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- Francisco Rodríguez-Henríquez, Çetin Kaya Koç
- IEEE Trans. Computers
- 2003

The state-of-the-art Galois field GF ð2Þ multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally spaced polynomial (ESP). Unfortunately, there exist only a few… (More)

This paper describes the design of a fast software library for the computation of the optimal ate pairing on a Barreto–Naehrig elliptic curve. Our library is able to compute the optimal ate pairing over a 254-bit prime field Fp, in just 2.33 million of clock cycles on a single core of an Intel Core i7 2.8GHz processor, which implies that the pairing… (More)

This paper describes the design of a fast multi-core library for the cryptographic Tate pairing over supersingular elliptic curves. For the computation of the reduced modified Tate pairing over F3509 , we report calculation times of just 2.94 ms and 1.87 ms on the Intel Core2 and Intel Core i7 architectures, respectively. We also try to answer one important… (More)

Cryptographic solutions using software methods can be used for those security applications where data traffic is not too large and low encryption rate is tolerable. On the other hand, hardware methods offer high-speed solutions making them highly suitable for applications where data traffic is fast and large data is required to be encrypted in real time.… (More)

- Nareli Cruz Cortés, Francisco Rodríguez-Henríquez, Carlos A. Coello Coello
- IEEE Transactions on Evolutionary Computation
- 2008

This paper deals with the optimal computation of finite field exponentiation, which is a well-studied problem with many important applications in the areas of error-correcting codes and cryptography. It has been shown that the optimal computation of finite field exponentiation is a problem which is closely related to finding a suitable addition chain with… (More)

- Francisco Rodríguez-Henríquez, Guillermo Morales-Luna, Nazar Abbas Saqib, Nareli Cruz Cortés
- Des. Codes Cryptography
- 2006

In this contribution, we derive a novel parallel formulation of the standard Itoh-Tsujii algorithm for multiplicative inverse computation overGF(2m). The main building blocks used by our algorithm are: field multiplication, field squaring and field square root operators. It achieves its best performance when using a special class of irreducible trinomials,… (More)

We implement asymmetric pairings derived from KachisaSchaefer-Scott (KSS), Barreto-Naehrig (BN), and Barreto-Lynn-Scott (BLS) elliptic curves at the 192-bit security level. Somewhat surprisingly, we find pairings derived from BLS curves with embedding degree 12 to be the fastest for our serial as well as our parallel implementations. Our serial… (More)

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 algorithms render the finite field F36·509 = F33054 weak for discrete logarithm cryptography in the sense that discrete logarithms in this field can be computed… (More)

- Cuauhtemoc Mancillas-López, Debrup Chakraborty, Francisco Rodríguez-Henríquez
- IEEE Transactions on Computers
- 2007

Tweakable enciphering schemes are length-preserving block cipher modes of operation that provide a strong pseudorandom permutation. It has been suggested that these schemes can be used as the main building blocks for achieving in-place disk encryption. In the past few years, there has been an intense research activity toward constructing secure and… (More)

- 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 computation of the scalar multiplication operation over binary elliptic curves. A software implementation of our formulas applied to a binary Galbraith–Lin–Scott… (More)