Low-Power Elliptic Curve Cryptography Using Scaled Modular Arithmetic

  • E. Öztürk
  • B. Sunar
  • E. Savaş
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3156)


We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus. Our inversion algorithm exhibits superior performance to the Euclidean algorithm and lends itself to efficient hardware implementation due to its simplicity. Using the scaled modulus technique and our specialized inversion algorithm we develop an elliptic curve processor architecture. The resulting architecture successfully utilizes redundant representation of elements in GF(p) and provides a low-power, high speed, and small footprint specialized elliptic curve implementation.


Elliptic Curve Clock Cycle Inversion Algorithm Elliptic Curve Cryptography Division Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • E. Öztürk
    • 1
  • B. Sunar
    • 1
  • E. Savaş
    • 2
  1. 1.Department of Electrical & Computer EngineeringWorcester Polytechnic InstituteWorcesterUSA
  2. 2.Faculty of Engineering and Natural SciencesSabanci UniversityIstanbulTurkey

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