scholarly journals Merkle-Hellman revisited: A cryptanalysis of the Qu-Vanstone cryptosystem based on group factorizations

1997 ◽  
pp. 198-212 ◽  
Author(s):  
Phong Nguyen ◽  
Jacques Stern
Keyword(s):  
Group Factorizations

Quasiperiodic Group Factorizations

2008 ◽  
Vol 51 (3-4) ◽  
pp. 319-338 ◽  
Author(s):  
John P. Steinberger
Keyword(s):  
Group Factorizations

ON GROUP FACTORIZATIONS USING FREE MAPPINGS

2008 ◽  
Vol 07 (05) ◽  
pp. 647-662
Author(s):  
VLADIMIR BOŽOVIĆ ◽  
NICOLA PACE
Keyword(s):  
Abelian Group ◽  
Prime Numbers ◽  
Group Factorizations ◽  
Interesting Connection

We say that a collection of subsets α = [B1,…, Bk] of a group G is a factorization if G = B1,…,Bk and each element of G is expressed in a unique way in this product. By using a special type of mappings between groups A and B, called free mappings, we exhibit an algorithmic way to construct nontrivial factorizations of a group G, such that G ≅ A × B. In Lemma 3.2 we give a simple way to construct free mappings. It turns out that this approach has greater importance when G is an abelian group. We give illustrative examples of this method in the cases ℤp × ℤp and ℤp × ℤq where p and q are different prime numbers. An interesting connection between free mappings and Rédei's theorem, with a number theoretic implication, is given.

scholarly journals Finite Group Factorizations and Braiding

1996 ◽  
Vol 181 (1) ◽  
pp. 112-151 ◽  
Author(s):  
E.J. Beggs ◽  
J.D. Gould ◽  
S. Majid
Keyword(s):  
Finite Group ◽  
Group Factorizations

Solitons for the Schrödinger flows on Hermitian symmetric spaces

2021 ◽  
pp. 2140013
Author(s):  
Hsiao-Fan Liu ◽  
Chuu-Lian Terng ◽  
Zhiwei Wu
Keyword(s):  
Symmetric Spaces ◽  
Soliton Solutions ◽  
Loop Group ◽  
Darboux Transformations ◽  
Hermitian Symmetric Spaces ◽  
Group Factorizations

We use loop group factorizations to construct Darboux transformations, Permutability formulas, Scaling Transformations, and explicit soliton solutions of the [Formula: see text]-d Schrödinger flows on compact Hermitian symmetric spaces.

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