Publicação
Towards an efficient lattice basis reduction implementation
| Resumo: | The security of most digital systems is under serious threats due to major technology breakthroughs we are experienced in nowadays. Lattice-based cryptosystems are one of the most promising post-quantum types of cryptography, since it is believed to be secure against quantum computer attacks. Their security is based on the hardness of the Shortest Vector Problem and Closest Vector Problem. Lattice basis reduction algorithms are used in several fields, such as lattice-based cryptography and signal processing. They aim to make the problem easier to solve by obtaining shorter and more orthogonal basis. Some case studies work with numbers with hundreds of digits to ensure harder problems, which require Multiple Precision (MP) arithmetic. This dissertation presents a novel integer representation for MP arithmetic and the algorithms for the associated operations, MpIM. It also compares these implementations with other libraries, such as GNU Multiple Precision Arithmetic Library, where our experimental results display a similar performance and for some operations better performances. This dissertation also describes a novel lattice basis reduction module, LattBRed, which included a novel efficient implementation of the Qiao’s Jacobi method, a Lenstra-LenstraLovasz (LLL) algorithm and associated parallel implementations, a parallel variant of the ´ Block Korkine-Zolotarev (BKZ) algorithm and its implementation and MP versions of the the Qiao’s Jacobi method, the LLL and BKZ algorithms. Experimental performances measurements with the set of implemented modifications of the Qiao’s Jacobi method show some performance improvements and some degradations but speedups greater than 100 in Ajtai-type bases. |
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| Autores principais: | Gonçalves, Hélder José Alves |
| Assunto: | Engenharia e Tecnologia::Engenharia Eletrotécnica, Eletrónica e Informática |
| Ano: | 2016 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | The security of most digital systems is under serious threats due to major technology breakthroughs we are experienced in nowadays. Lattice-based cryptosystems are one of the most promising post-quantum types of cryptography, since it is believed to be secure against quantum computer attacks. Their security is based on the hardness of the Shortest Vector Problem and Closest Vector Problem. Lattice basis reduction algorithms are used in several fields, such as lattice-based cryptography and signal processing. They aim to make the problem easier to solve by obtaining shorter and more orthogonal basis. Some case studies work with numbers with hundreds of digits to ensure harder problems, which require Multiple Precision (MP) arithmetic. This dissertation presents a novel integer representation for MP arithmetic and the algorithms for the associated operations, MpIM. It also compares these implementations with other libraries, such as GNU Multiple Precision Arithmetic Library, where our experimental results display a similar performance and for some operations better performances. This dissertation also describes a novel lattice basis reduction module, LattBRed, which included a novel efficient implementation of the Qiao’s Jacobi method, a Lenstra-LenstraLovasz (LLL) algorithm and associated parallel implementations, a parallel variant of the ´ Block Korkine-Zolotarev (BKZ) algorithm and its implementation and MP versions of the the Qiao’s Jacobi method, the LLL and BKZ algorithms. Experimental performances measurements with the set of implemented modifications of the Qiao’s Jacobi method show some performance improvements and some degradations but speedups greater than 100 in Ajtai-type bases. |
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