- Intro
- Installation
- The UI
- Internal Rep
- Implementation
- Floating Slash Nums
- The C++ Interface
- Example Programs
- The MIRACL Routines
- Instance Variables
- MIRACL Error Messages
- Hardware Compiler Interface
- Bibliography
[Blake] BLAKE, SEROUSSI, and SMART. Elliptic Curves in Cryptography, London Mathematical Society Lecture Notes Series 265, Cambridge University Press. ISBN 0 521 65374 6, July 1999.
[Brassard] BRASSARD, G. Modern Cryptology. Lecture Notes in Computer Science, Vol. 325. Springer-Verlag 1988.
[Brent76] BRENT, R.P. Fast Multiprecision Evaluation of Elementary Functions. J. ACM, 23, 2 (April 1976), 242-251.
[Brent78] BRENT, R.P. A Fortran Multiprecision Arithmetic Package. ACM Trans. Math. Software 4,1 (March 1978), 57-81.
[Brick] BRICKELL, E, et al, Fast Exponentiation with Precomputation, Proc. Eurocrypt 1992, Springer-Verlag 1993.
[Cherry] CHERRY, L. and MORRIS, R. BC - An Arbitrary Precision Desk-Calculator Language. in ULTRIX-32 Supplementary Documents Vol. 1 General Users. Digital Equipment Corporation 1984.
[Comba] COMBA, P.G. Exponentiation Cryptosystems on the IBM PC. IBM Systems Journal, 29,4 (1990), pp 526-538.
[CS] CRAMER, R. and SHOUP, V. A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack Proc. Crypto 1998, Springer-Verlag 1999.
[DSS] Digital Signature Standard, Communications of the ACM, July 1992, Vol. 35 No. 7.
[Gruen] GRUENBERGER, F. Computer Recreations. Scientific American, April 1984.
[Jurisic] JURISIC, A and MENEZES A.H. Elliptic Curves and Cryptography, Dr. Dobbs Journal, #264, April 1997.
[Knuth73] KNUTH, D.E. The Art of Computer Programming, Vol 1: Fundamental Algorithms. Addison-Wesley, Reading, Mass., 1973.
[Knuth81] KNUTH, D.E. The Art of Computer Programming, Vol 2: Seminumerical Algorithms. Addison-Wesley, Reading, Mass., 1981.
[Korn83] KORNERUP, P. and MATULA, D.W. Finite Precision Rational Arithmetic: An Arithmetic Unit. IEEE Trans. Comput., C-32, 4 (April 1983), 378-387.
[Korn85] KORNERUP, P. and MATULA, D.W. Finite Precision Lexicographic Continued Fraction Number Systems. Proc. 7th Sym. on Comp. Arithmetic, IEEE Cat. #85CH2146-9, 1985, 207-214.
[LimLee] LIM, C.H. and LEE, P.J. A Key Recovery Attack on Discrete Log-based Schemes Using a Prime Order Subgroup. Advances in Cryptology, Crypto '97, Springer-Verlag 1998.
[Marsaglia] MARSAGLIA, G.M. and ZAMAN, A. A New Class of Random Number Generators. The Annals of Applied Probability, Vol. 1, 3, 1991, 462-480.
[Matula85] MATULA, D.W. and KORNERUP, P. Finite Precision Rational Arithmetic: Slash Number Systems. IEEE Trans. Comput., C-34, 1 (January 1985), 3-18.
[Maurer] MAURER, U.M. and YACOBI, Y. Non-Interactive Public Key Cryptography. Advances in Cryptography, Eurocrypt '91, Springer Verlag, 1992.
[Menezes] MENEZES, A.J. Elliptic Curve Public key Cryptosystems, Kluwer Academic Publishers, 1993.
[HAC] Handbook of Applied Cryptography, CRC Press, 2001.
[McCurley] McCURLEY, K.S. A Key Distribution System Equivalent to Factoring. J. Cryptology, Vol. 1. No. 2, 1988.
[Monty85] MONTGOMERY, P. Modular Multiplication Without Trial Division. Math. Comput., 44, (April 1985), 519-521.
[Monty87] MONTGOMERY, P. Speeding the Pollard and Elliptic Curve Methods. Math. Comput., 48, (January 1987), 243-264.
[Morrison] MORRISON, M.A. and BRILLHART, J. A Method of Factoring and the Factorization of F7. Math. Comput., 29, 129 (January 1975), 183-205.
[Pollard71] POLLARD, J.M. Fast Fourier Transform in a Finite Field. Math. Comput., 25, 114 (April 1971), 365-374.
[Pollard78] POLLARD, J.M. Monte Carlo Methods for Index Computation (mod p). Math. Comp. Vol. 32, No. 143, pp 918-924, 1978.
[Pomerance] POMERANCE, C. The Quadratic Sieve Factoring Algorithm. In Advances in Cryptology, Lecture Notes in Computer Science, Vol. 209, Springer-Verlag, 1985, 169-182.
[Reisel] REISEL, H. Prime Numbers and Computer methods for Factorisation. Birkhauser 1987.
[Richter] RICHTER, J. Advanced Windows. Microsoft Press.
[RSA] RIVEST, R., SHAMIR, A. and ADLEMAN, L. A Method for obtaining Digital Signatures and Public-Key Cryptosystems. Comm. ACM, 21,2 (February 1978), 120-126.
[Rubin] RUBIN, P. Personal Communication.
[Sch] SCHOOF, R. Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p. Math. Comp. Vol. 44, No. 170. April 1985, pp 483-494.
[Scott89a] SCOTT, M.P.J. Fast rounding in multiprecision floating-slash arithmetic. IEEE Transactions on Computers, July 1989, 1049-1052.
[Scott89b] SCOTT, M.P.J. On Using Full Integer Precision in C. Dublin City University Working Paper CA 0589, 1989.
[Scott89c] SCOTT, M.P.J. Factoring Large Integers on Small Computers. National Institute for Higher Education Working Paper CA 0189, 1989.
[Scott92] SCOTT, M.P.J. and SHAFA'AMRY, M. Implementing an Identity-based Key Exchange algorithm. Available from ftp.computing.dcu.ie /pub/crypto/ID-based_key_exchange.ps .
[Scott93] SCOTT, M.P.J. Novel Chaining Methods for Block Ciphers, Dublin City University, School of Computer Applications Working Paper CA-1993.
[Scott96] SCOTT, M.P.J. Comparison of methods for modular multiplication on 32-bit Intel 80x86 processors. Available from ftp.computing.dcu.ie /pub/crypto/timings.ps .
[Shoup] SHOUP, V. A New Polynomial Factorisation Algorithm and Its Implementation. Jl. Symbolic Computation, 1996.
[Stinson] STINSON, D.R. Cryptography, Theory and practice. CRC Press, 1995.
[Silverman] SILVERMAN, R.D. The Multiple Polynomial Quadratic Sieve, Math. Comp. 48, 177, (January 1987), 329-339.
[Walmsley] WALMSLEY, M., Multi-Threaded Programming in C++. Springer-Verlag 1999.
[WeiDai] DAI , W. Personal Communication.