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- Thomaz Oliveira, Julio López Hernandez, Diego F. Aranha, Francisco Rodríguez-Henríquez
- Journal of Cryptographic Engineering
- 2013

In this work, we present new arithmetic formulas for a projective version of the affine point representation $$(x,x+y/x),$$ ( x , x + y / x ) , for $$x\ne 0,$$ x ≠ 0 , which leads to an efficient… (More)

In this work we present the λ-coordinates, a new system for representing points in binary elliptic curves. We also provide efficient elliptic curve operations based on the new representation and… (More)

- Gora Adj, Alfred Menezes, Thomaz Oliveira, Francisco Rodríguez-Henríquez
- IACR Cryptology ePrint Archive
- 2013

In 2013, Joux and then Barbulescu et al. presented new algorithms for computing discrete logarithms in finite fields of small characteristic. Shortly thereafter, Adj et al. presented a concrete… (More)

- Gora Adj, Alfred Menezes, Thomaz Oliveira, Francisco Rodríguez-Henríquez
- IACR Cryptology ePrint Archive
- 2013

In 2013, Joux, and then Barbulescu, Gaudry, Joux and Thomé, presented new algorithms for computing discrete logarithms in finite fields of small and medium characteristic. We show that these new… (More)

- Thomaz Oliveira, Julio López Hernandez, Francisco Rodríguez-Henríquez
- Journal of Cryptographic Engineering
- 2017

In this survey paper, we present a careful analysis of the Montgomery ladder procedure applied to the computation of the constant-time point multiplication operation on elliptic curves defined over… (More)

- Gora Adj, Alfred Menezes, Thomaz Oliveira, Francisco Rodríguez-Henríquez
- IACR Cryptology ePrint Archive
- 2014

- Thomaz Oliveira, Diego F. Aranha, Julio López Hernandez, Francisco Rodríguez-Henríquez
- Selected Areas in Cryptography
- 2014

In this paper we introduce new methods for computing constant-time variable-base point multiplications over the Galbraith-Lin-Scott (GLS) and the Koblitz families of elliptic curves. Using a… (More)

- Thomaz Oliveira, Julio López Hernandez, Francisco Rodríguez-Henríquez
- IACR Cryptology ePrint Archive
- 2016

In this work, we retake an old idea that Koblitz presented in his landmark paper [21], where he suggested the possibility of defining anomalous elliptic curves over the base field F4. We present a… (More)

- Thomaz Oliveira, Julio López Hernandez, Diego F. Aranha, Francisco Rodríguez-Henríquez
- IACR Cryptology ePrint Archive
- 2013

In this work we present the λ-coordinates, a new system for representing points in binary elliptic curves. We also provide efficient elliptic curve operations based on the new representation and… (More)

- Gora Adj, Alfred Menezes, Thomaz Oliveira, Francisco Rodríguez-Henríquez
- ACM Comm. Computer Algebra
- 2015

In 2013, Joux presented a new algorithm for solving the discrete logarithm problem in finite fields of small characteristic with a main novelty involving the resolution of bilinear equation systems.… (More)