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Simplified DES (SDES) was designed for educational purposes only, to help students learn about modern cryptanalytic techniques. SDES has similar structure and properties to DES, but has been simplified to make it much easier to perform encryption and decryption by hand with pencil and paper.
The most common form of SDEs in the literature is an ordinary differential equation with the right hand side perturbed by a term dependent on a white noise variable. In most cases, SDEs are understood as continuous time limit of the corresponding stochastic difference equations. This understanding of SDEs is ambiguous and must be complemented ...
The SDES method does not address the "end-to-end" media encryption. For example, if user A is talking to user B via a proxy P, SDES allows negotiation of keys between A and P or between B and P, but not between A and B. For end-to-end media security you must first establish a trust relationship with the other side.
One of the most studied SPDEs is the stochastic heat equation, [3] which may formally be written as = +, where is the Laplacian and denotes space-time white noise.Other examples also include stochastic versions of famous linear equations, such as the wave equation [4] and the Schrödinger equation.
An area that has benefited significantly from SDEs is mathematical biology. As many biological processes are both stochastic and continuous in nature, numerical methods of solving SDEs are highly valuable in the field. The graphic depicts a stochastic differential equation solved using the Euler-Maruyama method.
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Stochastic Differential Equations, Backward SDEs, Partial Differential Equations. Stochastic modeling and applied probability. Springer International Publishing Switzerland. Zhang, Jianfeng (2017). Backward stochastic differential equations. Probability theory and stochastic modeling. Springer New York, NY.
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