Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

More documents

Recommendations

Info

Modular Inversion • Ratio Modular Inversion/Modular Multiplication is critical for the implementation of ECC systems: • Known values from software implementations (Menezes et.al. 2000) – GF(p): 80 to 1 – GF(2 n ): 10 to 1 • Comparison affine/projective coordinates: projective coordinates are preferred for a ratio of 10 to 1 or higher. • Smaller ratios are possible in hardware, for typical smartcard coprocessors this is not feasible due to area and power consumption restrictions. Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23 1
History of Philips <strong>Coprocessors</strong> • CORSAIR (COprocessor for RSA In a Rush) - 1991 – optimized for 512 bit RSA – signature generation in less than 1 sec (512 bit) • Fame (Fast Accelerator for Modular Exponentiation) (1995) • FameX (eXtended) (1997) – optimized for 1024 bit RSA, less than 400 ms – flexible usage for other Public Key Crypto systems – scalable length of operands up to 2048 bit and higher • FameX+GF(2 n ) prototype (2000): Cooperation with Oberthur • FameXE (ECC) (2002): part of new <strong>Smart</strong>MX platform – 1024 bit RSA, 100 ms – optimized for ECC based algorithms – GF(2 n ), scalable length of operands Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23 1
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: Arithmetic in Hardware • Importan
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

Create successful ePaper yourself

Delete template?

Save as template?