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A Survey on Hardware Implementations of Elliptic Curve Cryptosystems
[article]
2017
arXiv
pre-print
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We first discuss different elliptic curves, point multiplication algorithms and underling finite field operations over binary fields F2m and prime fields Fp which are used in the literature for hardware ...
In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly advanced. ...
The chip for hardware realization processor is fabricated using UMC 130nm 1P8M process, resulting in a core area of 0.54 mm 2 . The energy consumption to perform one point multiplication is 5.1µJ. ...
arXiv:1710.08336v1
fatcat:g3gpz5lzgvc27fboa5tv4kdhze
Low-energy encryption for medical devices
2013
Proceedings of the 50th Annual Design Automation Conference on - DAC '13
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It only needs 5.1µJ of energy in a 0.13 µm CMOS technology for one point multiplication and includes a selected set of countermeasures against physical attacks. ...
It will be illustrated with the design of a low energy elliptic curve based public key programmable co-processor. ...
At the operating frequency of 847.5kHz and core voltage V dd = 1V , the processor consumes 50.4µW and uses only 5.1µJ for one point-multiplication. ...
doi:10.1145/2463209.2488752
dblp:conf/dac/FanRRV13
fatcat:f4qeuxyc3jekncgbsqlcqhcsmu
The design space of ultra-low energy asymmetric cryptography
2014
2014 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS)
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Then, we augment our processor design with simple, yet beneficial instruction set extensions for GF (p) computation and evaluate the improvement in terms of energy per cryptographic operation compared ...
cryptographic operation. ...
Elliptic Curve Cryptography The Elliptic Curve Cryptography (ECC) analog of modular exponentiation is scalar point multiplication, which involves repeated addition-and-doubling of points on an elliptic ...
doi:10.1109/ispass.2014.6844461
dblp:conf/ispass/TarghettaOG14
fatcat:ghiu2f6srfe5temv2tft7ywkqu
Software Implementation of Binary Elliptic Curves: Impact of the Carry-Less Multiplier on Scalar Multiplication
[chapter]
2011
Lecture Notes in Computer Science
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algorithms for binary field arithmetic and scalar multiplication over elliptic curves. ...
levels, and a new speed record for side-channel resistant scalar multiplication in a random curve at the 128-bit security level. ...
this project was discussed, planned and a portion of the development phase of this work was done. ...
doi:10.1007/978-3-642-23951-9_8
fatcat:fgygdub5t5gkfjqqacobpq7xuu
Efficient FPGA-based ECDSA Verification Engine for Permissioned Blockchains
[article]
2021
arXiv
pre-print
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The Elliptic Curve Digital Signature Algorithm (ECDSA) is the most commonly used cryptographic scheme in permissioned blockchains. ...
Our Hyperledger Fabric-specific ECDSA engine can perform a single verification in 368μ s with a throughput of 2,717 verifications per second. ...
Fast Im-
of 1, 315 verifications per second, which is ~2.5× faster than [8, 18]. plementation of NIST P-256 Elliptic Curve Cryptography on 8-Bit AVR Processor. ...
arXiv:2112.02229v1
fatcat:r3bw4kn4tnhzvhh3cjqugnj65m
Using Abelian Varieties to Improve Pairing-Based Cryptography
2008
Journal of Cryptology
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We show that supersingular abelian varieties can be used to obtain higher MOV security per bit, in all characteristics, than supersingular elliptic curves. ...
on supersingular elliptic curves. ...
Let E : y 2 = f (x) be a supersingular elliptic curve over F q , and let P ∈ E(F q ) be a point of large prime order . Let c denote the cryptographic exponent c E,q defined in Definition 4.5. ...
doi:10.1007/s00145-008-9022-1
fatcat:ixmje3vbtzgfnihehyilj3pdui
Unified Compact ECC-AES Co-Processor with Group-Key Support for IoT Devices in Wireless Sensor Networks
2018
Sensors
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In this paper, a compact and unified co-processor for enabling Elliptic Curve Cryptography along to Advanced Encryption Standard with low area requirements and Group-Key support is presented. ...
Security is a critical challenge for the effective expansion of all new emerging applications in the Internet of Things paradigm. ...
Users U j , j = 1, . . . , n agree on an elliptic curve and a generator P of E. We are assuming that the user who acts as a key manager node in the set up stage is user U n . ...
doi:10.3390/s18010251
pmid:29337921
pmcid:PMC5795697
fatcat:2kwatdliejgllk3z7nayvpk5o4
Euclidean addition chains scalar multiplication on curves with efficient endomorphism
2018
Journal of Cryptographic Engineering
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In this work, we show how to generalize this method to random point scalar multiplication on elliptic curves with an efficiently computable endomorphism. ...
In order to do so we generalize results from [21] on the relation of random Euclidean chains generation and elliptic curve point distribution obtained from those chains. ...
Corollary 1 Let E be an elliptic curve and a point P ∈ E of order N . ...
doi:10.1007/s13389-018-0190-0
fatcat:g4eobbjb7rd3dnnxzz6dyn27rm
Parallel Collision Search with Cryptanalytic Applications
1999
Journal of Cryptology
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GF(2 155 ) thereby defeating a proposed elliptic curve cryptosystem in expected time 32 days, the second finds MD5 collisions in expected time 21 days, and the last recovers a double-DES key from 2 known ...
The practical significance of the technique is illustrated by giving the design for three $10 million custom machines which could be built with current technology: one finds elliptic curve logarithms in ...
Acknowledgments We would like to thank John Pollard for correcting a note about [4] and for clarifying a fundamental difference between his two rho-methods. ...
doi:10.1007/pl00003816
fatcat:ghvadeagyfhztevb4erc62cyey
Software Implementation of the NIST Elliptic Curves Over Prime Fields
[chapter]
2001
Lecture Notes in Computer Science
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This paper presents an extensive study of the software implementation on workstations of the NIST-recommended elliptic curves over prime fields. ...
We present the results of our implementation in C and assembler on a Pentium II 400 MHz workstation. We also provide a comparison with the NIST-recommended curves over binary fields. ...
This operation is called point multiplication and dominates the execution time of elliptic curve cryptographic schemes. ...
doi:10.1007/3-540-45353-9_19
fatcat:gns2qihi5jdvtlzehtwq6wjfmy
Fault-Based Attack on Montgomery's Ladder Algorithm
2010
Journal of Cryptology
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We show that with a different "value" for curve parameter a, there exists a cryptographically weaker group in nine of the ten NIST-recommended elliptic curves over F 2 m . ...
In this report we present invalid-curve attacks that apply to the Montgomery ladder elliptic curve scalar multiplication (ECSM) algorithm. ...
In this way, the computation could be performed in a cryptographically less secure elliptic curve. ...
doi:10.1007/s00145-010-9087-5
fatcat:szqofhbbufb7tmvhkscw377ndm
The Elliptic Curve Digital Signature Algorithm (ECDSA)
2001
International Journal of Information Security
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They can be viewed as elliptic curve analogues of the older discrete logarithm (DL) cryptosystems in which the subgroup of ¦ § © is replaced by the group of points on an elliptic curve over a finite field ...
For this reason, the strength-per-key-bit is substantially greater in an algorithm that uses elliptic curves. ...
THE TWIST OF AN ELLIPTIC CURVE OVER I µ ) Ä û T A ) C S D ¶ . 4.2. Compute´¿ ( SHA-1 I y ¿ T . ...
doi:10.1007/s102070100002
fatcat:bfrrjgymlzdupfdziqfju2utqu
Public Key Cryptography on Hardware Platforms: Design and Analysis of Elliptic Curve and Lattice-based Cryptoprocessors
2017
Zenodo
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Aiming to secure resource-constrained connected devices, we design a lightweight elliptic-curve coprocessor for a 283-bit Koblitz curve, which offers 140-bit security. ...
We optimize the scalar conversion which is an important part of point multiplication, and we introduce lightweight countermeasures against timing and power side-channel attacks. ...
A.2 Hardware architecture We use these optimizations to design a high-speed and pipelined scalar conversion architecture. The architecture is described in details our publication ...
doi:10.5281/zenodo.2643389
fatcat:sozmpjtc3jbddpgdqa7cic24k4
Batching CSIDH Group Actions using AVX-512
2021
Transactions on Cryptographic Hardware and Embedded Systems
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for the standard elliptic curve Diffie-Hellman protocol. ...
The CSIDH protocol is based on the action of an ideal class group on a set of supersingular elliptic curves and comes with some very attractive features, e.g. the ability to serve as a "drop-in" replacement ...
A TLS termination proxy equipped with a high-end 64-bit Intel processor clocked at 4 GHz is (in theory) able to perform 40,000 X25519 key exchanges per second per core since, as mentioned before, a variable-base ...
doi:10.46586/tches.v2021.i4.618-649
fatcat:onlwu4m2anettm727l4zipmvuu
Unified Point Addition Formulæ and Side-Channel Attacks
[chapter]
2006
Lecture Notes in Computer Science
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or timing, has motivated the recent development of unified formulae for elliptic curve point operations. ...
In this paper, we give a version of a previously-developed family of unified point addition formulae that uses projective coordinates for improved efficiency. ...
The central operation in an elliptic curve cryptosystem is the point multiplication operation, in which a point is multiplied by a scalar. ...
doi:10.1007/11894063_28
fatcat:ub2sni6d7jacxjfkd3nom7jtvq
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