Spring 2001

Efficient Implementation of Elliptic Curve Cryptosystems on the TI MSP430x33x Family of Microcontrollers

Jorge Guajardo, WPI Graduate Student
Wednesday, February 7th; 1:30 pm; Room: AK 218

This talk describes joint work with Rainer Blemel, Uwe Krieger, and Christof Paar.

Abstract

This contribution describes a methodology used to efficiently implement elliptic curves (EC) over GF(p) on the 16-bit TI MSP430x33x family of low-cost microcontrollers. We show that it is possible to implement EC Cryptosystems in highly constrained embedded systems and still obtain acceptable performance at low cost. We modified the EC point addition and doubling formulae to reduce the number of intermediate variables while at the same time allowing for flexibility. We used a generalized-Mersenne prime to implement the arithmetic in the underlying field. We take advantage of the special form of the moduli to minimize the number of precomputations needed to implement inversion via Fermat's little theorem and the k-ary method of exponentiation. We apply these ideas to an implementation of an elliptic curve system over GF(p), where p=2¹²⁸ - 2⁹⁷-1. We show that a scalar point multiplication can be achieved in 3.4 seconds without any stored/precomputed values and the processor clocked at 1 MHz.

This work will also be presented next week at PKC 2001 in Korea.

Technology and Trust - A fruitful dialogue?

Lars Karle, Vice President, Fraunhofer Center for Research in Computer Graphics, Inc.
Thursday, March 29th, 11:00 am. Room: Gordon Library , 2nd floor

Abstract

The presentation will describe important technology trends in computer science and associated industrial disciplines, that drive the Research and development agenda at a Global R&D organization like the Fraunhofer Center for Research in Computer Graphics. The current issues in organizing and executing technology transfer will be highlighted to emphasize the importance of business aspects in addition to technology. Finally, the increased necessity of building and Maintaining trust in large networks will be explained.

Attacks on Cryptographic Hardware

Jonathan Towle, Intertrust Inc.
Wednesday, April 11th, 1:30 pm; Room: AK 218

Abstract

This will be a broad discussion of methods of attacking Cryptographic hardware. Attacks can be separated into three Main categories: Physical or probing attacks, fault induction attacks and eavesdropping attacks. Probing attacks are described in several white papers by Ross Anderson's group, see for example Anderson & Kuhn http://www.cl.cam.ac.uk/users/rja14/tamper.html.

Fault induction or glitch attacks are discussed by Kummerling & Kuhn http://www.cl.cam.ac.uk/~mgk25/ Design Principles for Tamper-Resistant Smart Card Processors. Side channel attacks in the form of TEMPEST attacks have been carried out since the 1950's. Recently Paul Kocher www.Cryptography.com and others have studied electrical power consumption of smart card processors and successfully recovered the internally stored secret keys, this will be the Main topic of discussion.

Application of the Mordell-Weil Group to Cryptographic Systems

Andre Weimerskirch , WPI Graduate Student
Thursday, April 19th, 2:00 pm; Room: AK 218

Abstract

This work examines the Mordell-Weil group for application in Cryptography. This approach has recently been proposed by Gerhard Frey. The use of the Mordell-Weil group for discrete logarithm schemes is a variant of elliptic curve Cryptosystems.

We extended the original idea by Frey with the goal of a performance improvement. The arithmetic complexity using the Mordell-Weil group will be compared to ordinary elliptic curve Cryptosystems. For the case of an extension degree of five, which is studied in detail here, a point multiplication, the crucial operation for Cryptosystems, is more than 20% less complex in the Mordell-Weil group than in an ordinary elliptic curve while preserving the same level of security. For higher extension degrees considerably higher performance gains seem possible.

Furthermore, for higher extension degree, the base field can be represented with less than 32-bits, which appears to be well suited for modern microprocessors. The speed-up of the Mordell-Weil group comes at the cost of a slightly larger bit-size needed to represent a curve point and a more costly curve generation.

Computer Architectures for Cryptosystems Based on Hyperelliptic Curves

Thomas Wollinger, WPI Graduate Student
Tuesday, May 1st, 12:30 pm; Room: AK 218

Abstract

Security issues play an important role in almost all modern communication and computer networks. As Internet applications continue to grow dramatically, security requirements have to be strengthened. Hyperelliptic curve Cryptosystems (HECC) allow for shorter operands at the same level of security than other public-key Cryptosystems, such as RSA or Diffie-Hellman. These shorter operands appear promising for many applications.

Hyperelliptic curves are a generalization of elliptic curves and they can also be used for building discrete logarithm public-key schemes. This thesis approaChes to a hardware implementation of a Crypto engine based on hyperelliptic curves. A major part of this work is the development of computer architectures for the different algorithms needed for HECC. The architectures are developed for a reconfigurable platform based on Field Programmable Gate Arrays (FPGAs). FPGAs combine the flexibility of software solutions with the security of traditional hardware implementations. In particular, it is possible to easily change all algorithm parameters such as curve coefficients and underlying finite field.

In this work we first summarized the theoretical Background of hyperelliptic curve Cryptosystems. In order to realize the operation addition and doubling on the Jacobian, we implemented composition and reduction algorithms in hardware. These in turn are based on arithmetic for arithmetic in the underlying field and for arithmetic in the polynomial ring. The architectures are described in VHDL (VHSIC Hardware Description Language) and mapped to Xilinx FPGA devices. An Architecture of a HECC over GF(2⁴¹) was implemented.

Security Issues in Communication Protocols for Embedded Systems

Andre Dancus, WPI Graduate Student
Thursday, May 3rd, 1:00 pm; Room: AK 218

Abstract

Embedded systems - which we define here as computing devices with limited Resources, such as PDAs, cell phones, intelligent appliances - require specific communication protocols, suited to the environments they operate in. Embedded devices are increasingly used in wireless ad-hoc networks; this talk first presents generic theoretical aspects of security in ad-hoc networks. We then describe the existing communication protocols suited for embedded systems, such as Bluetooth, IrDA, WAP, LonTalk, Jini, HomeRF, and see how security is addressed in each of these approaches.

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Last modified: Sep 22, 2006, 20:31 EDT