Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

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Overview • Introduction to elliptic and hyperelliptic curves. • Specific restraints in smart card environments. • Example: signature algorithms based on elliptic curves. • Some experiments with hyperelliptic curves on smartcards. • Focus on efficient implementations. • Secure implementations are considered in the next talk. Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23
Elliptic curves • Consider the equation E + 2 3 2 : y + a1xy + a3y = x + a2x + a4x a6 over a finite field GF(q n ). • E defines an elliptic curve over the finite field GF(q n ) (certain technical conditions have to be fulfilled). • The set E(GF(q n )) of points (x,y) satisfying the equation E form an abelian group. • The group law on E(GF(q n )) can be expressed in simple algebraic formulae. Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23
Page 1: Curve based cryptography - The stat
Page 5 and 6: Digital signatures based on ellipti
Page 7 and 8: Analysis of Signature algorithms
Page 9 and 10: ECC: Implementational choices • T
Page 11 and 12: ECC: Implementational Choices • Q
Page 13 and 14: Standard Smart Card IC Design Copro
Page 15 and 16: Arithmetic in Hardware • Importan
Page 17 and 18: History of Philips Coprocessors •
Page 19 and 20: Implementation of Signature algorit
Page 21 and 22: Implementation of ECDSA on HiPerSma
Page 23 and 24: Hyperelliptic curves • A hyperell
Page 25 and 26: Implications for Cryptography • N
Page 27 and 28: Analysis of Cantor Algorithm • Ne
Page 29 and 30: Explicit formulae • Especially in
Page 31: Thank you for your attention ! Semi

Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

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