We present an algorithm that by using the and 1 Frobenius operators concurrently allows us to obt... more We present an algorithm that by using the and 1 Frobenius operators concurrently allows us to obtain a parallelized version of the classical -and-add scalar multiplication algorithm for Koblitz elliptic curves. Furthermore, we report suitable irreducible polynomials that lead to efficient implementations of both and 1 , thus showing that our algorithm can be effectively applied on all the NIST-recommended curves. We also present design details of software and hardware implementations of our procedure. In a two-processor workstation software implementation, we report experimental data showing that our parallel algorithm is able to achieve a speedup factor of almost 2 when compared with the standard sequential point multiplication. In our hardware implementation, the parallel version yields a more modest acceleration of 17% when compared with the traditional point multiplication algorithm. Although the focus is on Koblitz curves, analogous strategies are discussed for other curves, in...
Communications in Computer and Information Science, 2017
The implementation of the RSA private operation tends to be expensive since its computationally c... more The implementation of the RSA private operation tends to be expensive since its computationally complexity is cubic with respect to the bit-size of its private key. As a consequence, considerable effort has been put into optimizing this operation. In this work, we present a parallel implementation of the RSA private operation using the Single Instruction Multiple Thread (SIMT) threading model of Graphics Processor Unit (GPU) platforms. The underlying modular arithmetic is performed by means of the Residue Number System (RNS) representation. By combining these two approaches, we present a GPU software library that achieves high-speed timings for the RSA private operation when using 1024-, 2048- and 3072-bit secret keys.
... Jonathan Taverne · Armando Faz-Hernández · Diego F. Aranha · Francisco Rodríguez-Henríquez · ... more ... Jonathan Taverne · Armando Faz-Hernández · Diego F. Aranha · Francisco Rodríguez-Henríquez · Darrel Hankerson · Julio López ... One of the most basic methods for computing a scalar multiplication is based on a double-and-add variant of Horner's rule. ...
We present an algorithm that by using the and 1 Frobenius operators concurrently allows us to obt... more We present an algorithm that by using the and 1 Frobenius operators concurrently allows us to obtain a parallelized version of the classical -and-add scalar multiplication algorithm for Koblitz elliptic curves. Furthermore, we report suitable irreducible polynomials that lead to efficient implementations of both and 1 , thus showing that our algorithm can be effectively applied on all the NIST-recommended curves. We also present design details of software and hardware implementations of our procedure. In a two-processor workstation software implementation, we report experimental data showing that our parallel algorithm is able to achieve a speedup factor of almost 2 when compared with the standard sequential point multiplication. In our hardware implementation, the parallel version yields a more modest acceleration of 17% when compared with the traditional point multiplication algorithm. Although the focus is on Koblitz curves, analogous strategies are discussed for other curves, in...
Communications in Computer and Information Science, 2017
The implementation of the RSA private operation tends to be expensive since its computationally c... more The implementation of the RSA private operation tends to be expensive since its computationally complexity is cubic with respect to the bit-size of its private key. As a consequence, considerable effort has been put into optimizing this operation. In this work, we present a parallel implementation of the RSA private operation using the Single Instruction Multiple Thread (SIMT) threading model of Graphics Processor Unit (GPU) platforms. The underlying modular arithmetic is performed by means of the Residue Number System (RNS) representation. By combining these two approaches, we present a GPU software library that achieves high-speed timings for the RSA private operation when using 1024-, 2048- and 3072-bit secret keys.
... Jonathan Taverne · Armando Faz-Hernández · Diego F. Aranha · Francisco Rodríguez-Henríquez · ... more ... Jonathan Taverne · Armando Faz-Hernández · Diego F. Aranha · Francisco Rodríguez-Henríquez · Darrel Hankerson · Julio López ... One of the most basic methods for computing a scalar multiplication is based on a double-and-add variant of Horner's rule. ...
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Papers by Francisco Henríquez