Post-Quantum Cryptography

Publication: ResearchPh.D. thesis – Annual report year: 2011

Standard

Post-Quantum Cryptography. / Gauthier Umana, Valérie; Knudsen, Lars Ramkilde (Supervisor); Leander, Gregor (Supervisor).

Kgs. Lyngby, Denmark : Technical University of Denmark (DTU), 2011. 156 p.

Publication: ResearchPh.D. thesis – Annual report year: 2011

Harvard

Gauthier Umana, V, Knudsen, LR & Leander, G 2011, Post-Quantum Cryptography. Ph.D. thesis, Technical University of Denmark (DTU), Kgs. Lyngby, Denmark.

APA

Gauthier Umana, V., Knudsen, L. R., & Leander, G. (2011). Post-Quantum Cryptography. Kgs. Lyngby, Denmark: Technical University of Denmark (DTU).

CBE

Gauthier Umana V, Knudsen LR, Leander G 2011. Post-Quantum Cryptography. Kgs. Lyngby, Denmark: Technical University of Denmark (DTU). 156 p.

MLA

Gauthier Umana, Valérie, Lars Ramkilde Knudsen, and Gregor Leander Post-Quantum Cryptography Kgs. Lyngby, Denmark: Technical University of Denmark (DTU). 2011.

Vancouver

Gauthier Umana V, Knudsen LR, Leander G. Post-Quantum Cryptography. Kgs. Lyngby, Denmark: Technical University of Denmark (DTU), 2011. 156 p.

Author

Gauthier Umana, Valérie; Knudsen, Lars Ramkilde (Supervisor); Leander, Gregor (Supervisor) / Post-Quantum Cryptography.

Kgs. Lyngby, Denmark : Technical University of Denmark (DTU), 2011. 156 p.

Publication: ResearchPh.D. thesis – Annual report year: 2011

Bibtex

@phdthesis{91e57b9fa4894b5581295dfd6985b7f7,
title = "Post-Quantum Cryptography",
publisher = "Technical University of Denmark (DTU)",
author = "{Gauthier Umana}, Valérie and Knudsen, {Lars Ramkilde} and Gregor Leander",
year = "2011",

}

RIS

TY - BOOK

T1 - Post-Quantum Cryptography

A1 - Gauthier Umana,Valérie

AU - Gauthier Umana,Valérie

A2 - Knudsen,Lars Ramkilde

A2 - Leander,Gregor

ED - Knudsen,Lars Ramkilde

ED - Leander,Gregor

PB - Technical University of Denmark (DTU)

PY - 2011

Y1 - 2011

N2 - The security of almost all the public-key cryptosystems used in practice depends on the fact that the prime factorization of a number and the discrete logarithm are hard problems to solve. In 1994, Peter Shor found a polynomial-time algorithm which solves these two problems using quantum computers. The public key cryptosystems that can resist these emerging attacks are called quantum resistant or post-quantum cryptosystems. There are mainly four classes of public-key cryptography that are believed to resist classical and quantum attacks: code-based cryptography, hash-based cryptography, lattice-based cryptography and multivariate public-key cryptography. In this thesis, we focus on the rst two classes. In the rst part, we introduce coding theory and give an overview of code-based cryptography. The main contribution is an attack on two promising variants of McEliece's cryptosystem, based on quasi-cyclic alternant codes and quasi-dyadic codes (joint work with Gregor Leander). We also present a deterministic polynomial-time algorithm to solve the Goppa Code Distinguisher problem for high rate codes (joint work with Jean-Charles Faugere, Ayoub Otmani, Ludovic Perret and Jean-Pierre Tillich). In the second part, we rst give an overview of hash based signature schemes. Their security is based on the collision resistance of a hash function and is a good quantum resistant alternative to the used signature schemes. We show that several existing proposals of how to make multiple-time signature schemes are not any better than using existing one-time signature schemes a multiple number of times. We propose a new variant of the classical one-time signature schemes based on (near-)collisions resulting in two-time signature schemes. We also give a new, simple and ecient algorithm for traversing a tree in tree-based signature schemes (joint work with Lars R. Knudsen and Sren S. Thomsen).

AB - The security of almost all the public-key cryptosystems used in practice depends on the fact that the prime factorization of a number and the discrete logarithm are hard problems to solve. In 1994, Peter Shor found a polynomial-time algorithm which solves these two problems using quantum computers. The public key cryptosystems that can resist these emerging attacks are called quantum resistant or post-quantum cryptosystems. There are mainly four classes of public-key cryptography that are believed to resist classical and quantum attacks: code-based cryptography, hash-based cryptography, lattice-based cryptography and multivariate public-key cryptography. In this thesis, we focus on the rst two classes. In the rst part, we introduce coding theory and give an overview of code-based cryptography. The main contribution is an attack on two promising variants of McEliece's cryptosystem, based on quasi-cyclic alternant codes and quasi-dyadic codes (joint work with Gregor Leander). We also present a deterministic polynomial-time algorithm to solve the Goppa Code Distinguisher problem for high rate codes (joint work with Jean-Charles Faugere, Ayoub Otmani, Ludovic Perret and Jean-Pierre Tillich). In the second part, we rst give an overview of hash based signature schemes. Their security is based on the collision resistance of a hash function and is a good quantum resistant alternative to the used signature schemes. We show that several existing proposals of how to make multiple-time signature schemes are not any better than using existing one-time signature schemes a multiple number of times. We propose a new variant of the classical one-time signature schemes based on (near-)collisions resulting in two-time signature schemes. We also give a new, simple and ecient algorithm for traversing a tree in tree-based signature schemes (joint work with Lars R. Knudsen and Sren S. Thomsen).

BT - Post-Quantum Cryptography

ER -