[PDF] Guide to Elliptic Curve Cryptography | Semantic Scholar (2024)

The paper outlines ECC’s vulnerability against quantum attacks and references one possible solution to that problem, and 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 principal attraction of elliptic curve cryptography compared to RSA is that it offers equal security for a smaller key-size, especially in environments where short keys are important.

This thesis explores efficient hardware architectures for elliptic curve cryptography over binary Galois fields using FPGA designs for two of the most important field primitives namely multiplication and inversion and proposes a novel finite field multiplier based on the recursive Karatsuba algorithm.

The theory of ECC is described and implementation details that would help students, practitioners, and researchers understand, implement and experiment with such algorithms work are shown.

A new message mapping algorithm coupled with Elgamal encryption based on an elliptic curve defined over a finite prime field is defined and the execution time of the message mapping, encryption, reverse message mapping and decryption, increase linearly versus data sizes.

This work uses the latest vector instructions of Intel processors to implement the prime field arithmetic and devise a parallel scheduling of the complete formulas for point addition law, which is 15% and 40% faster than the OpenSSL library for computing ECDSA signatures and the ECDH protocol, respectively.

The thesis at hand is a step towards showing the practicability of PKC and in particular ECC on constrained devices, and investigates the potential of software/hardware co-design for architectural enhancements including instruction set extensions for low-level arithmetic used in ECC, most notably to speed-up multiplication in the finite fields.

The research paper aims to discuss and implement Koblitz mapping technique on a given ECC curve and it is also proved to be secured to encode and decode the textual information during data transfer.

An FPGA-based coprocessor that communicates with the host processor via a 32-bit bus that implements ECC over an elliptic curve that offers roughly 128-bit security and is the first hardware implementation that uses the recently introduced lambda coordinates and the Galbraith-Lin-Scott GLS technique with fast endomorphisms.

Three additional “trusted security acceptance criteria” which need to be met by the elliptic curves aimed for cryptography are proposed and two cryptographically secure elliptic curves over 256 bit and 384 bit prime fields are demonstrated.

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A study of software counter measures against side channel attacks for elliptic curve cryptosystems is presented, and two new counter measures are introduced, namely, hom*ogeneous group operations and a non-deterministic method of point exponentiation with precomputations.

It is shown that, for many elliptic curves, such a DPA-protection of the "scalar" multiplication is not sufficient and the problem of randomizing the basepoint may be more difficult than expected and that "standard" techniques have still to be improved, which may also have an impact on the performances of the implementations.

This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems, to help engineers and computer scientists wishing (or needing) to actually implement such systems.

This paper presents a new defence against Simple Power Analysis (SPA), based on the NAF (non-adjacent form) representation of a scalar and requires 44% fewer additions and 11% extra doublings than the commonly recommended defence of performing a point addition in every loop of the binary scalar multiplication algorithm.

A programmable hardware accelerator to speed up point multiplication for elliptic curves over binary polynomial fields GF(2m) and delivers optimized performance for a set of commonly used curves through hard-wired reduction logic.

This work presents algorithms that are especially suited to high-performance devices like large-scaled server computers and shows how to perform an efficient field multiplication for operands of arbitrary size, and how to achieve efficient field reduction for dense polynomials.

A practical software implementation of a cryptographic library which supports 160-bit elliptic curve DSA (ECDSA) signature generation, verification and SHA-1 on the processor and this library also includes general integer arithmetic routines for applicability to other cryptographic algorithms.

A mixed system that combines the superior key management capabilities inherent in public key cryptosystems with the much higher bulk-encryption speed obtainable with the Data Encryption Algorithm is discussed.

This paper shows how to rewrite the addition on the general Weierstras form of elliptic curves so that the same formulae apply equally to add two different points or to double a point.

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