3 edition of **Serial-parallel multiplication in Galois fields** found in the catalog.

Serial-parallel multiplication in Galois fields

- 59 Want to read
- 39 Currently reading

Published
**1987** by National Aeronautics and Space Administration in [Washington, DC] .

Written in English

- Galois theory.,
- Numerical analysis.

**Edition Notes**

Other titles | Serial parallel multiplication in Galois fields. |

Statement | Shu Lin, Tadao Kasami. |

Series | NASA-CR -- 181210., NASA contractor report -- NASA CR-181210. |

Contributions | Kasami, Tadao, 1930-, United States. National Aeronautics and Space Administration. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL18031423M |

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SERIAL-PARALLEL MULTIPLICATION IN GALOIS FIELDS 1. MultiDlication over Subfields In this note, we present a method for multiplying two elements from a Galois field over a subfield. contains the field GF(2') as a subfield and may be regarded as an extension field of.

Signed serial-/parallel multiplication. A straightforward method to multiply two binary numbers is to repeatedly shift the first argument a, and add to a register if the corresponding bit in the other argument b is set.

The idea is similar to multiplication as taught in school, but a simple and-gate determines the product of two digits. The structure of fields [by] David Winter; Serial-parallel multiplication in Galois fields [microform] / Shu Lin, Tadao Kasami; Galois theory and a general notion of central extension / G.

Janelidze and G.M. Kelly; Galois theory in some function fields / Carl F. Moppert; The separable Galois theory of commutative rings [by] Andy R.

Magid. A PB is a basis of the form {1,x,x 2,y,x mÀ1 }, where x is a root of an irreducible polynomial F(x) of degree m with coefficients from GF(2). This paper presents a design for an efficient architecture of a reconfigurable bit-serial polynomial basis multiplier for Galois field GF(2m).

The multiplier operates on the Most Significant Serial-parallel multiplication in Galois fields book (MSB)-first for finite field by: 6. Multiplication in finite fields is used Serial-parallel multiplication in Galois fields book many applications, especially in cryptography. It is a basic and the most computationally intensive operation from among all such operations.

This paper presents a novel serial-parallel architecture for finite field multiplications over GF(2m) defined by irreducible trinomials as field polynomials. By recursive decomposition of one of the operands, and Serial-parallel multiplication in Galois fields book pre-reduction of the other, it is possible to feed multiple bits in parallel Serial-parallel multiplication in Galois fields book the serial-parallel structure.

Addition and Multiplication in Galois Fields, GF(2n) The group theory is used to introduce another algebraic system, called a field.

A field is a set of elements in which we can do addition, subtraction, multiplication and division without leaving the set.

In this paper, we propose a novel design technique for reliable and low power Galois field (GF) arithmetic processor. The aim is to tolerate faults in the GF processor during on-line computation at reduced system costs, while maintaining high : Vinu K. Narayanan, Rishad A.

Shafik, Jimson Mathew, Dhiraj K. Pradhan. In particular, we focus on the implementation Serial-parallel multiplication in Galois fields book hardware architectures for addition, multiplication, and inversion in ﬁelds GF(pm).

The ﬁrst part of the dissertation surveys previous architectures used to implement addition and mul-tiplication over GF(p) as such operations are the basic building blocks used to implement GF(pm) multipliers. Moboluwaji Olusegun Sanu, Ph.D.

The University of Texas at Austin, Supervisor: Earl E. Swartzlander, Jr. Modular multiplication is a core operation in virtually all public -key cryptosystems in use today. In this research, parallel, high -speed designs for modular multiplication are presented.

We have designed pass-transistor logic (PTL)-based D flip-flop and T flip-flop to be used in finite field multiplication. Since both CMOS and PTL have their respective advantages in area, speed, and power, we have compared two different designs (conventional implementation and improved implementation) of serial-parallel finite field multiplication using pure CMOS, pure PTL, and hybrid PTL/CMOS.

Meher P, Ha Y and Lee C An optimized design for serial-parallel finite field multiplication over GF(2) based on all-one polynomials Proceedings of the Asia and South Pacific Design Automation Conference, (). Meher, Yajun Ha, Chiou-Yng Lee, An optimized design for serial-parallel finite field multiplication over GF(2 m) based on all-one polynomials, Proceedings of the Asia and South Pacific Design Automation Conference, January, Yokohama, JapanCited by: Information Processing Letters 46 () Elsevier Parallel algorithms for addition and multiplication on processor arrays with reconfigurable bus systems P.

Thangavel Department of Mathematics, Bharathidasan University, TiruchirapalliIndia V.P. Muthuswamy Department of Mathematics and Computer Applications, Regional Engineering College, TiruchirapalliIndia Cited by: 8. Figure Serial-Parallel Multiplier. Multiplier Operation. The serial-parallel multiplier is based on the addition of bits in the corresponding column of the multiplication process as shown below.

Each column is added in one clock cycle generating the corresponding bit. compared to CSD serial/parallel multipliers. Besides complexity, throughput is also considered by deﬁning structures where the critical path, for bit-serial arithmetic, is no longer than one full adder.

Two algorithms for the design of multiple-constant multiplication using serial arithmetic are proposed. The difference between the proposed. Also Paar and Rosner gave a comparison of multiplication in composite fields, GF((2 n) m) and prime fields, GF(2 m), m is prime in.

Wei et al. and Wang used systolic architectures for parallel multiplication in [], [], by: In particular, [BRIC82] shows how multiplication mod n can be done in m+7 clock pulses if n is m bits. In [MONT85] it is shown how modular multiplication can avoid division. At the present time RSA decryption (encryption is slower) with a bit modulus has been performed at about.

3 [AJTA86] to ﬁnd the median of m elements, we can calculate SMEDIAN2D and MEDIAN2D in O(loglogW) time using O(N 2W) processors and O(N2W) processors respectively.

The resulting processor-time products are O(N2WloglogW) and O(N 2W loglogW).We develop algorithms which have good processor-time product (i.e., within polylogarithmic factor of the optimal serial algo.

This banner text can have markup. web; books; video; audio; software; images; Toggle navigation. Note that it is easy to compute K2 from K2 u since multiplication by u−1 can be computed with only one shift and one conditional XOR as shown in (2).

Comparison with XCBC TMAC is obtained from XCBC by replacing (K2, K3) with (K2 u, K2). The size of keys is. The book is very much aimed at learning CUDA, but with a focus on performance, having first achieved correctness. Your level of skill and understanding of writing high-performance code, especially for GPUs, will hugely benefit from this text.

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The arithmetic of exponential key exchange is not restricted to prime fields; it can also be done in Galois Fields with 2 n elements, or in prime product rings !, 68!. The `2 n ` approach has been taken by several people 64!, !, 56. because arithmetic in these fields can be performed with linear shift registers and is much faster than.

Bernard Sklar, “Digital Communications: Fundamentals and Applications with Fundamentals of Turbo Codes”, a Hand book, Second Edition (Prentice-Hall,ISBN ).

Multipliers-Serial-parallel Multiplier, array multiplier. High Density Memory-ROM, Static RAM, Dynamic RAM, SD RAM, Flash Memory. 5 Lectures 7. Physical Design: Floor Planning Methods-Block Placement & Channel Definition, Global and Channel Routing. 3 Lectures. Hardware cost and clock rate performance for three hybrid serial-parallel multiplications subtraction of the polynomials is per-formed exactly the same as addition in finite fields.

Multiplication. Galois field’s elements can be written as linear combinations of {1. The HDC provided significant functions such as serial/parallel conversion, data separation, and track formatting, and required matching to the drive (after formatting) in order to assure reliability.

Each control cable could serve two or more drives, while a dedicated (and smaller) data cable served each drive.

of Technical and Mathematical Terms. The Galois group of the degree 3 polynomial is of order 3. The corresponding number field has 2 fundamental units, 1/12*t^2-t+1/4 and -1/12*t^2+1/2*t+5/4, its class group is of order 1 and its index is equal to 2^6*3^2.

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A detailed introduction and comparison of the three methods are given. In the last, authors briefly summarize different methods and present the better method for multi-systems combination.

#e1# #s1# #abstracttxt# Compared with the. Finite ﬁelds play an important role in public-key cryptography. Many public-key algorithms are either based on arithmetic in prime ﬁelds or on extension ﬁelds of GF (2), denoted by GF (2 k).Examples of schemes which can be based on Galois ﬁelds of characteristic two are discrete logarithms schemes (see, e.g., [2]), elliptic curve schemes [3], and systems based on hyperelliptic curves [4].

The second edition retains the pdf purpose of the ﬁrst edition. It is a rigorous, introductory pdf to the subject of algebraic codes for data transmission. In fact, this phrase, “algebraic codes for data transmission,” has been chosen as the title of the second edition because it reﬂects a more modern perspective on the subject.A detailed comparison of efcient hardware architectures for Montgomery multi-plication and interleaved multiplication can be found in [3].

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[1] A. J.