Summer 2003

How to Compute Multiplicative Inverses Efficiently in Hardware

Prof. Erkay Savas, Sabanci University, Istanbul, Turkey
Friday, August 29, 2003, 3:00 PM, Atwater Kent, WPI, Room 108

Abstract

Computation of multiplicative inverses in finite fields GF(p) and GF(2^n) is the most time consuming operation in elliptic curve cryptography especially when affine coordinates are used. Since the existing algorithms based on extended Euclidean algorithm do not permit a fast software implementation, projective coordinates, which eliminate almost all of the inversion operations from the curve arithmetic, are preferred.

In this talk, it will be demonstrated that implementations using affine coordinates can provide a comparable speed to that of projective coordinates with careful hardware realization of existing algorithms for calculating inverses in both fields without utilizing special moduli or irreducible polynomials. Two inversion algorithms will be presented for binary extension and prime fields which are slightly modified versions of the Montgomery inverse algorithm. The similarity of the two algorithms allows to design a single unified hardware architecture that performs the computation of inversion in both fields. A hardware structure will also be presented where the field elements are represented using a multi-word format. This feature allows a scalable architecture which operates in a broad range of precision, which has certain advantages in cryptographic applications.

Pervasive Computing and the Future of Crypto Engineering

Prof, Christof Paar, Ruhr-University of Bochum and WPI
Thursday, August 7, 2003, 11:00 AM, Atwater Kent, WPI, Room 218

[Presentation Slides (ppt)]

Abstract

For a long time, the main concern of the IT security community was to secure traditional computer networks, such as LANs, intranets and the Internet. The next generation of IT applications might look quite different: Your clothes will talk to your car, your PDA will talk to the refrigerator, which in turn will communicate with the milk bottle. Those and many many other pervasive computing applications will have security solutions which are different from, say, building firewalls for a corporate network. In particular, the role of crypto engineering will become more crucial. By defintion almost all devices in a pervasive network are embedded nodes, and providing security for such devices is heavily dependend on the device hardware and firmware. For instance, running public-key operations can be a major challenge for the smart bar code label of a milk bottle.

In this talk we will first give an introduction to pervasive computing. We will then talk about the challenges for crypto engineers that lie ahead, with a focus on embedded cryptography for pervasive devices. The talk will conclude with some activities at U Bochum related to this topic.

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Last modified: Tuesday, 29-Jun-2004 09:33:57 EDT