Conference: Third Workshop on “Coding and Systems”

December 8/9, 2006:  Gary McGuire (CSI), Marcus Greferath (CSI), Eimear Byrne (CSI) attended the Third Workshop on “Coding and Systems” at the University of Zürich.

Gregor Leander will visit the Claude Shannon Institute (November 26-30 2007).

Gregor Leander (Ruhr University Bochum, Germany) will visit the Claude Shannon Institute from November 26-30 2007.

Keith Martin will visit the Claude Shannon Institue (November 26th- 27th 2007).

Keith Martin from Royal Holloway London (U.K. ) will visit the Claude Shannon Institue from November 26th- 27th 2007.

News of the Week:

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.

Claude Shannon Institute – Network Coding Seminars

Weekly Network Coding Seminars will begin again this Friday October 19th 2007 at the Claude Shannon Institute at UCD. For further information please contact Eimear Byrne at ebyrne@ucd.ie

Claude Shannon Institute – Algebra Seminar

Title: Hyperelliptic Curves in Cryptography

Date: Monday 22 October, 2007 at 4pm

Place: Mathematical Sciences Seminar Room, UCD
Presenter: Laura Hitt (UCD)

Abstract: I will give an overview of hyperelliptic curves in cryptography, and in particular, such curves that are suitable for pairing-based cryptography. These “pairing-friendly” hyperelliptic curves over a finite field $\F_q$, are those whose group of $\F_q$-rational points of the Jacobian has size divisible by a large prime, whose embedding degree is small enough for computations to be feasible, and whose minimal embedding field is large enough for the discrete logarithm problem in it to be difficult. I will construct a sequence of $\F_q$-isogeny classes for a family of Jacobians of curves of genus 2 over $\F_{q}$, for $q=2^m$, and give their corresponding small embedding degrees for the subgroup with large prime order. 

Claude Shannon Institute: Dublin Area Seminar Announcement

 
Title: On closed forms and minimization of quantum gate counts
Presenter: Colin Wilmott
Date: Tuesday October 23 at 4:00 pm
Place: Room 1.42 Ground Floor in The Callan Building, 
North Campus, National University of Ireland Maynooth (NUIM)
 
Title: Introduction to S-Boxes and Nonlinear Functions in Cryptography
Presenter: Gary McGuire
Date: Tuesday 23 October, 5.10 pm
Place: Room 1.42 Ground Floor in The Callan Building, 
North Campus, National University of Ireland Maynooth (NUIM)
Abstract: S-Boxes are an important part of many modern block ciphers.

We will give an introduction to S-Boxes, their design and their uses.

We will also discuss the cryptanalysis of these ciphers.

  
 

				

Marcus Greferath (CSI) speaks at NUI Galway

Title: Inversive Spaces, $0$-$1$-Geometries, and Low-Density Parity-Check Codes
Date: Thursday 18 October 2007, at 3:45 pm Place: NUI Galway
Presenter: Marcus Greferath (UCD)
Abstract: LDPC codes have been attracting attention over the recent decade. Originally introduced in the seminal work of Gallager in the sixties, they were (re)discovered soon after the famous TURBO codes. This talk will describe a family of LDPC codes that are derived from what are called 0-1-geometries which we have found in a geometric structure called inversive space. We will briefly discuss basic properties and show some performance diagrams. These diagrams suggest that these codes might be useful in various  applications like general communications as well as data storage.

Claude Shannon Institute – Algebra Seminar

Title: Galois theory and linear algebra.
Date: Monday 15 October, 2007 at 4pm
Place: Mathematical Sciences Seminar Room, UCD
Presenter: Rod Gow (UCD)
Abstract: We show how Artin’s independence of characters lemma implies an unusual realization of the algebra of linear transformations, and investigate some of the consequences of and problems raised by this realization in the cyclic case. 

Paper Published: Carl Bracken (CSI), Gary McGuire (CSI)

Title: Duals of quasi-3 designs are not necessarily quasi-3. Article published in Designs, Codes and Cryptography 44:1-3 September 2007. Authors: Carl Bracken (CSI), Gary McGuire (CSI).