Parameter Selection for Server-Aided RSA Computation Schemes
IEEE Transactions on Computers
Speeding Up Secret Computations with Insecure Auxiliary Devices
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Security and Performance of Server-Aided RSA Computation Protocols
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
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CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
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Communications of the ACM
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EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
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TCC'05 Proceedings of the Second international conference on Theory of Cryptography
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IEEE Journal on Selected Areas in Communications
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In this paper, we present several methods of secure outsourcing of numerical and scientific computations. Current outsourcing techniques are inspired by the numerous problems in computational mathematics, where a solution is obtained in the form of an approximation. Examples of such problems can be found in the fields of economics, military, petroleum industry, and in other areas. Many of today's scientific and numerical problems require large computational resources; therefore, they can only be solved on supercomputers or by using the capabilities of the largest computing systems, such as grid technology, cloud, etc. We believe that it is imperative to improve the mathematical framework to enable secure outsourcing. Therefore, the main goal of this paper is to present different methods of finding approximate solutions to some equations solved by an external computer. To accomplish this, we chose certain classes of algebraic and differential equations because, in most cases, modern computing problems are reduced to solving such systems of equations (differential equations, linear programming, etc.). As an important application example we are presenting a specific applied problem related to geological exploration.