|Title: Degree Reduction of Interval SB Curves|
|Author(s): O. Ismail|
|Pages: 1-5||Paper ID: 131504-9292-IJVIPNS-IJENS||Published: August, 2013|
Abstract: Ball basis was introduced for cubic polynomials by Ball, and was generalized for polynomials of higher degree by Said. An algorithmic approach to degree reduction of interval Said-Ball (SB) curve is presented in this paper. The four fixed Kharitonov's polynomials (four fixed SB curves) associated with the original interval SB curve are obtained. These four fixed SB curves are transformed into four fixed Bezier curves. The degree of the four fixed Bezier curves is reduced based on the matrix representations of the degree reduction process. The process of degree reductions k times are applied to the four fixed Bezier curves of degree n to obtain the four fixed Bezier curves of degree n-k without changing their shapes. The four fixed reduced Bezier curves are converted into SB curves of the same degree. Finally the reduced interval SB control points are obtained from the four fixed reduced SB control points. An illustrative example is included in order to demonstrate the effectiveness of the proposed method.
|Keywords: Image processing, CAGD, degree reduction, interval Said-Ball (SB) curve, interval Bezier curve.|
|Full Text (.pdf) | 467 KB|
|Title: Digital Image Confidentiality Depends upon Arnold Transformation and RC4 Algorithms|
|Author(s): Khalid Hamdnaalla, Abubaker Wahaballa, Osman Wahballa|
|Pages: 6-17||Paper ID: 135404-7575-IJVIPNS-IJENS||Published: August, 2013|
Abstract: With the development of digital image production and applications, digital image security has become very important in today’s world. This paper proposes image confidentiality relying on one spatial domain transformation (Arnold transformation) and one stream cipher algorithm (RC4). The paper has three phases; the first phase is the design and implementation of digital image scrambling using Arnold transformation based on best iteration. The second phase is the design and implementation of digital image encryption using RC4 stream cipher and the third phase makes use of both Arnold transform and RC4 algorithm based on best iteration which applies Arnold transform to scramble a digital image and then encrypt it using RC4. The input key to RC4 is generated using Blum Blum Shub (BBS) pseudo random bit generator algorithm. All phases are implemented using Matlab. Each phase is followed by some security evaluations. The security evaluations are presented by calculating a correlation coefficient and a security quality factor. The results show that for the same digital gray image, a correlation coefficient produced by Arnold transform based on best iteration is better than that produced by RC4; however an Arnold transform based on best iteration has a security quality factor of zero. Applying Arnold transform in scrambling before encrypting using RC4 gives a correlation coefficient as well as the Arnold transform in addition to the security quality factor better than encryption using RC4.
|Keywords: Algorithm, Arnold transformation, BBS, confidential, digital image, encryption, RC4 stream cipher and scrambling.|
|Full Text (.pdf) | 807 KB|