Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

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Further topics • Parallelism can be exploited when performing the group operations on an elliptic curve. This can lead to substantial speedup if the hardware supports this. • Key generation on smart cards is an interesting topic. For prime fields this does not seem promising (SEA algorithm, CM method), in characteristic 2 much more efficient methods are available due to Satoh, Skjeerna, Gaudry, Harley and others. Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23 2
Hyperelliptic curves • A hyperelliptic curve of genus g over a finite field k is given by C: v 2 +h(u)v=f(u) with f and h polynomials over k where: – h(u) is of degree at most g – f(u) is a monic polynomial of degree 2g+1 – certain technical conditions have to be satisfied. Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23 2
Page 1 and 2: Curve based cryptography - The stat
Page 3 and 4: Elliptic curves • Consider the eq
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: Implementation of ECDSA on HiPerSma
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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