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Low complexity word-level sequential normal basis multipliers
- Source :
- IEEE Transactions on Computers. 54:98-110
- Publication Year :
- 2005
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2005.
-
Abstract
- For efficient hardware implementation of finite field arithmetic units, the use of a normal basis is advantageous. In this paper, two classes of architectures for multipliers over the finite field GF(2/sup m/) are proposed. These multipliers are of sequential type, i.e., after receiving the coordinates of the two input field elements, they go through k, 1 /spl les/ k /spl les/ m, iterations (i.e., clock cycles) to finally yield all the coordinates of the product in parallel. The value of k depends on the word size w = /spl lceil/m/k/spl rceil/. For w > 1, these multipliers are highly area efficient and require fewer number of logic gates even when compared with the most area efficient multipliers available in the open literature. This makes the proposed multipliers suitable for applications where the value of m is large but space is of concern, e.g., resource constrained cryptographic systems. Additionally, if the field dimension m is composite, i.e., m = kn, then the extension of one class of the architectures yields a highly efficient multiplier over composite fields.
- Subjects :
- Discrete mathematics
Field (mathematics)
Type (model theory)
Theoretical Computer Science
Normal basis
Finite field
Computational Theory and Mathematics
Dimension (vector space)
Hardware and Architecture
Multiplier (economics)
Finite field arithmetic
Hardware_ARITHMETICANDLOGICSTRUCTURES
Arithmetic
Software
Word (computer architecture)
Mathematics
Subjects
Details
- ISSN :
- 00189340
- Volume :
- 54
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Computers
- Accession number :
- edsair.doi...........b1484713f8c0e337f10d577b0f384730