On the efficiency of lattice-based cryptographic schemes on graphical processing unit

Download

index.pdf

Date

2016

Author

Yüce Tok, Zaliha

Metadata

Show full item record

Item Usage Stats

145
views

71
downloads

Lattice-based cryptography, a quantum-resistant public key alternative, has received a lot of attention due to the asymptotic efficiency. However, there is a bottleneck to get this advantage on practice: scheme-based arithmetic operations and platform-based implementations. In this thesis, we discuss computational aspects of lattice-based cryptographic schemes focused on NTRU and GLP in view of the time complexity on both CPUs and Graphical Processing Units (GPU). We focus on the optimization of polynomial multiplication methods both on theoretical and implementation point of view. We propose a modified version of interleaved Montgomery modular multiplication algorithm for ideal lattices, sparse polynomial multiplication and its sliding window version for efficient implementations. We show that with the proposed algorithms we significantly improve the performance results of lattice-based signature schemes. We also implement parallelized version of well known polynomial multiplication algorithms such as schoolbook method, NTT by using CUDA and provide a library for selected lattice-based signature schemes on a GPU.

Subject Keywords

Graphics processing units., Cryptography., Lattice theory., Polynomials.

URI

http://etd.lib.metu.edu.tr/upload/12620635/index.pdf
https://hdl.handle.net/11511/26176

Collections

Graduate School of Applied Mathematics, Thesis

Suggestions

OpenMETU
Core

Analysis of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber Aksoy, Berkin; Cenk, Murat (2022-01-01) Since the beginning of the National Institute of Standards and Technology (NIST), The Post-Quantum Cryptog-raphy (PQC) Standardization Process, efficient implementations of lattice-based algorithms have been studied extensively. Lattice-based NIST PQC finalists use polynomial or matrix-vector multiplications on the ring with type Zq [x]/f(x). For convenient ring types, Number Theoretic Transform (NTT) can be used to perform multiplications as done in Crystals-KYBER among the finalists of the NIST PQC Standa...
On some cryptographic properties of Rijndael Kavut, S; Yucel, MD (2001-01-01) We examine diffusion properties of Rijndael which has been selected by US National Institute of Standards and Technology (NIST) for the proposed Advanced Encryption Standard (AES). Since the s-box of Rijndael applies a nonlinear transformation operating on each byte of the intermediate cipher result independently, its characteristics have significant effects on the strength of the entire system. The characteristics of Rijndael's s-box are investigated for the criteria of avalanche, strict avalanche, bit ind...
Some characterizations of generalized s-plateaued functions Çelik, Emircan; Özbudak, Ferruh; Department of Cryptography (2017) Plateaued functions play important role in cryptography because of their various desirable cryptographic features. Due to this characteristics they have been widely studied in the literature. This studies include p-ary functions and some generalizations of the boolean functions. In this thesis, we present some of this important work and show that plateaued functions can be generalized much more general framework naturally. Characterizations of generalized plateaued functions using Walsh power moments are al...
Analyzes of Block Recombination and Lazy Interpolation Methods and Their Applications to Saber Aksoy, Berkin; Cenk, Murat; Department of Cryptography (2022-2-28) Since the beginning of the National Institute of Standards and Technology (NIST), The Post-Quantum Cryptography (PQC) Standardization Process, efficient implementations of lattice-based algorithms have been studied extensively. Lattice-based NIST PQC finalists use polynomial or matrix-vector multiplications on the ring with type {Z}_{q}[x] / f(x). For convenient ring types, Number Theoretic Transform (NTT) can be used to perform multiplications as done in Crystals-KYBER among the finalists of the NIST PQC S...
An efficient RSA public key encryption scheme Aboud, Sattar J.; AL-Fayoumi, Mohammad A.; Al-Fayoumi, Mustafa; Jabbar, Haidar S. (2008-04-09) In this paper, we propose an efficient RSA public key encryption scheme, which is an improved version of original RSA scheme. The proposed RSA encryption scheme is based on linear group over the ring of integer mod a composite modulus n which is the product of two distinct prime numbers. In the proposed scheme the original message and the encrypted message are h x h square matrices with entities in z(n) indicated via l(h,z(n)). Since the original RSA Scheme is a block cipher in which the original message an...

Citation Formats

Z. Yüce Tok, “On the efficiency of lattice-based cryptographic schemes on graphical processing unit,” Ph.D. - Doctoral Program, Middle East Technical University, 2016.