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*Advanced Topics in Public-Key Encryption
Published in Jonathan Katz, Yehuda Lindell, Introduction to Modern Cryptography, 2020
The RSA and Rabin trapdoor permutations appear quite similar, with squaring in the case of Rabin corresponding to taking e = 2 in the case of RSA. (Of course, 2 is not relatively prime to ϕ(N) and so Rabin is not a special case of RSA.) In terms of the security offered by each construction, hardness of computing modular square roots is equivalent to hardness of factoring, whereas hardness of solving the RSA problem is not known to be implied by the hardness of factoring. The Rabin trapdoor permutation is thus based on a potentially weaker assumption: it is theoretically possible that someone might develop an efficient algorithm for solving the RSA problem, yet computing square roots will remain hard. Or, someone may develop an algorithm that solves the RSA problem faster than known factoring algorithms. Lemma 15.35 ensures, however, that computing square roots modulo N can never be much faster than the best available algorithm for factoring N.
A hybrid meta-heuristic approach for optimization of routing and spectrum assignment in Elastic Optical Network (EON)
Published in Enterprise Information Systems, 2021
The many different researchers proposed RSA algorithms based on the ILP model (Walkowiak and Klinkowski 2013; Yang et al. 2018; Yaghubi-Namaad, Rahbar, and Alizadeh 2018, 2018) in different scenarios but it is hard to find the feasible solution when the optical network structure is complex or large. In (Wang et al. 2014; Chen et al. 2015; Chatterjee, Fadini, and Oki 2016; Dos Santos et al. 2017; Afsharlar et al. 2017; Guo et al. 2017; Singh and Jukan 2017) proposed heuristic algorithms for RSA problem to find near-optimal solutions within the appropriate time. Heuristic algorithms produce attainable solutions with limited time but failed to provide the best solution. The Meta-heuristic algorithms are more powerful and capable to achieve better solutions compared to heuristic algorithms. The Meta-heuristic algorithms are iteratively executed until optimal solutions are achieved. This paper proposes a hybrid Meta-heuristic algorithm to allocate minimum spectrum guard and minimize fragmentation complexity at various dynamic bit rates.
An offline scheme for reducing cost of protection in all-optical WDM mesh networks with fast recovery
Published in International Journal of Parallel, Emergent and Distributed Systems, 2019
Vishal Dey, Abhishek Bandyopadhyay, Uma Bhattacharya, Monish Chatterjee
No matter which protection scheme is used (SPP or p-cycle or FIPP p-cycle) the algorithms or strategies used in flexible EONs are not directly comparable with that of fixed grid WDM optical networks. This is due to the fact that allocation of working and protection paths in WDM networks depends on solving the RWA problem whereas, for EONs employing O-OFDM, the allocation depends on solving the RSA problem.