3 research outputs found
Cryptographic Pairings: Efficiency and DLP security
This thesis studies two important aspects of the use of pairings in cryptography, efficient
algorithms and security.
Pairings are very useful tools in cryptography, originally used for the cryptanalysis of
elliptic curve cryptography, they are now used in key exchange protocols, signature schemes
and Identity-based cryptography.
This thesis comprises of two parts: Security and Efficient Algorithms.
In Part I: Security, the security of pairing-based protocols is considered, with a thorough
examination of the Discrete Logarithm Problem (DLP) as it occurs in PBC. Results on the
relationship between the two instances of the DLP will be presented along with a discussion
about the appropriate selection of parameters to ensure particular security level.
In Part II: Efficient Algorithms, some of the computational issues which arise when using
pairings in cryptography are addressed. Pairings can be computationally expensive, so
the Pairing-Based Cryptography (PBC) research community is constantly striving to find
computational improvements for all aspects of protocols using pairings. The improvements
given in this section contribute towards more efficient methods for the computation of pairings,
and increase the efficiency of operations necessary in some pairing-based protocol
Constructing Tower Extensions for the implementation of Pairing-Based Cryptography
A cryptographic pairing evaluates as an element in an extension field, and the evaluation itself involves a considerable
amount of extension field arithmetic. It is recognised that organising the extension field as a ``tower\u27\u27 of subfield extensions has many
advantages. Here we consider criteria that apply when choosing the best towering construction, and the associated choice of
irreducible polynomials for the implementation of pairing-based cryptosystems. We introduce a method for automatically constructing efficient towers
for more congruency classes than previous methods, some of which allow faster arithmetic