Numerical modular symbols for elliptic curves
We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more effcient than current implementations as the conductor of the curve increases.
| Main Author: | Wuthrich, Christian |
|---|---|
| Format: | Article |
| Published: |
American Mathematical Society
2017
|
| Online Access: | https://eprints.nottingham.ac.uk/41549/ |
Similar Items
Vanishing of some Galois cohomology groups for elliptic curves
by: Lawson, Tyler, et al.
Published: (2016)
by: Lawson, Tyler, et al.
Published: (2016)
A moduli interpretation for the non-split Cartan modular curve
by: Rebolledo, Marusia, et al.
Published: (2018)
by: Rebolledo, Marusia, et al.
Published: (2018)
Kolyvagin Derivatives of Modular Points on Elliptic Curves
by: Hatton, Richard
Published: (2020)
by: Hatton, Richard
Published: (2020)
Modular forms and elliptic curves over imaginary
quadratic fields
by: Lingham, Mark Peter
Published: (2005)
by: Lingham, Mark Peter
Published: (2005)
Anabelian geometry of punctured elliptic curves
by: Porowski, Wojciech
Published: (2020)
by: Porowski, Wojciech
Published: (2020)
A survey on elliptic curve cryptography
by: Mohamed, Mohamad Afendee
Published: (2014)
by: Mohamed, Mohamad Afendee
Published: (2014)
Multi-Threading Elliptic Curve Cryptosystems.
by: Kanniah, Uma S., et al.
Published: (2007)
by: Kanniah, Uma S., et al.
Published: (2007)
Committal deniable signatures over elliptic curves
by: Han, Song, et al.
Published: (2004)
by: Han, Song, et al.
Published: (2004)
Fourier coefficients of Eisenstein series formed with
modular symbols and their spectral decomposition
by: Bruggeman, Roelof, et al.
Published: (2016)
by: Bruggeman, Roelof, et al.
Published: (2016)
A new encryption algorithm over elliptic curve
by: Han, Song, et al.
Published: (2005)
by: Han, Song, et al.
Published: (2005)
An improved public key cryptography based on the elliptic curve
by: Al-Daoud, Essam Faleh
Published: (2002)
by: Al-Daoud, Essam Faleh
Published: (2002)
Encrypting text data using elliptic curve cryptography
by: Ali, Abas Abdullahi
Published: (2018)
by: Ali, Abas Abdullahi
Published: (2018)
High performance methods of elliptic curve scalar multiplication
by: Al Saffar, Najlae Falah Hameed, et al.
Published: (2014)
by: Al Saffar, Najlae Falah Hameed, et al.
Published: (2014)
Improved arithmetic on elliptic curves over prime field
by: Al Saffar, Najlae Falah Hameed, et al.
Published: (2014)
by: Al Saffar, Najlae Falah Hameed, et al.
Published: (2014)
Addition chain heuristics in application to elliptic curve cryptosystems
by: Mohamed, Mohamad Afendee, et al.
Published: (2024)
by: Mohamed, Mohamad Afendee, et al.
Published: (2024)
Elliptic net scalar multiplication upon Koblitz curves
by: Muslim, Norliana, et al.
Published: (2020)
by: Muslim, Norliana, et al.
Published: (2020)
Improved algorithms of elliptic curve point multiplication over binary and prime fields using elliptic net
by: Muslim, Norliana
Published: (2022)
by: Muslim, Norliana
Published: (2022)
On the design of projective binary Edwards elliptic curves over GF (p) benefitting from mapping elliptic curves computation to variable degree of parallel design
by: Al-Khatib, Mohammad Hussein Fayiz, et al.
Published: (2011)
by: Al-Khatib, Mohammad Hussein Fayiz, et al.
Published: (2011)
Robust and secure image steganography based on elliptic curve cryptography
by: Ahmed, Diaa Eldein Mustafa, et al.
Published: (2014)
by: Ahmed, Diaa Eldein Mustafa, et al.
Published: (2014)
K1-congruences between L-values of elliptic curves
by: Ward, Thomas
Published: (2009)
by: Ward, Thomas
Published: (2009)
Key exchange in elliptic curve cryptography based on the decomposition problem
by: Hilyati Hanina Zazali,, et al.
Published: (2012)
by: Hilyati Hanina Zazali,, et al.
Published: (2012)
An improved binary method for scalar multiplication in elliptic curve cryptography
by: Mohamed, Mohamad Afendee, et al.
Published: (2010)
by: Mohamed, Mohamad Afendee, et al.
Published: (2010)
Signed decomposition method for scalar multiplication in elliptic curve cryptography
by: Md. Said, Mohamad Rushdan, et al.
Published: (2010)
by: Md. Said, Mohamad Rushdan, et al.
Published: (2010)
Mathematical Geosciences: Hybrid Symbolic-Numeric Methods
by: Awange, Joseph, et al.
Published: (2018)
by: Awange, Joseph, et al.
Published: (2018)
Elliptical curve cryptography-kerberos authentication model for keystone in open stack
by: Shamugam, V., et al.
Published: (2017)
by: Shamugam, V., et al.
Published: (2017)
A new elliptic curve cryptographic system over the finite fields
by: Priyatharsan, U., et al.
Published: (2017)
by: Priyatharsan, U., et al.
Published: (2017)
Quantum-Elliptic curve Cryptography for Multihop Communication in 5G Networks
by: Khan, A.S., et al.
Published: (2017)
by: Khan, A.S., et al.
Published: (2017)
Saturation of Mordell-Weil Groups of Elliptic Curves over Number Fields
by: Prickett, Martin
Published: (2004)
by: Prickett, Martin
Published: (2004)
An efficient identity-based group signature scheme over elliptic curves
by: Han, Song, et al.
Published: (2004)
by: Han, Song, et al.
Published: (2004)
On the Improvement of Addition Chain in Applications to Elliptic Curve Cryptosystem
Status: Submitted
by: Mohamed, Mohamad Afendee
Published: (2011)
by: Mohamed, Mohamad Afendee
Published: (2011)
On the mathematical complexity and the time implementation
of proposed variants of elliptic curves cryptosystems
by: Al-Saffar, Najlae F. Hameed, et al.
Published: (2013)
by: Al-Saffar, Najlae F. Hameed, et al.
Published: (2013)
Integer Sub-Decomposition (Isd)
Method For Elliptic Curve
Scalar Multiplication
by: Ajeena, Ruma Kareem K.
Published: (2015)
by: Ajeena, Ruma Kareem K.
Published: (2015)
The Construction Of Efficiently
Computable Endomorphisms For
Scalar Multiplication On Some
Elliptic Curves
by: Antony, Siti Noor Farwina Mohamad Anwar
Published: (2019)
by: Antony, Siti Noor Farwina Mohamad Anwar
Published: (2019)
New Representation Method For Integers And Its Application On Elliptic Curve Cryptography
by: Eghdamian, Arash
Published: (2020)
by: Eghdamian, Arash
Published: (2020)
Choices on designing GF (p) elliptic curve coprocessor benefiting from mapping homogeneous curves in parallel multiplications
by: Al-Haija, Qasem Abu, et al.
Published: (2011)
by: Al-Haija, Qasem Abu, et al.
Published: (2011)
Harmonics elimination based on curve fitting method for modular multilevel converters
by: Tohtayong, Majdee, et al.
Published: (2017)
by: Tohtayong, Majdee, et al.
Published: (2017)
An algorithm to enhance elliptic curves scalar multiplication combining MBNR with point halving
by: M. Ismail, Abdulwahed, et al.
Published: (2010)
by: M. Ismail, Abdulwahed, et al.
Published: (2010)
Tripling formulae of elliptic curve over binary field in Lopez-Dahab model
by: Md Yasin, Sharifah, et al.
Published: (2015)
by: Md Yasin, Sharifah, et al.
Published: (2015)
Securing the image through the combination of elliptic curve cryptosystem and hill cipher encryption
by: Sulaiman, Saniah
Published: (2019)
by: Sulaiman, Saniah
Published: (2019)
Improving the security and encryption performance of cloud storage by using elliptic curve cryptography
by: Ismaeel, Nooruldeen Qutaiba
Published: (2016)
by: Ismaeel, Nooruldeen Qutaiba
Published: (2016)
Similar Items
-
Vanishing of some Galois cohomology groups for elliptic curves
by: Lawson, Tyler, et al.
Published: (2016) -
A moduli interpretation for the non-split Cartan modular curve
by: Rebolledo, Marusia, et al.
Published: (2018) -
Kolyvagin Derivatives of Modular Points on Elliptic Curves
by: Hatton, Richard
Published: (2020) -
Modular forms and elliptic curves over imaginary
quadratic fields
by: Lingham, Mark Peter
Published: (2005) -
Anabelian geometry of punctured elliptic curves
by: Porowski, Wojciech
Published: (2020)