Elliptic curves
Elliptic Curves
... I would like to thank all of the wonderful professors I have had at CSUSB. I am grateful for all they have taught me. I would like to thank Professor Chavez for always having an enjoyable class and making so much sense. ...
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Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms
... for elliptic curves over number ...on elliptic curves over number fields, which involves determining complex elliptic logarithms (see Chapter 4) of all generators of Mordell–Weil ...all ...
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On Efficient Pairings on Elliptic Curves over Extension Fields
... use curves de- fined over certain extension fields, such as the extension fields with small charac- teristics, and the optimal extension fields which possess the fast field multiplica- tion and ...pairing-friendly ...
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Explicit n descent on elliptic curves III Algorithms
... 6. Inside the “Black Box”: How to trivialise a matrix algebra Our work on n-descent on elliptic curves requires us to make the Hasse principle explicit. In the case n = 2 this means we have to solve a conic ...
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2-Selmer groups and Heegner points on elliptic curves
... certain elliptic curves E/Q : y 2 = F (x) with additive reduction at 2, we deter- mine their 2-Selmer ranks in terms of the 2-rank of the class group of the cubic field L = Q[x]/F ...
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Binary quadratic forms, elliptic curves and Schoof's algorithm
... liptic curves over a nite eld with a number of elements less than or equal to ...an elliptic curve E over F q with a bad behavior in E [`] , with ` not necessary in the set S used by the Schoof's ...
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A note on high-security general-purpose elliptic curves
... high-efficiency elliptic curves tailored for security levels beyond 2 128 ...legacy-level curves at standard security levels. The choice of curves was made to facilitate state-of-the-art ...
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Faster arithmetic on elliptic curves using Fp2. Application to GLV-GLS and NIST elliptic curves over Fp isomorphic to twisted Hessian curves over fields extension
... some elliptic curves with cofactor 1 isomorphic twisted Hessian curves in …elds ...NIST curves over large prime …elds: NIST P-224 and NIST P-256 the degree of such extension is 2 so we can ...
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Hashing to elliptic curves of $j$-invariant $1728$
... [12] Donten M. On Kummer 3-folds. // Revista Matem´ atica Complutense, 2011. Vol. 24(2). P. 465–492. [13] El Mrabet N., Joye M. Guide to pairing-based cryptography. — New York.: Chapman and Hall, 2016. [14] Fouque P.-A., ...
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A New Family of Pairing-Friendly elliptic curves
... BLS curves are the original small discriminant parameterised family of fami- lies of pairing-friendly elliptic curves ...friendly curves which support the maximal twist of d = 6, and have a ...
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Point Decomposition Problem in Binary Elliptic Curves
... during the relation collection step to solve PDP(n, m, n 0 ). Faug` ere et al. further argue that, Groebner basis techniques may improve the running time by a factor m in the exponent, where m is the decomposition ...
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TNFS Resistant Families of Pairing-Friendly Elliptic Curves
... pairing-friendly elliptic curves for prime embedding degrees that have not previously appeared in the liter- ature, due to a larger ...pairing-friendly elliptic curve parameters can be chosen ...
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Uniformization of modular elliptic curves via p-adic periods
... runs into difficulty as the periods of f do not suffice in general. For example, it is well known (see [Kur78, EGM82]) that the periods of a weight 2 Bianchi newform f span a one-dimensional lattice in R. Due to the lack ...
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Group law and the Security of elliptic curves on Fp [e1, … , en]
... The elliptic curves are a very fashionable subject in ...the elliptic curves over local ring F p [] = F p [X]/(X 2 )[2], and a proposed a new public key cryptosystem which is a variant of the ...
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Improved Arithmetic on Elliptic Curves over Prime Field
... [3] Ian F. Blake, Gadiel Seroussi, and Nigel Smart. Elliptic Curves in Cryptography. London Mathematical Society Lecture Note Series 265. Cambridge University Press, Cambridge, 1999. [4] Eric Brier and Marc ...
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Proxy Signcrypion Scheme Based on Hyper Elliptic Curves
... This paper presents an efficient proxy signcrypion based on hyper elliptic curves. As compared to previous schemes the proposed scheme reduces 48% computation cost and 27% communication overhead. The scheme ...
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Efficient Pairings Computation on Jacobi Quartic Elliptic Curves
... For elliptic curves with embedding degrees k = 8, we consider the parameters for 112 bits and 128 bits security ...consider elliptic curves with embedding de- grees k = 16 at 128 bits and 192 ...
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New algorithm for the discrete logarithm problem on elliptic curves
... A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic ...
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Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves
... efficiency. Elliptic Curve Cryptography (ECC) pro- vides equivalent cryptographic primitives, but with significant improvements in terms of speed and memory, and is now recommended by governmental orga- nizations ...
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Scalable Zero Knowledge via Cycles of Elliptic Curves
... and elliptic curves, there is also an engineering ...MNT curves? Or cycles of length greater than 2? Are these easier to find, achieve smaller bit size and higher 2-adicity, or admit faster ...
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