843 research outputs found
A Novel Pseudo-Random Number Generator Based on Multi-Objective Optimization for Image-Cryptographic Applications
Pseudo-random number generators (PRNGs) play an important role to ensure the
security and confidentiality of image cryptographic algorithms. Their primary
function is to generate a sequence of numbers that possesses unpredictability
and randomness, which is crucial for the algorithms to work effectively and
provide the desired level of security. However, traditional PRNGs frequently
encounter limitations like insufficient randomness, predictability, and
vulnerability to cryptanalysis attacks. To overcome these limitations, we
propose a novel method namely an elliptic curve genetic algorithm (ECGA) for
the construction of an image-dependent pseudo-random number generator (IDPRNG)
that merges elliptic curves (ECs) and a multi-objective genetic algorithm
(MOGA). The ECGA consists of two primary stages. First, we generate an EC-based
initial sequence of random numbers using pixels of a plain-image and parameters
of an EC, that depart from traditional methods of population initialization. In
our proposed approach, the image itself serves as the seed for the initial
population in the genetic algorithm optimization, taking into account the
image-dependent nature of cryptographic applications. This allows the PRNG to
adapt its behavior to the unique characteristics of the input image, leading to
enhanced security and improved resistance against differential attacks.
Furthermore, the use of a good initial population reduces the number of
generations required by a genetic algorithm, which results in decreased
computational cost. In the second stage, we use well-known operations of a
genetic algorithm to optimize the generated sequence by maximizing a
multi-objective fitness function that is based on both the information entropy
and the period of the PRNG. By combining elliptic curves and genetic
algorithms, we enhance the randomness and security of the ECGA.Comment: Keywords: Pseudo-random number generator, Elliptic curve, Genetic
algorithm, Multi-objective optimizatio
Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves
This paper proposes a pseudorandom sequence generator for stream ciphers based on elliptic curves (EC). A detailed analysis of various EC based random number generators available in the literature is done and a new method is proposed such that it addresses the drawbacks of these schemes. Statistical analysis of the proposed method is carried out using the NIST (National Institute of Standards and Technology) test suite and it is seen that the sequence exhibits good randomness properties. The linear complexity analysis shows that the system has a linear complexity equal to the period of the sequence which is highly desirable. The statistical complexity and security against known plain text attack are also analysed. A comparison of the proposed method with other EC based schemes is done in terms of throughput, periodicity, and security, and the proposed method outperforms the methods in the literature. For resource constrained applications where a highly secure key exchange is essential, the proposed method provides a good option for encryption by time sharing the point multiplication unit for EC based key exchange. The algorithm and architecture for implementation are developed in such a way that the hardware consumed in addition to point multiplication unit is much less
A low-memory algorithm for finding short product representations in finite groups
We describe a space-efficient algorithm for solving a generalization of the
subset sum problem in a finite group G, using a Pollard-rho approach. Given an
element z and a sequence of elements S, our algorithm attempts to find a
subsequence of S whose product in G is equal to z. For a random sequence S of
length d log_2 n, where n=#G and d >= 2 is a constant, we find that its
expected running time is O(sqrt(n) log n) group operations (we give a rigorous
proof for d > 4), and it only needs to store O(1) group elements. We consider
applications to class groups of imaginary quadratic fields, and to finding
isogenies between elliptic curves over a finite field.Comment: 12 page
- …