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- John Boxall, Nadia El Mrabet, Fabien Laguillaumie, Duc-Phong Le
- Pairing
- 2010

Miller’s algorithm is at the heart of all pairing-based cryptosystems since it is used in the computation of pairing such as that of Weil or Tate and their variants. Most of the optimizations of this algorithm involve elliptic curves of particular forms, or curves with even embedding degree, or having an equation of a special form. Other improvements… (More)

- Duc-Phong Le, Matthieu Rivain, Chik How Tan
- CT-RSA
- 2014

At CT-RSA 2009, a new principle to secure RSA (and modular/group exponentiation) against fault-analysis has been introduced by Rivain. The idea is to perform a so-called double exponentiation to compute a pair (md,mφ(N)−d) and then check that the output pair satisfies the consistency relation: m ·mφ(N)−d ≡ 1 mod N . The author then proposed an efficient… (More)

- Duc-Phong Le, Chik How Tan
- ICISC
- 2012

At Pairing 2010, Lauter et al’s analysis showed that Ate pairing computation in affine coordinates may be much faster than projective coordinates at high security levels. In this paper, we further investigate techniques to speed up Ate pairing computation in affine coordinates. On the one hand, we improve Ate pairing computation over elliptic curves… (More)

- Duc-Phong Le, Chao-Liang Liu
- Comput. J.
- 2011

In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a special forms to exploit a possible twist during Tate pairing… (More)

- Duc-Phong Le, Alexis Bonnecaze, Alban Gabillon
- Pairing
- 2009

A multisignature scheme allows a group of signers to cooperate to generate a compact signature on a common document. The length of the multisignature depends only on the security parameters of the signature schemes and not on the number of signers involved. The existing state-of-the-art multisignature schemes suffer either from impractical key setup… (More)

- Duc-Phong Le, Alexis Bonnecaze, Alban Gabillon
- ICISS
- 2008

The aim of timestamping systems is to provide a proof-ofexistence of a digital document at a given time. Such systems are important to ensure integrity and non-repudiation of digital data over time. Most of the existing timestamping schemes use the notions of round (a period of time) and round token (a single value aggregating the timestamping requests… (More)

- Duc-Phong Le
- IACR Cryptology ePrint Archive
- 2011

Ciet et al. proposed a very elegant method for trading inversions for multiplications when computing 2P + Q from given points P and Q on elliptic curves of Weierstrass form. In this paper we extend their method and present a fast algorithm for computing 4P with only one inversion in affine coordinates. Our algorithm is faster than two repeated doublings… (More)

Digital multisignatures improve security of digital signatures and reduce fraud by collusion. In this paper we first present a new secure signature scheme which is based on a variant of Strong Diffie-Hellman Assumption, called SDH2 assumption. Then, we extend this signature for a new multisignature scheme without interaction between users. Our proposed… (More)

- Duc-Phong Le, Chik How Tan
- IEEE Trans. Computers
- 2014

Since Edwards curves were introduced to elliptic curve cryptography by Bernstein and Lange in 2007, they have received a lot of attention due to their very fast group law operation. Pairing computation on such curves is slightly slower than on Weierstrass curves. However, in some pairing-based cryptosystems, they might require a number of scalar… (More)

- Duc-Phong Le, Chik How Tan, Michael Tunstall
- IACR Cryptology ePrint Archive
- 2015

In this paper, we present novel randomized techniques to enhance Montgomery powering ladder. The proposed techniques increase the resistance against side-channel attacks and especially recently published correlation collision attacks in the horizontal setting. The first of these operates by randomly changing state such that the difference between registers… (More)