TY - BOOK

T1 - Curves, Codes, and Cryptography

AU - Peters, Christiane

A2 - Lange, Tanja

A2 - Bernstein, Daniel J.

PY - 2011

Y1 - 2011

N2 - Elliptic curves and error-correcting codes are the mathematical objects investigated
in this thesis for cryptographic applications. The main focus lies on public-key cryptography
but also a code-based hash function is investigated. Public-key cryptography
was invented by Diffie and Hellman [DH76] in 1976 with the goal to remove
the need for in-person meetings or trusted couriers to exchange secret keys. While
symmetric cryptography uses the same key for encryption and decryption, publickey
cryptography uses a key pair consisting of a public key used for encryption and
a private key used for decryption. In order to generate lots of possible key pairs
mathematical one-way functions are used —functions which are easy to compute
but hard to invert. In practice a sender can efficiently compute a ciphertext given
the public key, but only the holder of the private key can use the hidden information
for decryption. Parameters for public-key cryptography need to be chosen in a way
that encryption and decryption can be carried out very fast. Simultaneously, those
parameters have to guarantee that it is computationally infeasible to retrieve the
original message from the ciphertext, or even worse, the private key from the public
key.
Parameters for cryptography are chosen to provide b-bit security against the best
attack known. This means that given the public key and public system parameters
it takes at least 2b bit operations to retrieve the original message from a given
ciphertext; or in the context of the hash function that it takes at least 2b bit operations
to find a collision. The encryption and decryption algorithms in this thesis are
mostly text-book versions. Understanding the underlying mathematical problems
and structures is a fundamental object of this thesis. This thesis does not investigate
protocols trying to provide security against malicious attackers who exploit
(partial) knowledge on e.g., ciphertexts or private keys. Those protocols can be
added as another layer to strengthen the security of the schemes investigated here.

AB - Elliptic curves and error-correcting codes are the mathematical objects investigated
in this thesis for cryptographic applications. The main focus lies on public-key cryptography
but also a code-based hash function is investigated. Public-key cryptography
was invented by Diffie and Hellman [DH76] in 1976 with the goal to remove
the need for in-person meetings or trusted couriers to exchange secret keys. While
symmetric cryptography uses the same key for encryption and decryption, publickey
cryptography uses a key pair consisting of a public key used for encryption and
a private key used for decryption. In order to generate lots of possible key pairs
mathematical one-way functions are used —functions which are easy to compute
but hard to invert. In practice a sender can efficiently compute a ciphertext given
the public key, but only the holder of the private key can use the hidden information
for decryption. Parameters for public-key cryptography need to be chosen in a way
that encryption and decryption can be carried out very fast. Simultaneously, those
parameters have to guarantee that it is computationally infeasible to retrieve the
original message from the ciphertext, or even worse, the private key from the public
key.
Parameters for cryptography are chosen to provide b-bit security against the best
attack known. This means that given the public key and public system parameters
it takes at least 2b bit operations to retrieve the original message from a given
ciphertext; or in the context of the hash function that it takes at least 2b bit operations
to find a collision. The encryption and decryption algorithms in this thesis are
mostly text-book versions. Understanding the underlying mathematical problems
and structures is a fundamental object of this thesis. This thesis does not investigate
protocols trying to provide security against malicious attackers who exploit
(partial) knowledge on e.g., ciphertexts or private keys. Those protocols can be
added as another layer to strengthen the security of the schemes investigated here.

M3 - Ph.D. thesis

SN - 978-90-386-2476-1

BT - Curves, Codes, and Cryptography

PB - Universiteit Eindhoven

CY - Eindhoven

ER -