TY - GEN

T1 - Fully homomorphic encryption for parallel implementation of approximate methods for solving differential equations

AU - Vishnevsky, Artem K.

AU - Krendelev, Sergey F.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A parallel fully homomorphic encryption for rational numbers is developed in this paper. Parallelism of processing is achieved by using methods of modular arithmetic. Encryption is constructed by mapping the field of rational numbers onto a vector space. Two operations, namely addition and multiplication, are defined. Addition and multiplication tables are constructed, which ensures that a vector space is closed under these mathematical operations. We show the implementation of protected recursive computations in rings of the form ZM, M = m1m2…mk. We give a criterion of effective use of encryption for the numerical solution of the Cauchy problem. It is proved that the efficiency of encryption increases with increasing volumes and accuracy of computations.

AB - A parallel fully homomorphic encryption for rational numbers is developed in this paper. Parallelism of processing is achieved by using methods of modular arithmetic. Encryption is constructed by mapping the field of rational numbers onto a vector space. Two operations, namely addition and multiplication, are defined. Addition and multiplication tables are constructed, which ensures that a vector space is closed under these mathematical operations. We show the implementation of protected recursive computations in rings of the form ZM, M = m1m2…mk. We give a criterion of effective use of encryption for the numerical solution of the Cauchy problem. It is proved that the efficiency of encryption increases with increasing volumes and accuracy of computations.

KW - Chinese remainder theorem

KW - Cloud computations

KW - Differential equations

KW - Fully homomorphic encryption

KW - Modular arithmetic

KW - Numerical methods

KW - Parallel computations

KW - Secure computations

UR - http://www.scopus.com/inward/record.url?scp=85053197577&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-99673-8_9

DO - 10.1007/978-3-319-99673-8_9

M3 - Conference contribution

AN - SCOPUS:85053197577

SN - 9783319996721

T3 - Communications in Computer and Information Science

SP - 119

EP - 134

BT - Parallel Computational Technologies - 12th International Conference, PCT 2018, Revised Selected Papers

A2 - Sokolinsky, L

A2 - Zymbler, M

PB - Springer-Verlag GmbH and Co. KG

T2 - 12th International Scientific Conference on Parallel Computational Technologies, PCT 2018

Y2 - 2 April 2018 through 6 April 2018

ER -