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Optimal extension fields for fast arithmetic in public-key algorithms

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/3-540-44750-4_4openalex-snapshot
Fast Key Exchange with Elliptic Curve Systems
inferredcites →https://doi.org/10.1007/3-540-47555-9_14openalex-snapshot
Public-Key Cryptosystems with Very Small Key Lengths
inferredcites →https://doi.org/10.1007/3-540-48071-4_25openalex-snapshot
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
inferredcites →https://doi.org/10.1007/bf02252872openalex-snapshot
Hyperelliptic cryptosystems
inferredcites →https://doi.org/10.1007/bfb0034836openalex-snapshot
A fast software implementation for arithmetic operations in GF(2n)
inferredcites →https://doi.org/10.1007/bfb0052247openalex-snapshot
Efficient algorithms for elliptic curve cryptosystems
inferredcites →https://doi.org/10.1017/cbo9781107360211openalex-snapshot
Elliptic Curves in Cryptography
inferredcites →https://doi.org/10.1090/s0025-5718-1987-0866109-5openalex-snapshot
Elliptic Curve Cryptosystems
inferredcites →https://doi.org/10.1201/9781439821916openalex-snapshot
Handbook of Applied Cryptography
inferredcites →https://doi.org/10.2307/2317055openalex-snapshot
The Art of Computer Programming. Volume 2: Seminumerical Algorithms.
inferredcites →https://doi.org/10.5860/choice.34-4512openalex-snapshot
Handbook of applied cryptography

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Elliptic‐curve cryptography for wireless sensor network nodes without hardware multiplier support
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Pseudo-Mersenne Prime
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Over F p vs. over F $_{2^{n}}$ and on Pentium vs. on Alpha in Software Implementation of Hyperelliptic Curve Cryptosystems
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Speeding Up Elliptic Scalar Multiplication with Precomputation
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Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves
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Efficient Multi-bit Shifting Algorithm in Multiplicative Inversion Problems
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Scalar Multiplication on Elliptic Curves Defined over Fields of Small Odd Characteristic
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Efficient Hardware Implementation of Elliptic Curve Cryptography over GF(p m )
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Efficient FPGA-Based Karatsuba Multipliers for Polynomials over ${\mathbb F}_{2}$
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Efficient Exponentiation in GF(p m ) Using the Frobenius Map
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A High-Speed Square Root Algorithm in Extension Fields
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Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves
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Optimal Extension Fields for XTR
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Efficient GF(p m ) Arithmetic Architectures for Cryptographic Applications
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Power Analysis Breaks Elliptic Curve Cryptosystems Even Secure against the Timing Attack
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Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
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Efficient Inversion Algorithm for Optimal Normal Bases Type II
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An Efficient Algorithm for Computing Inverses in GF(2m) Using Dual Bases
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Elliptic Curves of Prime Order over Optimal Extension Fields for Use in Cryptography
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Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form
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A Cyclic Window Algorithm for ECC Defined over Extension Fields
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Fast Elliptic Curve Algorithm Combining Frobenius Map and Table Reference to Adapt to Higher Characteristic
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Elliptic Curve Public-Key Cryptosystems — An Introduction
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Elliptic Curve Cryptography on Smart Cards without Coprocessors
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Modular Integer Arithmetic for Public Key Cryptography
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The State of Elliptic Curve Cryptography
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Efficient Software Implementation of GMT6-672 and GMT8-542 Pairing-Friendly Curves for a 128-Bit Security Level
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Fast Computation of Frobenius Map Iterates in Optimal Extension Fields
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Elliptic Curve Cryptography on Constrained Microcontrollers Using Frequency Domain Arithmetic
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Systolic and Scalable Architectures for Digit-Serial Multiplication in Fields GF(p m )
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Linear Recurrences with Polynomial Coefficients and Computation of the Cartier-Manin Operator on Hyperelliptic Curves
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A General Expansion Method Using Efficient Endomorphisms
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Efficient Scalar Multiplication in Hyperelliptic Curves Using A New Frobenius Expansion
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Computation of Multiplicative Inverses in GF(2 n ) Using Palindromic Representation
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Comparing Elliptic Curve Cryptography and RSA on 8-bit CPUs
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Reconfigurable Instruction Set Extension for Enabling ECC on an 8-Bit Processor
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Elliptic Curves with the Montgomery-Form and Their Cryptographic Applications
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Fast Implementation of Elliptic Curve Arithmetic in GF(p n )
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Optimal Extension Field Inversion in the Frequency Domain
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Highly Regular Right-to-Left Algorithms for Scalar Multiplication
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Efficient Explicit Formulae for Genus 2 Hyperelliptic Curves over Prime Fields and Their Implementations
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Explicit Formulas for Efficient Multiplication in $\mathbb{F}_{3^{6m}}$
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Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions
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Improved base- ɸ expansion method for Koblitz curves over optimal extension fields
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Efficient ECC Processor Designs for IoT Using Edwards Curves and Exploiting FPGA Embedded Components
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Architectural Extensions for Elliptic Curve Cryptography over GF(2^m ) on 8-bit Microprocessors
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Recherche de primitives pour la cryptographie à base de couplage.
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