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Elligator Squared: Uniform Points on Elliptic Curves of Prime Order as Uniform Random Strings [chapter]

Mehdi Tibouchi
2014 Lecture Notes in Computer Science  
Their proposal has the advantage of being very efficient, but suffers from several limitations: -Since only a subset of all elliptic curve points can be encoded as a string, their approach only applies  ...  curves as close to uniform random strings.  ...  The only other known injective encoding to ordinary curves is due to Farashahi [10] and applies to curves of order divisible by 3.  ... 
doi:10.1007/978-3-662-45472-5_10 fatcat:3gtkqcsjkvdwpf7k3z5qg6k3p4

How to Hash into Elliptic Curves [chapter]

Thomas Icart
2009 Lecture Notes in Computer Science  
The function requires to compute a cube root. As an application we show how to hash deterministically into an elliptic curve.  ...  We describe a new explicit function that given an elliptic curve E defined over Fpn, maps elements of Fpn into E in deterministic polynomial time and in a constant number of operations over Fpn .  ...  I wish to thank Jean-Sébastien Coron for the time he spent to help me write this paper.  ... 
doi:10.1007/978-3-642-03356-8_18 fatcat:jxb7hwxjsre4llnfzle2qvauri

Network Security in Cloud Computing with Elliptic Curve Cryptography

Victor O. Waziri, Ojeniyi J. Adebayo, Hakimi Danladi, Audu Isah, Abubakar S. Magaji, Muhammad Bashir Abdullahi
2013 Network and Communication Technologies  
We reviewed various literatures on the elliptic curves and applied the cyclic elliptic curve group based-on finite field modulo q.  ...  With the theory established, we applied the Elliptic Curve Digital Signature Algorithm as developed by ElGamal to carry out some exemplified computational sequences.  ...  Experiments In this experimental section, we give two types of curves: Ordinary elliptic curves and the pseudo-random curve of type P-192.  ... 
doi:10.5539/nct.v2n2p43 fatcat:lbnlusturndzhcawf6qcuxo3ae

On Division Polynomial PIT and Supersingularity [article]

Javad Doliskani
2018 arXiv   pre-print
For an elliptic curve E over a finite field _q, where q is a prime power, we propose new algorithms for testing the supersingularity of E.  ...  Acknowledgment The author would like to thank Felipe Voloch for his valuable feedback on Section 4, and Luca De Feo for helpful comments.  ...  Since most of the elliptic curves E/F q are ordinary, generating random ordinary curves amounts to simply choosing random coefficients a, b for the Weierstrass equation.  ... 
arXiv:1801.02664v2 fatcat:bmawsa4z7zhbtlnuw5poxwel7m

Pairings on hyperelliptic curves [article]

Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm, Kirsten Eisentraeger, Katherine Stange, Edlyn Teske
2009 arXiv   pre-print
We discuss the techniques used to optimize the pairing computation on hyperelliptic curves, and present many directions for further research.  ...  We also showcase the hyperelliptic pairings proposed to date, and develop a unifying framework.  ...  Thanks to Alan Silvester for conscientious technical editing. Thanks to Jonathan Wise. The work of the first author has been supported by a National Science Foundation Graduate Research Fellowship.  ... 
arXiv:0908.3731v2 fatcat:6nnfdtdi2rgnzpeyk642nf3mum

Set It and Forget It! Turnkey ECC for Instant Integration [article]

Dmitry Belyavsky, Billy Bob Brumley, Jesús-Javier Chi-Domínguez, Luis Rivera-Zamarripa, Igor Ustinov
2020 arXiv   pre-print
Historically, Elliptic Curve Cryptography (ECC) is an active field of applied cryptography where recent focus is on high speed, constant time, and formally verified implementations.  ...  .\ a library may feature such X25519 or P-256 code, but not for all curves.  ...  571, as well as the Koblitz curve variant of each binary curve.  ... 
arXiv:2007.11481v1 fatcat:yzkl3tfyrvhpxckt337mhrbtt4

Robust Finite Field Arithmetic for Fault-Tolerant Public-Key Cryptography [chapter]

Gunnar Gaubatz, Berk Sunar
2006 Lecture Notes in Computer Science  
Our approach is closely related to, but not limited by the theory of cyclic binary and arithmetic codes.  ...  We present a new approach to fault tolerant public key cryptography based on redundant arithmetic in finite rings.  ...  particular Elliptic Curve Cryptography.  ... 
doi:10.1007/11889700_18 fatcat:wzqcbyorlzg7rn7self5xrxeda

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries

P Ajith, Michael Boyle, Duncan A Brown, Bernd Brügmann, Luisa T Buchman, Laura Cadonati, Manuela Campanelli, Tony Chu, Zachariah B Etienne, Stephen Fairhurst, Mark Hannam, James Healy (+36 others)
2012 Classical and quantum gravity  
The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions.  ...  The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data.  ...  Similar noise curves will be used to simulate the Advanced Virgo detector.  ... 
doi:10.1088/0264-9381/29/12/124001 fatcat:2xuaqprdqvd55p53cgickvcufa

Computing the endomorphism ring of an ordinary abelian surface over a finite field [article]

Caleb Springer
2019 arXiv   pre-print
curves.  ...  The output of the algorithm is an ideal in the maximal totally real subfield of the endomorphism algebra, generalizing the elliptic curve case.  ...  The first algorithm for computing End(E) for an ordinary elliptic curve E was given by Kohel in his thesis [21] .  ... 
arXiv:1810.12270v2 fatcat:espnorn7bzgclbw2yt7m4nx7fy

Algorithm Agility – Discussion on TPM 2.0 ECC Functionalities [chapter]

Liqun Chen, Rainer Urian
2016 Lecture Notes in Computer Science  
The TPM 2.0 specification has been designed to support a number of Elliptic Curve Cryptographic (ECC) primitives, such as key exchange, digital signatures and Direct Anonymous Attestation (DAA).  ...  In order to meet the requirement that di↵erent TPM users may favor di↵erent cryptographic algorithms, each primitive can be implemented from multiple algorithms.  ...  The TPM 2.0 specification has been designed to support a new family of Elliptic Curve (EC) based DAA protocols.  ... 
doi:10.1007/978-3-319-49100-4_6 fatcat:wswm47cd2vc2vo5zeydifiocfq

Sponge-Based Control-Flow Protection for IoT Devices [article]

Mario Werner, Thomas Unterluggauer, David Schaffenrath, Stefan Mangard
2018 arXiv   pre-print
For example, software attackers perform code injection and code-reuse attacks on their remote interfaces, and physical access to IoT devices allows to tamper with code in memory, steal confidential Intellectual  ...  Property (IP), or mount fault attacks to manipulate a CPU's control flow.  ...  This becomes especially visible for the two implementations of elliptic curves.  ... 
arXiv:1802.06691v1 fatcat:2oil6wsjevh5xclbf3qyxcpza4

Linearly Time Efficiency in Unattended Wireless Sensor Networks [chapter]

Faezeh Sadat, Fattaneh Bayat
2012 Real-Time Systems, Architecture, Scheduling, and Application  
Moreover, according to [2] , the Elliptic Curve Cryptography (ECC) schemes show an important drawback of the re-encryption solutions,since the exponentiation is not as suitable as polynomial operations  ...  Mathematical encoding solution In this section, we used the Ordinary Differential Equation(denoted as ODE) for encoding the data shares.  ... 
doi:10.5772/39275 fatcat:hwzccffstrb3bj6eicqpqjchcy

Improved Security Performance for VANET Simulations

Raphael Riebl, Markus Monz, Simon Varga, Leandros Maglaras, Helge Janicke, Ali H. Al-Bayatti, Christian Facchi
2016 IFAC-PapersOnLine  
This paper presents a standard compliant simulation model capable to handle secured messages.  ...  Upcoming deployments of Vehicular Ad Hoc Networks (VANETs) in Europe are expected to sign and verify packets secured by cryptographic signatures by default.  ...  ACKNOWLEDGEMENTS Remarkable implementation efforts concerning various security features of Vanetza have to be attributed to following students: Stefan Kopitzki, Robert Lamprecht, Christina Obermaier, Aaron  ... 
doi:10.1016/j.ifacol.2016.11.173 fatcat:2gcsxgsffbe3tg3lgurgngt6ry

Coherent searches for periodic gravitational waves from unknown isolated sources and Scorpius X-1: results from the second LIGO science run [article]

The LIGO Scientific Collaboration
2006 arXiv   pre-print
The second search targets the accreting neutron star in the low-mass X-ray binary Scorpius X-1, covers the frequency bands 464-484 Hz and 604-624 Hz, and two binary orbit parameters.  ...  For isolated neutron stars our 95% confidence upper limits on the gravitational wave strain amplitude range from 6.6E-23 to 1E-21 across the frequency band; For Scorpius X-1 they range from 1.7E-22 to  ...  Depending on the field configuration, accretion rate, and temperature, the ellipticity from this mechanism could be up to 10 −5 even for ordinary neutron stars.  ... 
arXiv:gr-qc/0605028v1 fatcat:cngmhz3ob5hw7el6zsu4pws72q

A Steganographic Design Paradigm for General Steganographic Objectives [article]

Aubrey Alston
2017 arXiv   pre-print
Beyond the standard scope of private-key steganography, steganography is also potentially interesting from other perspectives; for example, the prospect of steganographic parallels to components in public-key  ...  This work is by-and-large a survey of applications of this paradigm: specifically, I use the framework to achieve provably secure distributed steganography, obtain new public-key steganographic constructions  ...  the elliptic curve Diffie-Hellman assumption; we design it using the OEE paradigm.  ... 
arXiv:1707.00076v1 fatcat:jr43an7y3ffibjszgq2hfvarxm
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