An improved public key cryptography based on the elliptic curve
Elliptic curve cryptography offers two major benefits over RSA: more security per bit, and a suitable key size for hardware and modern communication. Thus, this results to smaller size of public key certificates, lower power requirements and smaller hardware processors. Three major approaches ar...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English English |
| Published: |
2002
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/8681/1/FSKTM_2002_2%20IR.pdf |
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| Summary: | Elliptic curve cryptography offers two major benefits over RSA: more security
per bit, and a suitable key size for hardware and modern communication. Thus, this
results to smaller size of public key certificates, lower power requirements and
smaller hardware processors.
Three major approaches are used in this dissertation to enhance the elliptic curve
cryptsystems: reducing the number of the elliptic curve group arithmetic operations,
speeding up the underlying finite field operations and reducing the size of the
transited parameters. A new addition formula in the projective coordinate is
introduced, where the analysis for this formula shows that the number of
multiplications over the finite field is reduced to nine general field element
multiplications. Thus this reduction will speed up the computation of adding two
points on the elliptic curve by 11 percent. Moreover, the new formula can be used
more efficiently when it is combined with the suggested sparse elements algorithms. To speed up the underlying finite field operations, several new algorithms are
introduced namely: selecting random sparse elements algorithm, finding sparse base
points, sparse multiplication over polynomial basis, and sparse multiplication over
normal basis. The complexity analysis shows that whenever the sparse techniques
are used, the improvement rises to 33 percent compared to the standard projective
coordinate formula and improvement of 38 percent compared to affine coordinate. A
new algorithm to compress and decompress the sparse elements algorithms are
introduced to reduce the size of the transited parameters.
The enhancements are applied on three protocols and two applications. The
protocols are Diffie-Hellman, ELGamal and elliptic curve digital signature. In these
protocols the speed of encrypting, decrypting and signing the message are increased
by 23 to 38 percent. Meanwhile, the size of the public keys are reduced by 37 to 48
percent. The improved algorithms are applied to the on-line and off-line electronic
payments systems, which lead to probably the best solution to reduce the objects
size and enhance the performance in both systems. |
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