1 research outputs found
Implementation and analysis of the generalised new Mersenne number transforms for encryption
PhD ThesisEncryption is very much a vast subject covering myriad techniques to conceal
and safeguard data and communications. Of the techniques that are available,
methodologies that incorporate the number theoretic transforms (NTTs) have gained
recognition, specifically the new Mersenne number transform (NMNT). Recently, two
new transforms have been introduced that extend the NMNT to a new generalised
suite of transforms referred to as the generalised NMNT (GNMNT). These two
new transforms are termed the odd NMNT (ONMNT) and the odd-squared NMNT
(O2NMNT).
Being based on the Mersenne numbers, the GNMNTs are extremely versatile with
respect to vector lengths. The GNMNTs are also capable of being implemented
using fast algorithms, employing multiple and combinational radices over one or
more dimensions. Algorithms for both the decimation-in-time (DIT) and -frequency
(DIF) methodologies using radix-2, radix-4 and split-radix are presented, including
their respective complexity and performance analyses.
Whilst the original NMNT has seen a significant amount of research applied to it
with respect to encryption, the ONMNT and O2NMNT can utilise similar techniques
that are proven to show stronger characteristics when measured using established
methodologies defining diffusion. Analyses in diffusion using a small but reasonably
sized vector-space with the GNMNTs will be exhaustively assessed and a comparison
with the Rijndael cipher, the current advanced encryption standard (AES) algorithm,
will be presented that will confirm strong diffusion characteristics.
Implementation techniques using general-purpose computing on graphics processing
units (GPGPU) have been applied, which are further assessed and discussed. Focus
is drawn upon the future of cryptography and in particular cryptology, as a
consequence of the emergence and rapid progress of GPGPU and consumer based
parallel processing