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Normal Bases over Finite Fields
, 1993
"... Interest in normal bases over finite fields stems both from mathematical theory and practical applications. There has been a lot of literature dealing with various properties of normal bases (for finite fields and for Galois extension of arbitrary fields). The advantage of using normal bases to repr ..."
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Interest in normal bases over finite fields stems both from mathematical theory and practical applications. There has been a lot of literature dealing with various properties of normal bases (for finite fields and for Galois extension of arbitrary fields). The advantage of using normal bases to represent finite fields was noted by Hensel in 1888. With the introduction of optimal normal bases, large finite fields, that can be used in secure and e#cient implementation of several cryptosystems, have recently been realized in hardware. The present thesis studies various theoretical and practical aspects of normal bases in finite fields. We first give some characterizations of normal bases. Then by using linear algebra, we prove that F q n has a basis over F q such that any element in F q represented in this basis generates a normal basis if and only if some groups of coordinates are not simultaneously zero. We show how to construct an irreducible polynomial of degree 2 n with linearly i...
Eastern Heights
, 1999
"... I declare that the work submitted in this thesis is my own, except as acknowledged in the text and footnotes, and has not been previously submitted for a degree at the University of Queensland or any other institution. Yours sincerely, ..."
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I declare that the work submitted in this thesis is my own, except as acknowledged in the text and footnotes, and has not been previously submitted for a degree at the University of Queensland or any other institution. Yours sincerely,
A New Approach for Secured Transition using Prime Field Elliptic Curve Cryptography System
"... The demands of secured electronic transactions are increasing rapidly. Prime Field Elliptic curve cryptosystems (PFECC) are becoming most popular because of the reduced number of key bits required in comparison to other cryptosystems. PFECC is emerging as an attractive alternative to traditional pub ..."
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The demands of secured electronic transactions are increasing rapidly. Prime Field Elliptic curve cryptosystems (PFECC) are becoming most popular because of the reduced number of key bits required in comparison to other cryptosystems. PFECC is emerging as an attractive alternative to traditional publickey cryptosystems. PFECC offers equivalent security with smaller key sizes resulting in faster computations, lower power consumption, as well as memory and bandwidth savings. While these characteristics make PFECC especially appealing for small devices, they can also alleviate the computational burden on secure web servers.
Monash University
"... TCP Transport layer protocols provide for end to end communication between two or more hosts. The Standard TCP (TCP Reno) is not suitable for high bandwidth, large RTT networks because of its low performance in high throughput. Standard TCP is a reliable transport protocol that is well tuned to perf ..."
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TCP Transport layer protocols provide for end to end communication between two or more hosts. The Standard TCP (TCP Reno) is not suitable for high bandwidth, large RTT networks because of its low performance in high throughput. Standard TCP is a reliable transport protocol that is well tuned to perform in traditional networks. TCP performance depends upon the product of the transfer rate and the roundtrip delay. TCP survived the days of low bandwidth, high latency, and high error rates. But for several reasons it is not able to cope efficiently with the evolving new environment. Several experiments and analysis have shown that this protocol is not suitable for huge data transfer in high bandwidth environment such as Gigabit and highspeed long distance networks with large round trip time. This is because of its slow start and conservative congestion control mechanism. Our focus on introduction to new transport protocols FAST TCP is to improve performance when compared to standard TCP in low bandwidth or small RTT networks and much better than standard TCP in high bandwidth, large RTT networks. Grid Applications need immediate deployment of modified transport protocols to utilize the huge bandwidth.