Smart Card IC Design EEPROM RAM ROM CPU Coprocessors Logic

More documents

Recommendations

Info

Arithmetic in Hardware • Long-integer multiplication and addition is well suited for hardware implementation. • Modular arithmetic: – “traditional” modular arithmetic is not well suited for hardware implementation. – Reason: “school book” division with remainder is costly. – Much more efficient modular reduction techniques are available, which utilize computations modulo “transformed” moduli. – For example: Montgomery multiplication, uses the fact the reduction modulo perfect powers of two is easy. Semiconductors, BUID, CCC Kim Nguyen, Essen, 2002-09-23 1
Arithmetic in Hardware • Important topic: Modular inversion. • Basically two ways to implement this: – Computation of x -1 using Fermat’s Little Theorem: x -1 mod p = x p-2 mod p (modular exponentiation) – Computation of x -1 using the Extended Euclidean Algorithm: Gcd(x,p)=1 => 1=a*p+b*x => 1=b*x mod p. • Modular exponentiation: slow, but easy to implement. • Extended Euclidean Algorithm: fast, but more costly to implement. 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: Standard Smart Card IC Design Copro
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?