Open AccessJournal Article
Comparing elliptic curve cryptography and RSA on 8-bit CPUs
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In this paper, an Atmel ATmega128 at 8 MHz was used to implement ECC point multiplication over fields using pseudo-Mersenne primes as standardized by NIST and SECG.Abstract:
Strong public-key cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160-bit, 192-bit, and 224-bit NIST/SECG curves over GF(p) and RSA-1024 and RSA-2048 on two 8-bit microcontrollers. To accelerate multiple-precision multiplication, we propose a new algorithm to reduce the number of memory accesses. Implementation and analysis led to three observations: 1. Public-key cryptography is viable on small devices without hardware acceleration. On an Atmel ATmega128 at 8 MHz we measured 0.81s for 160-bit ECC point multiplication and 0.43s for a RSA-1024 operation with exponent e = 2 16 +1. 2. The relative performance advantage of ECC point multiplication over RSA modular exponentiation increases with the decrease in processor word size and the increase in key size. 3. Elliptic curves over fields using pseudo-Mersenne primes as standardized by NIST and SECG allow for high performance implementations and show no performance disadvantage over optimal extension fields or prime fields selected specifically for a particular processor architecture.read more
Citations
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TinyECC: A Configurable Library for Elliptic Curve Cryptography in Wireless Sensor Networks
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A survey of security issues in wireless sensor networks
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Energy analysis of public-key cryptography for wireless sensor networks
TL;DR: Measurements on an Atmel ATmega128L low-power microcontroller platform indicate that public-key cryptography is very viable on 8-bit energy-constrained platforms even if implemented in software.
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References
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Book
Guide to Elliptic Curve Cryptography
TL;DR: This guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment, as well as side-channel attacks and countermeasures.
Journal Article
Efficient elliptic curve exponentiation using mixed coordinates
TL;DR: A new coordinate system and a new mixed coordinates strategy are proposed, which significantly improves on the number of basic operations needed for elliptic curve exponentiation.
Journal ArticleDOI
Speeding up the computations on an elliptic curve using addition-subtraction chains
François Morain,Jorge Olivos +1 more
TL;DR: Notre meilleur algorithme est 11,11% plus rapide que la methode binaire ordinaire and cela permet d'accelerer en consequence les algorithmes de primalite and de factorisation qui utilisent les courbes elliptiques.
Journal Article
Optimal extension fields for fast arithmetic in public-key algorithms
Daniel V. Bailey,Christof Paar +1 more
TL;DR: A class of Galois field used to achieve fast finite field arithmetic which is called an Optimal Extension Field (OEF) is introduced, well suited for implementation of public-key cryptosystems based on elliptic and hyperelliptic curves.