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An RNS Montgomery modular multiplication algorithm
TLDR
The authors present a new RNS modular multiplication for very large operands based on Montgomery's method adapted to mixed radix, and is performed using a residue number system.
A High Speed Hough Transform Using CORDIC
TLDR
The pipelined CORDIC structure proposed in this paper can reach a high calculation speed using only adders, thus realizing the Hough Transform in real time, and more area efficient than a ROM and array-multiplier based implementation, capable of running at the same speed.
Modular multiplication and base extensions in residue number systems
TLDR
A new RNS modular multiplication for very large operands is presented, based on Montgomery's (1985) method adapted to residue arithmetic, which achieves an effect corresponding to a redundant high-radix implementation by choosing the moduli of the RNS system reasonably large.
High-radix modular multiplication for cryptosystems
  • Peter Kornerup
  • Computer Science, Mathematics
    Proceedings of IEEE 11th Symposium on Computer…
  • 29 June 1993
Two algorithms for modular multiplication with very large moduli are analyzed specifically for their applicability when a high radix is used for the multiplier. Both algorithms perform modulo
An Algorithm for Redundant Binary Bit-Pipelined Rational Arithmetic
TLDR
A redundant binary representation of the rationals and an associated algorithm for computing the sum, difference, product, quotient, and other useful functions of two rational operands, using this representation are introduced.
Digit selection for SRT division and square root
  • Peter Kornerup
  • Mathematics, Computer Science
    IEEE Transactions on Computers
  • 1 March 2005
TLDR
The minimally redundant, radix-4 combined divide and square root algorithm is analyzed and it is shown that, in this case, it can be implemented without such a special table to determine initial digits for the square root.
Msb-first Digit Serial Arithmetic 1
We develop a formal account of digit serial number representations by describing them as strings from a language. A preex of a string represents an interval approximating a number by enclosure.
A Systolic, Linear-Array Multiplier for a Class of Right-Shift Algorithms
TLDR
It is shown how the multiplier, with some simple back-end connections, can compute modular inverses and perform modular division for a power of two as modulus.
Finite Precision Number Systems and Arithmetic
TLDR
This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms.
Digit-Set Conversions: Generalizations and Application
  • Peter Kornerup
  • Computer Science, Mathematics
    IEEE Trans. Computers
  • 1 May 1994
TLDR
The problem of digit set conversion for fixed radix is investigated, and O(1) time algorithms for converting into redundant digit sets are generalized based on a very simple lemma, which provides a framework for all conversions into redundancies.
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