Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

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Explicit formulae • For genus two we have explicit formulae which can replace the general Cantor algorithm: • Spallek (Ph.D. thesis, Essen 1996) • Harley • Takahashi (SCIS 2002) • Miyamoto,Doi,Matsuo,Chao,Tsuji (SCIS 2002) • Boston, Clancy (CHES 2002) • Lange (Preprint, 9-2002) • For genus three first results were obtained by Pelzl, Paar (Uni Bochum). Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23 2
Explicit formulae • Especially interesting for smartcard applications: We have “affine” and “projective” formulae – affine meaning one inversion for each addition or doubling step is used – projective meaning one inversion is used at the end of the scalar multiplication • Idea behind “projective” computations: use representation of divisor with non-normalized polynomials Normalize at the very end of scalar multiplication. • This idea can also be applied to the Cantor algorithm itself (Diploma thesis U. Krieger,1997) 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 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: Analysis of Cantor Algorithm • Ne
Page 31: Thank you for your attention ! Semi

Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

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