Blog

Journal: Advances in Mathematics of Communications. November 2007. This journal is jointly published by the American Institute of Mathematical Sciences and Shandong University (PRC). Editor in Chief is Marcus Greferath (CSI). Patrick Fitzpatrick (CSI) and Eimear Byrne (CSI) are on the editorial board.

CSI Maynooth Reading Group Launched
Text: Elliptic Curves, Number Theory and Cryptography by LawrenceWashington.
Format: Presentations on chapters from the book
Time: Thursdays at 12:00 pm (Check web site for details)
Web Site: All presentations and future dates are available at: http://sta31.cs.nuim.ie:8001/mjrc/ (select research then select reading group).

On Thursday 8th of November, Shannon Institute members Ezekiel Kachisa and Mike Scott discovered a new pairing friendly family of elliptic curves with an embedding degree K of 36. Until now no families of curves were known which were particularly suitable at the highest levels of security, equivalent to the use of the Advanced Encryption Standard (AES) with a key size of 256 bits. The new family of curves were found by Computer search. Here is the actual Computer print-out…

K= 36, D= 3, rho= 7/6
p= 882400566168216899094908646319+
1238703941681299773215317568690679*x+
80733645 1514649393958822730194130787*x*x+
323808479358810657102538821500194402002*x3 +
89288299946412768299531422748832884314161*x4+
17905983136766322910895026522 548758079591534*x5+
2693165420667732569527262063048411299197649290*x6+
30862 3188406935151152101396193109347295131314346*x7+
2707759954024115996693658353 1798612825582531873111*x8+
1810057758005996140163943006751181162551125266504 574*x9+
90747766586239914037494048345627879554078488464992643*x10+
330884737 6911274369941033302634813094151876977361049672*x11+
829449985581016853798487 19551040150476155190883892501838*x12+
12795294393567197029999319773074405834 88531914560796424014*x13+
91642231818800036725323977119112130878704045868730 28498749*x14 t= 1238521382045476+868445151522065613*x+
260978358826886222466*x*x+435706552724 39907140970*x3+
4364504419607578015316190*x4+
262317360751146188910784278*x^ 5+
8758840655324856893143016502*x6+
125339925335955356307102330222*x7 r=
1939059218664007120117+
2330843769087281198202618*x+
1284152792146597612197057 159*x*x+
428781749377658327878940176680*x3+
96640608550275675764191319577300* x4+
15488896753793997104785417632115998*x5+
18101231413610572718911176997710 74679*x6+
155418308186129318102365866430169973576*x7+
9730228532323675448878 302033974208559095*x8+
433192938561011762260630747463762325769140*x9+
130179 76087829819323934710828051257599516034*x10+
23709458001204908187760468900579 3857921119076*x11+
1979161463637165811527078166152023118865926921*x12

Although complex looking, curves based on these formulae are easy to find, and efficient to implement.
A week later on the 15th November a new (and more complex) curve was also found for the case K=32.

November 22 2007: Vitaly Skachek (CSI) visited EPFL in Lausanne for research discussions with Amin Shokrollahi. He gave the following talk while he was there:

Title: Expander Codes: Constructions and Bounds
Presenter: Vitaly Skachek
Date: Thursday November 22 2007
Place: EPFL in Lausanne

November 21 2007: Vitaly Skachek (CSI) visited the University of Zurich for research discussions with Joachim Rosenthal and his students. He gave the following talk while he was there:

Title: Expander Codes: Constructions and Bounds
Presenter: Vitaly Skachek
Date: Wednesday November 21 2007
Place: University of Zurich

Conferences/Workshops Attended:

November 3rd 2007: Luis Dominguez (CSI) attended the Annual General Meeting of the Irish Linux User Group.

November 13-15 2007: Gary McGuire (CSI) was invited to attend the Certicom® Elliptic Curve Cryptography conference in Toronto, Canada.

November 21-23 2007: Gary McGuire (CSI) was invited to attend the 60th Birthday Symposium for Tor Helleseth at the Selmer Centre in Bergen, Norway.

November 29 2007: Elva O’Sullivan (CSI) attended a 1 day workshop given by Dr. Sean McCarthy from Hyperion LTD and hosted by Enterprise Ireland. The course was entitled How to write a competitive proposal for Framework 7.

November 16 2007: Gary McGuire (CSI) was invited to visit the University of Waterloo, Ontario, Canada, and spoke in the Tutte seminar (see details below):

Title: New Nonlinear Functions for S-Boxes in Cryptography and their Fourier Transform
Presenter: Gary McGuire (CSI)
Date: Friday, November 16 2007
Place: University of Waterloo, Canada

November 15-18 2007: Fernando Hernando (CSI) attended the meeting "Toric Geometry IV" in Caceres (Spain) and gave the following talk while he was there:

Title: The semigroup of reducible Quasi-Ordinary singularities
Presenter: Fernando Hernando (CSI)
Date: Thursday November 15 2007
Place: Toric Geometry IV, Caceres (Spain)

November 9 2007: Vitaly Skachek (CSI) visited Emanuel Popovici (CSI) and Liam Marnane (CSI) at University College Cork for research discussions.

UCD 2007 Patent Filing: An encoding scheme and a decoding scheme using a series of LDPC codes based on finite inversive spaces, Dr Mark Flanagan, UCD School of Electrical, Electronic and Mechanical Engineering and Dr Marcus Greferath, UCD School of Mathematical Science.
An Irish priority patent application.