A scalable elliptic curve cryptography (ECC) processor is presented in this paper. The proposed ECC processor supports all five Koblitz curves recommended by...

Scalable ECC processor | FPGA | Elliptic Curve Cryptography (ECC) | Finite field arithmetic | Koblitz curves | ECC processor | Scalable | Curve | Cryptography (ECC) | Elliptic | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | GF(2(M)) | MULTIPLICATION | COMPUTER SCIENCE, THEORY & METHODS | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC

Scalable ECC processor | FPGA | Elliptic Curve Cryptography (ECC) | Finite field arithmetic | Koblitz curves | ECC processor | Scalable | Curve | Cryptography (ECC) | Elliptic | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | GF(2(M)) | MULTIPLICATION | COMPUTER SCIENCE, THEORY & METHODS | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

IEEE Transactions on Parallel and Distributed Systems, ISSN 1045-9219, 06/2015, Volume 26, Issue 6, pp. 1668 - 1677

High-performance and fast implementation of point multiplication is crucial for elliptic curve cryptographic systems. Recently, considerable research has...

Logic gates | Elliptic curve cryptography | Elliptic curves | Gaussian processes | Computer architecture | Clocks | double-hybrid multiplier | Gaussian normal basis | generalized Hessian curves | binary Edwards curves | Elliptic curve cryptography (ECC) | PROCESSOR | FPGA | IMPLEMENTATION | ENGINEERING, ELECTRICAL & ELECTRONIC | GF(2(M)) | ARCHITECTURE | POINT MULTIPLICATION | KOBLITZ CURVES | COMPUTER SCIENCE, THEORY & METHODS

Logic gates | Elliptic curve cryptography | Elliptic curves | Gaussian processes | Computer architecture | Clocks | double-hybrid multiplier | Gaussian normal basis | generalized Hessian curves | binary Edwards curves | Elliptic curve cryptography (ECC) | PROCESSOR | FPGA | IMPLEMENTATION | ENGINEERING, ELECTRICAL & ELECTRONIC | GF(2(M)) | ARCHITECTURE | POINT MULTIPLICATION | KOBLITZ CURVES | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Microprocessors and Microsystems, ISSN 0141-9331, 08/2016, Volume 45, pp. 10 - 22

The parallelization of scalable elliptic curve cryptography (ECC) processors (ECPs) is investigated in this paper. The proposed scalable ECPs support all 5...

Elliptic curve point multiplication (ECPM) | Binary finite field arithmetic | FPGA | Elliptic curve cryptography (ECC) | GF(2(N)) | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMPLEMENTATION | KOBLITZ CURVES | POINT MULTIPLICATION | COMPUTER SCIENCE, THEORY & METHODS | ENGINEERING, ELECTRICAL & ELECTRONIC | Reduction | Multiplication | Algorithms | Computation | Mathematical analysis | Parallel processing | Processors | Arithmetic

Elliptic curve point multiplication (ECPM) | Binary finite field arithmetic | FPGA | Elliptic curve cryptography (ECC) | GF(2(N)) | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | IMPLEMENTATION | KOBLITZ CURVES | POINT MULTIPLICATION | COMPUTER SCIENCE, THEORY & METHODS | ENGINEERING, ELECTRICAL & ELECTRONIC | Reduction | Multiplication | Algorithms | Computation | Mathematical analysis | Parallel processing | Processors | Arithmetic

Journal Article

IEICE Electronics Express, ISSN 1349-2543, 05/2016, Volume 13, Issue 9, p. pp20160044

This paper presents a very efficient scheme for point multiplication on Koblitz curves. The proposed scheme reduces the critical path in the data dependency...

Parallel processing | Field-programmable gate array (FPGA) | Point multiplication | Koblitz curves | Cryptoprocessor | Elliptic curve cryptography (ECC) | point multiplication | SCALAR MULTIPLICATION | PARALLELIZATION | NORMAL BASES | cryptoprocessor | field-programmable gate array (FPGA) | parallel processing | elliptic curve cryptography (ECC) | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | Critical path | Multiplication

Parallel processing | Field-programmable gate array (FPGA) | Point multiplication | Koblitz curves | Cryptoprocessor | Elliptic curve cryptography (ECC) | point multiplication | SCALAR MULTIPLICATION | PARALLELIZATION | NORMAL BASES | cryptoprocessor | field-programmable gate array (FPGA) | parallel processing | elliptic curve cryptography (ECC) | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | Critical path | Multiplication

Journal Article

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, ISSN 1063-8210, 08/2012, Volume 20, Issue 8, pp. 1453 - 1466

Efficient implementation of point multiplication is crucial for elliptic curve cryptographic systems. This paper presents the implementation results of an...

Binary Edwards curves (BECs) | generalized Hessian curves (GHCs) | Elliptic curves | Gaussian processes | Elliptic curve cryptography | Gaussian normal basis (GNB) | Hardware | Complexity theory | Field programmable gate arrays | elliptic curve cryptography (ECC) | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | PROCESSOR | FIELD MULTIPLICATION | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | GF(2(M)) | PARALLELIZATION | CRYPTOSYSTEMS | COMPLEXITY | NORMAL BASES | KOBLITZ CURVES | Studies | Algorithms | Multiplication & division | Integrated circuits | Multiplication | Computation | Parallel processing | Very large scale integration | Gaussian | Cryptography

Binary Edwards curves (BECs) | generalized Hessian curves (GHCs) | Elliptic curves | Gaussian processes | Elliptic curve cryptography | Gaussian normal basis (GNB) | Hardware | Complexity theory | Field programmable gate arrays | elliptic curve cryptography (ECC) | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | PROCESSOR | FIELD MULTIPLICATION | CRYPTOGRAPHY | ENGINEERING, ELECTRICAL & ELECTRONIC | GF(2(M)) | PARALLELIZATION | CRYPTOSYSTEMS | COMPLEXITY | NORMAL BASES | KOBLITZ CURVES | Studies | Algorithms | Multiplication & division | Integrated circuits | Multiplication | Computation | Parallel processing | Very large scale integration | Gaussian | Cryptography

Journal Article

Analog Integrated Circuits and Signal Processing, ISSN 0925-1030, 10/2015, Volume 85, Issue 1, pp. 129 - 138

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 06/2018, Volume 1974, Issue 1

Let E be an elliptic curve defined over F2m and T denotes the Frobenius endomorphism from the set E(F2m) to itself. The Koblitz curves are a special type of...

Frobenius endomorphism | Koblitz Curve | Scalar multiplication | Integers | Multiplication | Elliptic functions

Frobenius endomorphism | Koblitz Curve | Scalar multiplication | Integers | Multiplication | Elliptic functions

Journal Article

IEEE Transactions on Circuits and Systems I: Regular Papers, ISSN 1549-8328, 04/2014, Volume 61, Issue 4, pp. 1144 - 1155

Recently, considerable research has been performed in cryptography and security to optimize the area, power, timing, and energy needed for the point...

wireless sensor networks | RFID | Registers | Complexity theory | point multiplication | security | Koblitz curves | Gaussian processes | Computer architecture | Elliptic curve cryptography | Gaussian normal basis (GNB) | Hardware | Crypto-processor | GF(2(M)) | PROCESSOR | Gaussian normal basis ( GNB) | INVERSION | ENGINEERING, ELECTRICAL & ELECTRONIC | Integrated circuits | Energy consumption | Usage | Analysis | Innovations | Cryptography | Semiconductor chips | Multiplication & division | Multiplication | Multipliers | Algorithms | Architecture | Rewiring | Representations

wireless sensor networks | RFID | Registers | Complexity theory | point multiplication | security | Koblitz curves | Gaussian processes | Computer architecture | Elliptic curve cryptography | Gaussian normal basis (GNB) | Hardware | Crypto-processor | GF(2(M)) | PROCESSOR | Gaussian normal basis ( GNB) | INVERSION | ENGINEERING, ELECTRICAL & ELECTRONIC | Integrated circuits | Energy consumption | Usage | Analysis | Innovations | Cryptography | Semiconductor chips | Multiplication & division | Multiplication | Multipliers | Algorithms | Architecture | Rewiring | Representations

Journal Article

Journal of Cryptographic Engineering, ISSN 2190-8508, 11/2018, Volume 8, Issue 4, pp. 285 - 300

Koblitz curves allow very efficient elliptic curve cryptography. The reason is that one can trade expensive point doublings to cheap Frobenius endomorphisms by...

Elliptic curve cryptography | Lightweight cryptography | Koblitz curves | ECDSA | Integers | CMOS | Computer systems | Algorithms | Elliptic functions | Cryptography | Radio frequency identification | Arithmetic

Elliptic curve cryptography | Lightweight cryptography | Koblitz curves | ECDSA | Integers | CMOS | Computer systems | Algorithms | Elliptic functions | Cryptography | Radio frequency identification | Arithmetic

Journal Article

Analog Integrated Circuits and Signal Processing, ISSN 0925-1030, 10/2015, Volume 85, Issue 1, pp. 129 - 138

Efficient computation of the finite field arithmetic is required for elliptic curve cryptography over $$G\!F\!(2^{m})$$ G F ( 2 m ) . In order to achieve the...

Engineering | Digit-level multiplier | Signal, Image and Speech Processing | Koblitz curves | Circuits and Systems | Gaussian normal basis | Cryptography | Scalar point multiplication | Electrical Engineering

Engineering | Digit-level multiplier | Signal, Image and Speech Processing | Koblitz curves | Circuits and Systems | Gaussian normal basis | Cryptography | Scalar point multiplication | Electrical Engineering

Journal Article

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, ISSN 1063-8210, 09/2008, Volume 16, Issue 9, pp. 1162 - 1175

This paper discusses parallelization of elliptic curve cryptography hardware accelerators using elliptic curves over binary fields F 2m . Elliptic curve point...

Elliptic curve cryptography (ECC) | Delay | Application specific integrated circuits | Elliptic curves | field-programmable gate arrays (FPGAs) | Koblitz curves | Parallel processing | Elliptic curve cryptography | Public key cryptography | Hardware | Acceleration | Field programmable gate arrays | Arithmetic | Field-programmable gate arrays (FPGAs) | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHM | IMPLEMENTATION | INVERSES | parallel processing | ENGINEERING, ELECTRICAL & ELECTRONIC | GF(2(N)) | GF(2(M)) | public key cryptography | CRYPTOSYSTEMS | POINT MULTIPLICATION | elliptic curve cryptography (ECC) | Multiplication & division | Multiplication | Accelerators | Architecture | High speed | Very large scale integration | Cryptography | Processors

Elliptic curve cryptography (ECC) | Delay | Application specific integrated circuits | Elliptic curves | field-programmable gate arrays (FPGAs) | Koblitz curves | Parallel processing | Elliptic curve cryptography | Public key cryptography | Hardware | Acceleration | Field programmable gate arrays | Arithmetic | Field-programmable gate arrays (FPGAs) | DESIGN | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ALGORITHM | IMPLEMENTATION | INVERSES | parallel processing | ENGINEERING, ELECTRICAL & ELECTRONIC | GF(2(N)) | GF(2(M)) | public key cryptography | CRYPTOSYSTEMS | POINT MULTIPLICATION | elliptic curve cryptography (ECC) | Multiplication & division | Multiplication | Accelerators | Architecture | High speed | Very large scale integration | Cryptography | Processors

Journal Article

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