Hélder Gonçalves | Universidade do Minho (original) (raw)
Address: Braga, Distrito de Braga, Portugal
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Teaching Documents by Hélder Gonçalves
—Lattice-based cryptography methods are well known primitives from the asymmetric cryptographic p... more —Lattice-based cryptography methods are well known primitives from the asymmetric cryptographic primitives set. Although widely studied for decades they have gained new notoriety in the last years because it is believe in the field of cryptography that these methods can withstand attacks by upcoming quantum computers. This paper describes how we optimized the Enumeration algorithm's serial code and then we suggest a new way to parallelize it using PThreads. The results shown in the results section are very promising and show that we can obtain significant performance improvements over the said implementation.
Thesis Chapters by Hélder Gonçalves
The security of most digital systems is under serious threats due to major technology breakthroug... more 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-Lenstra-Lovász (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.
—Lattice-based cryptography methods are well known primitives from the asymmetric cryptographic p... more —Lattice-based cryptography methods are well known primitives from the asymmetric cryptographic primitives set. Although widely studied for decades they have gained new notoriety in the last years because it is believe in the field of cryptography that these methods can withstand attacks by upcoming quantum computers. This paper describes how we optimized the Enumeration algorithm's serial code and then we suggest a new way to parallelize it using PThreads. The results shown in the results section are very promising and show that we can obtain significant performance improvements over the said implementation.
The security of most digital systems is under serious threats due to major technology breakthroug... more 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-Lenstra-Lovász (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.