2:30-3:30 pm

Room 8405, CUNY Graduate Center

365 Fifth Avenue at 34th Street

Room Peirce 220, Stevens Institute of Technology

Hoboken, NJ

directions

Security seminars at Stevens

**October 5, Graduate Center**: Alexander Ushakov (Stevens Institute of
Technology), *A Practical Attack on Shifted Conjugacy Based Authentication Protocol*

**Abstract: ** A left self-distributive operation on a set
S is a binary operation satisfying the law u*(v*w)=(u*v)*(u*w).
For example, conjugation in groups satisfies self-distributive
condition. There might be other self-distributive operations in specific groups.
P. Dehornoy showed that this property can be naturally used for
cryptographic purposes, namely for authentication schemes.
In this talk I will discuss security assumptions of a new cryptographic
primitive proposed by P. Dehornoy, called "Shifted Conjugacy Problem",
in braid groups and present two attacks on his scheme.

**October 19, Graduate Center**: Vladimir Shpilrain (The City College of
New York), *Authentication schemes and digital signatures*

**Abstract: ** Until now, noncommutative public-key cryptography has been primarily focused on key
establishment protocols. In this talk, I will show that there is an "hierarchy" of cryptographic products in
terms of difficulties in their design, with designing a (secure) key establishment protocol being the most
difficult task, followed by designing an authentication scheme, followed by designing a digital signature
scheme. In particular, it is possible to design a zero-knowledge authentication scheme whose breaking (i.e.,
obtaining a secret key) is NP-complete. My talk will mostly focus on authentication schemes, although I will
discuss digital signatures as well.

**Tuesday, October 23, Stevens Institute, room
Peirce 309**: Jaime Gutierrez (University of Cantabria, Spain), *Lattices in Cryptography*

**Abstract: ** Our world is not linear. Many phenomena, however, are often
"linearized" because only then a reasonably well-working mathematical
machinery can describe the phenomena and produce meaningful forecasts.
Lattices are geometric objects that have been used to solve many
problems in mathematics and computer science. Lattice reduction strategies or the so called
LLL-techniques seem inherently linear. The general idea
of this technique is to translate our non linear problem to finding a
short vector in a lattice built from the nonlinear equation. Then, the
so-called Shortest Vector Problem and Closest Vector Problem in
lattices play a major role. In recent years, these techniques have
been used repeatedly in algorithmic coding theory and cryptography.

In this talk I will investigate lattice reduction technique on
some cryptography problems, namely

- finding roots of multivariate integer polynomials and attacking
cryptosystems,

- Integer factoring and RSA,

- predicting pseudorandom number congruential generators over
Elliptic Curves

**November 2, Graduate Center**: Ayan Mahalanobis (Stevens Institute),
*The MOR cryptosystem and finite p-groups*

**Abstract: ** This talk focuses on using p-groups for the MOR cryptosystem.
We start with the question: is the MOR cryptosystem over an elementary
abelian p-group better than that over a finite field? We then follow the
direction this answer leads us to.

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