scholarly journals Self-dual normal bases for infinite odd abelian Galois ring extensions

2006 ◽  
Vol 123 (1) ◽  
pp. 1-8
Author(s):  
Patrik Lundström
Keyword(s):  
Galois Ring ◽  
Normal Bases ◽  
Ring Extensions

scholarly journals Normal bases for infinite Galois ring extensions

1999 ◽  
Vol 79 (2) ◽  
pp. 235-240 ◽  
Author(s):  
Patrik Lundström
Keyword(s):  
Galois Ring ◽  
Normal Bases ◽  
Ring Extensions

scholarly journals Normal Bases on Galois Ring Extensions

2018 ◽  
Author(s):  
Zhang Aixian ◽  
Feng Keqin
Keyword(s):  
Finite Field ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Ring Extension ◽  
Normal Bases ◽  
Ring Extensions

In this paper we study the normal bases for Galois ring extension ${{R}} / {Z}_{p^r}$ where ${R}$ = ${GR}$(pr, n). We present a criterion on normal basis for ${{R}} / {Z}_{p^r}$ and reduce this problem to one of finite field extension $\overline{R} / \overline{Z}_{p^r}=F_{q} / F_{p}  (q=p^n)$ by Theorem 1. We determine all optimal normal bases for Galois ring extension.

scholarly journals Normal Bases on Galois Ring Extensions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 702
Author(s):  
Aixian Zhang ◽  
Keqin Feng
Keyword(s):  
Signal Processing ◽  
Finite Field ◽  
Block Cipher ◽  
Field Extension ◽  
Galois Ring ◽  
Normal Basis ◽  
Galois Rings ◽  
Ring Extension ◽  
Galois Fields ◽  
Normal Bases

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.

Units on the Gauss extension of a Galois ring

2015 ◽  
Vol 15 (02) ◽  
pp. 1650028
Author(s):  
Weining Chen ◽  
Gaohua Tang ◽  
Huadong Su
Keyword(s):  
Unit Group ◽  
Galois Ring ◽  
Ring Theory ◽  
Ring Extensions ◽  
Extension Ring

Ring extensions are a well-studied topic in ring theory. In this paper, we study the structure of the Gauss extension of a Galois ring. We determine the structures of the extension ring and its unit group.

Galois ring extensions and localized modular rings of invariants of p-groups

2012 ◽  
Vol 18 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Peter Fleischmann ◽  
Chris Woodcock
Keyword(s):  
Galois Ring ◽  
Ring Extensions

Extensions of Rings Having McCoy Condition

2009 ◽  
Vol 52 (2) ◽  
pp. 267-272 ◽  
Author(s):  
Muhammet Tamer Koşan
Keyword(s):  
Positive Integer ◽  
Associative Ring ◽  
Nonzero Element ◽  
Ring Extensions

AbstractLet R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f (x)g(x) = 0 (over R[x]), where 0 ≠ f (x), g(x) ∈ R[x], implies that there exists a nonzero element c ∈ R such that f (x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy ring, then R[x]/(xn) is a right McCoy ring for any positive integer n ≥ 2.

scholarly journals True Random Number Generator Based on Fibonacci-Galois Ring Oscillators for FPGA

2021 ◽  
Vol 11 (8) ◽  
pp. 3330
Author(s):  
Pietro Nannipieri ◽  
Stefano Di Matteo ◽  
Luca Baldanzi ◽  
Luca Crocetti ◽  
Jacopo Belli ◽  
...  
Keyword(s):  
Field Programmable Gate Array ◽  
Random Number ◽  
Random Number Generator ◽  
Random Number Generation ◽  
Galois Ring ◽  
Number Generator ◽  
True Random Number Generator ◽  
Number Generation ◽  
Field Programmable ◽  
Gate Array

Random numbers are widely employed in cryptography and security applications. If the generation process is weak, the whole chain of security can be compromised: these weaknesses could be exploited by an attacker to retrieve the information, breaking even the most robust implementation of a cipher. Due to their intrinsic close relationship with analogue parameters of the circuit, True Random Number Generators are usually tailored on specific silicon technology and are not easily scalable on programmable hardware, without affecting their entropy. On the other hand, programmable hardware and programmable System on Chip are gaining large adoption rate, also in security critical application, where high quality random number generation is mandatory. The work presented herein describes the design and the validation of a digital True Random Number Generator for cryptographically secure applications on Field Programmable Gate Array. After a preliminary study of literature and standards specifying requirements for random number generation, the design flow is illustrated, from specifications definition to the synthesis phase. Several solutions have been studied to assess their performances on a Field Programmable Gate Array device, with the aim to select the highest performance architecture. The proposed designs have been tested and validated, employing official test suites released by NIST standardization body, assessing the independence from the place and route and the randomness degree of the generated output. An architecture derived from the Fibonacci-Galois Ring Oscillator has been selected and synthesized on Intel Stratix IV, supporting throughput up to 400 Mbps. The achieved entropy in the best configuration is greater than 0.995.

scholarly journals Injective modules under faithfully flat ring extensions

2015 ◽  
Vol 144 (3) ◽  
pp. 1015-1020 ◽  
Author(s):  
Lars Winther Christensen ◽  
Fatih Köksal
Keyword(s):  
Injective Modules ◽  
Flat Ring ◽  
Ring Extensions
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