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Montgomery Modular Arithmetic over Gaussian Integers
- Source :
- 2020 24th International Conference on Information Technology (IT).
- Publication Year :
- 2020
- Publisher :
- IEEE, 2020.
-
Abstract
- The Montgomery multiplication is an efficient method for modular arithmetic. Typically, it is used for modular arithmetic over integer rings to prevent the expensive inversion for the modulo reduction. In this work, we consider modular arithmetic over rings of Gaussian integers. Gaussian integers are subset of the complex numbers such that the real and imaginary parts are integers. In many cases Gaussian integer rings are isomorphic to ordinary integer rings. We demonstrate that the concept of the Montgomery multiplication can be extended to Gaussian integers. Due to independent calculation of the real and imaginary parts, the computation complexity of the multiplication is reduced compared with ordinary integer modular arithmetic. This concept is suitable for coding applications as well as for asymmetric key cryptographic systems, such as elliptic curve cryptography or the Rivest-Shamir-Adleman system.
- Subjects :
- Discrete mathematics
Modular arithmetic
Gaussian integer
business.industry
Modulo
020206 networking & telecommunications
Cryptography
02 engineering and technology
Public-key cryptography
symbols.namesake
Integer
0202 electrical engineering, electronic engineering, information engineering
symbols
020201 artificial intelligence & image processing
Hardware_ARITHMETICANDLOGICSTRUCTURES
Elliptic curve cryptography
business
Complex number
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- 2020 24th International Conference on Information Technology (IT)
- Accession number :
- edsair.doi...........e8019d872c38fb454b94aac95b6bfd13