In this paper, Cyclic Elliptic Curves of the form with order M is considered. A finite field GF(p) (p ≥ N, where N is the order of point P) is considered. Random sequence {k i } of integers is generated using Linear Feedback Shift Register (LFSR) over GF(p) for maximum period. Every element in sequence {k i } is mapped to k i P which is a point on Cyclic Elliptic Curve with co-ordinates say (x i , y i ). The sequence {k i P} is a random sequence of elliptic curve points. From the sequence (x i , y i ) several binary and non-binary sequences are derived and their randomness properties are investigated. The results are discussed. It is found that these sequences pass FIPS-140, NIST tests and exhibit good Hamming Correlation properties. These sequences find applications in Stream Cipher Systems. Here, Cyclic Elliptic Curve over GF(2 8 ) is chosen for analysis.
Researchers have put forward many variations of schemes for secret image sharing on grounds of visual cryptography and polynomials. The authors of this paper put forward a novel scheme for sharing multiple secret images with perfect reconstruction and authentication for cheating prevention. The perfect reconstruction of all shared secret images is obtained by applying polynomial-based encryption and decryption, and one-time authentication is done for all shared secret images by stacking the intelligible shares created by using extended visual cryptography. Properties' analysis, experimental results and comparisons are given to exhibit the potency of the scheme. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Residue Number Systems (RNS) based on ChineseRemainder Theorem (CRT) permits the representation of large integers in terms of combinations of smaller ones. The set of all integers from 0 to M-1 with RNS representation and component wise modular addition and multiplication constitutes direct sum of smaller commutative rings. Encryption and decryption algorithm based on the properties of direct sum of smaller rings offers distinct advantages over decimal or fixed radix arithmetic. In this paper representation of integer using RNS, is successfully utilized in additive, multiplicative and affine stream cipher systems.The property of the cipher system based on RNS number system allow speeding up the encryption / decryption algorithm, reduce the time complexity and provides immunity to side channel, algebraic, and known plain text attacks. In this paper, the characteristics of additive, multiplicative and affine stream cipher systems, the key generation, and encryption and decryption based on RNS number system representation are discussed.
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