Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems

8.5 BIBLIOGRAPHY

[BAI2001] D. V. Bailey and C. Paar, Efficient arithmetic in finite field extensions with application in elliptic curve cryptography. J. Cryptol., 14(3): 153–176 (2001).

[ITO1988] T. Itoh and S. Tsujii, A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases. Math. Computation 44(4): 519–521 (1985).

[MON1985] P. Montgomery, modular multiplication without trial division. Math. Computation 44(4): 519–521 (1985).

[ROS1999] M. Rosing, Elliptic Curve Cryptography. Manning Publications, Greenwich, CT, 1999.

[WOO2000] A. D. Woodbury, Elliptic curve cryptography on smart cards without coprocessors. IFIP CARDIS, 71–92 (2000).

APPENDIX 8.1 COMPUTATION OF f_ki

First compute the value of q(i) such that pⁱ = q(i).n + 1.

Lemma A8.1

Proof By induction,

so that

Then compute c^q(i) mod p.

Lemma A8.2

Proof By induction,

It remains to compute

Lemma A8.3

Proof ...