Combining leak-resistant arithmetic for elliptic curves defined over and RNS representation
JC Bajard, S Duquesne… - … . Algèbre et théorie …, 2013 - pmb.centre-mersenne.org
In this paper we give a survey of a method combining the residue number system (RNS)
representation and the leak-resistant arithmetic on elliptic curves. These two techniques are …
representation and the leak-resistant arithmetic on elliptic curves. These two techniques are …
RNS arithmetic in 𝔽pk and application to fast pairing computation
S Duquesne - Journal of Mathematical Cryptology, 2011 - degruyter.com
In this work, we are interested in arithmetic on large prime field and their extensions of small
degree. We explain why it is very interesting to use RNS arithmetic for the base field 𝔽 p …
degree. We explain why it is very interesting to use RNS arithmetic for the base field 𝔽 p …
Residue systems efficiency for modular products summation: Application to Elliptic Curves Cryptography
JC Bajard, S Duquesne, M Ercegovac… - Advanced Signal …, 2006 - spiedigitallibrary.org
Residue systems of representation, like Residue Number Systems (RNS) for primary field
(GF (p)) or Trinomial Residue Arithmetic for binary field (GF (2 k)), are characterized by …
(GF (p)) or Trinomial Residue Arithmetic for binary field (GF (2 k)), are characterized by …
[PDF][PDF] Combining Montgomery ladder for elliptic curves defined over Fp and RNS representation
In this paper, we combine the RNS representation and the Montgomery ladder on elliptic
curves in Weierstrass form. These two techniques are relevant for implementation of elliptic …
curves in Weierstrass form. These two techniques are relevant for implementation of elliptic …
A residue approach of the finite fields arithmetics
JC Bajard - 2007 Conference Record of the Forty-First Asilomar …, 2007 - ieeexplore.ieee.org
Finite fields arithmetic is one of the challenges in current computer arithmetic. It occurs, in
particular, in cryptography where the needs increase with the evolution of the technologies …
particular, in cryptography where the needs increase with the evolution of the technologies …
[PDF][PDF] Useful Arithmetic for Cryptography
JC Bajard - 2013 - webusers.imj-prg.fr
Useful Arithmetic for Cryptography Page 1 Arithmetic and Cryptography 1/116 Useful Arithmetic
for Cryptography Jean Claude Bajard LIP6 - UPMC (Paris 6)/ CNRS France 8 Jul. 2013 Page …
for Cryptography Jean Claude Bajard LIP6 - UPMC (Paris 6)/ CNRS France 8 Jul. 2013 Page …
Efficient computation for pairing based cryptography: A state of the art
N El Mrabet - Theory and Practice of Cryptography and Network …, 2013 - books.google.com
Cryptographic protocols are divided in two main classes, symmetric systems where keys are
secret and asymmetric approaches with public keys. The security of this second category is …
secret and asymmetric approaches with public keys. The security of this second category is …