**Secret Key Encryption**

- Fast hashing on the Pentium, A. Bosselaers, R. Govaerts, and J. Vandewalle, Advances in Cryptology, Proceedings Crypto’96, LNCS 1109, Springer-Verlag, 1996, pp.298-312
- Even faster hashing on the Pentium, A. Bosselaers, Presented at the rump session of Eurocrypt’97, Konstanz, Germany, May 12–15, 1997, and updated on November 13, 1997.
- Designing Encryption Algorithms for Optimal Software Speed on the Intel Pentium Processor, B. Schneier and D. Whiting, Fast Software Encryption, Fourth International Workshop Proceedings (January 1997), Springer-Verlag, 1997, pp. 242-259
- Fast Implementations of AES Candidates, Kazumaro Aoki, Helger Lipmaa, Third AES Candidate Conference, New York City, USA, 13–14 April 2000
- Efficient Implementation of “Large” Stream Cipher Systems, Palash Sarkar & Subhamoy Maitra, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2001-11

**Encryption Implementation**

- Square-Root Algorithms for the Discrete Logarithm Problem(A Survey), Edlyn Teske, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2001-07 .
**[Modular Operation]** - Modular multiplication without trial division, P.L.Montgomery, Math. Comp., 44, 1985, pp.519-521.
- Fast exponentiation with precomputation: Algorithms and Lower Bounds, E. Brickell, D. Gordon, K. McCurley and D. Wilson, Advances in Cryptology – Eurocrypt ’92, LNCS 658, 1993, 200-207 .
- Comparison of three modular reduction functions, A.Bosselaers, R.Govaerts and J.Vandewalle, In Advances in Cryptology-CRYPTO’93, LNCS 773, Springer-Verlag, 1994, pp.175-186 .
- More flexible exponentiation with precomputation, C. Lim and P. Lee, Advances in Cryptology – Crypto ’94, LNCS 839, 1994, 95-107 .
- New modular multiplication algorithms for fast modular exponentiation, S.M.Hong, S.Y.Oh and H.S.Yoon, In Advances in Cryptology-EUROCRYPT’96, LNCS 1070, Springer-Verlag, 1996, pp.166-177.
- Fast Modular Reduction With Precomputation, Chae Hoon Lim, Hyo Sun Hwang, Pil Joong Lee, Proc. of JW-ISC’97, Oct. 1997. pp.65-79.
- Fast Batch Verification for Modular Exponentiation and Digital Signatures. Mihir Bellare, Juan A. Garay, and Tal Rabin, Advances in Cryptology – Eurocrypt 98 Proceedings, LNCS 1403, Springer-Verlag, 1998.
- A survey of fast exponentiation methods, D. Gordon, Journal of Algorithms, 27(1998), 129-146.
- On Computation of Polynomial Modular Reduction, Huapeng Wu, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2000-31.
- On Modular Reduction, Huapeng Wu, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2000-36.
**[GF(2**^{n})] - Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes, J. Guajardo, C. Paar, to appear Designs, Codes and Cryptography, 2001.
- Efficient computation of Multiplicative Inverses for Cryptographic Applications, M.A. Hasan, Technical Report of CACR, 2001.
- Montgomery Multiplier and Squarer in GF(2
^{m}), H. Wu, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2000-28. - On Complexity of Squaring Using Polynomial Basis in GF(2
^{m}), H. Wu, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2000-27. - High-speed Software Multiplication in F_2
^{m}, Julio Lopez, Ricardo Dahab, 2000. - Squaring Architecture for GF(2
^{m}) and its Applications in Cryptographic Systems, G. Orlando, C. Paar, Electronic Letters, June 2000, vol. 36, no. 13, pp. 1116-1117. - Storage-Efficient Basis Conversion Techniques, Leo Reyzin and Burt Kaliski, February 18, 2000.
- Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents. C. Paar, P. Fleischmann, and P. Soria-Rodriguez, IEEE Transactions on Computers, October 1999, vol. 48, no. 10, pp. 1025-1034.
- Efficient Finite Field Basis Conversion Techniques, Burt Kaliski, Moses Liskov and Yiqun Lisa Yin, April 1999.
- Montgomery multiplication in GF(2
^{k}), C. Koc and T. Acar, Designs, Codes and Cryptography, 14 (1998), 57-69. - Improved algorithms for elliptic curve arithmetic in GF(2
^{n}), Julio Lopez and R. Dahab, Technical report, IC-98-39, October 1998. - A fast software implementation for arithmetic operations in GF(2
^{n}), E. De Win, A. Bosselaers, S. Vandenberghe, P. De Gersem, and J. Vandewalle, Advances in Cryptology, Proceedings Asiacrypt’96, LNCS 1163, Springer-Verlag, 1996, pp. 65-76 . - Analysis and implementation of arithmetic operations in GF(2
^{n}), P. De Gersem and E. De Win, Thesis, K.U.Leuven, 1995 - Efficient Arithemtic in Finite Field Extensions with Application in Elliptic Curve Cryptography, Daniel V. Bailey and Christof Paar, To appear in Journal of Cryptology. (local copy)
**[GF(2**^{n}) : Normal Basis] - Fast Normal Basis Multiplication Using General Purpose Processors, Arash Reyhani-Masoleh and M. A. Hasan, Technical Report of CACR, 2001.
- Efficient Arithmetic in GF (2 super n) through Palindromic Representation, Ian F. Blake, Ron M. Roth and Gadiel, Seroussi, Technical Report HPL-98-134, 1998.
- Improved normal basis inversion in GF(2^m), S.M. Yen, IEE Electronics Letters, Vol.33, No.3, pp.196-197, Jan. 1997.
- Normal Bases over Finite Fields, Shuhong Gao, Thesis of Waterloo Universiy, 1993.
- A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases, T. Itoh and S. Tsujii, Information and Computation, vol 78, pp.171-177, 1988. (Page 1, Page 2, Page 3, Page 4, Page 5, Page 6, Page 7)
**[GF(p**^{n})] - Computation in Optimal Extension Fields, Daniel V. Bailey, Master Thesis in Worchester Polytechnic Institute, 2000.

**Elliptic Curve Implementation**

- An High-Speed ECC-based Wireless Authentication Protocol on an ARM Microprocessor, M. Aydos, T. Yanik and C. K. Koc, 16th Annual Computer Security Applications Conference, December 11-15, 2000.
- Performance of Elliptic Curve Cryptosystems, Julio Lopez, Ricardo Dahab, 2000.
- Software Implementation of the NIST Elliptic Curves Over Prime Fields, M. Brown, D. Hankerson, J. Lopez, and A. Menezes, Centre for Applied Cryptographic Research (CACR) at the University of Waterloo, CORR 2000-56.
- Software Implementation of Elliptic Curve Cryptography Over Binary Fields, Darrel Hankerson, Julio Lopez Hernandez, Alfred Menezes, CHES 2000, pp.1-24, 2000.
- Fast implementation of elliptic curve arithmetic in GF(p
^{n}), C.H.Lim and H.S.Hwang, Public Key Cryptography 2000, Jan.18-20, 2000, Melbourne, Australia. LNCS 1751, pp.405-421. - Elliptic scalar multiplication using point halving, E. Knudsen, Advances in Cryptology – Asiacrypt ’99, LNCS 1716, 1999, 135-149.
- Speeding up Elliptic Scalar Multiplication with Precomputation, C.H.Lim and H.S.Hwang. Information Security and Cryptography – ICISC’99, Dec.9-10, 1999, Seoul, Korea. LNCS 1787, pp.102-119
- On the performance of signature schemes based on elliptic curves, E. De Win, S. Mister, B. Preneel, and M. Wiener, Algorithmic Number Theory Symposium III, LNCS 1423, Springer-Verlag, 1998, pp. 252-266.
- Efficient Algorithms for Elliptic Curve Cryptosystems, Jorge Guajardo, Christof Paar, 1997.
- Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography, D. Bailey, C. Paar, To appear in the Journal of Cryptology.
**[Anomalous Binary Curves]** - Speeding up the Arithmetic on Koblitz Curves of Genus Two, C.Gunther, T. Lange and A. Stein, Technical Report of CACR, 2000.
- Efficient arithmetic on Koblitz curves, J. Solinas, Designs, Codes and Cryptography, 19 (2000), 195-249
- Improved Algorithms for Arithmeric on Anomalous Binary Curves, Jerome A. Solinas, Corrected version of Crypto’97. 1999.
- An Improved Algorithm for Arithmetic on a Family of Elliptic Curves, Jerome A. Solinas, Crypto’ 97, pp.357-371, 1997.

**Hardware Encryption Implementation**

- High-Speed RSA Implementation, Cetin Kaya Koc, November 1994.
- RSA Hardware Implementation, Cetin Kaya Koc, August 1995.
- Architectural considerations for cryptanalytic hardware, Ian Goldberg’s and David Wagner, Spring 1996 .
- Cryptographic processor prototype RICO(High-performance RSA engine), IBM, April 1997.
- Fast DES Implementation for FPGAs and its Application to a Universal Key-Search Machine, J.-P. Kaps, and C. Paar, 5th Annual Workshop on Selected Areas in Cryptography (SAC ’98), August 17-18, Queen’s University, Kingston, Ontario, Canada.
- Montgomery Modular Multiplication on Reconfigurable Hardware, T. Blum, and C. Paar, 14th IEEE Symposium on Computer Arithmetic (ARITH-14), April 14-16, 1999, Adelaide, Australia.
- Building a High-Performance, Programmable Secure Coprocessor, S.W. Smith, and S.H. Weingart, Computer Networks (Special Issue on Computer Network Security), 31: 831-860. April 1999.
- Implementation of the Twofish Cipher Using FPGA Devices, Pawel Chodowiec, and Kris Gaj, Technical Report, Electrical and Computer Engineering, George Mason University, July 1999.
- Cryptographic processor MEAC1024(High-performance cryptographic engine), IBM, February 1999.
- Accessing the Intel(R) Random Number Generator with CDSA, Barry Pivitt, Intel Platform Security Division, 1999.
- An FPGA Implementation and Performance Evaluation of the Serpent Block Cipher, A. Elbirt, and C. Paar, Eighth ACM International Symposium on Field-Programmable Gate Arrays (FPGA 2000), Monterey, California, February 10-11, 2000 .
- An FPGA Implementation and Performance Evaluation of the AES Block Cipher Candidate Algorithm Finalists, A. J. Elbirt, W. Yip, B. Chetwynd, and C. Paar, The Third Advanced Encryption Standard (AES3) Candidate Conference, April 13-14, 2000, New York, USA.
- How Well Are High-End DSPs Suited for the AES Algorithms? AES Algorithms on the TMS320C6x DSP, T. Wollinger, M. Wang, J. Guajardo, and C. Paar, The Third Advanced Encryption Standard (AES3) Candidate Conference, April 13-14, 2000, New York, USA.
- Improving DES Hardware Throughput for Short Operations, M. Lindemann, and S. W. Smith. IBM Research Report RC-21798, IBM T.J. Watson Research Center, July 2000.
- An Open-source Cryptographic Coprocessor, Peter Gutmann, Proceedings of the 9th USENIX Security Symposium, August 14-17, 2000.
- A high-performance reconfigurable elliptic curve processor for GF(2m), G. Orlando and C. Paar, Cryptographic Hardware and Embedded Systems, CHES ‘2000, August 17-18, 2000, Worcester MA, USA.
- Elliptic Curve Cryptography on Smart Cards Without Coprocessors, A. Woodbury, D. Bailey, and C. Paar, Presented at the Fourth Smart Card Research and Advanced Applications (CARDIS 2000) Conference, September 20-22, 2000, Bristol, UK .
- Reconfigurable Hardware in Modern Cryptography, C. Paar, Invited presentation at the 4th Workshop on Elliptic Curve Cryptography (ECC 2000), October 4-6, 2000, Institute for Experimental Mathematics, Essen, Germany.
- Trusted Computing Platform Alliance (TCPA): Main Specification Version 1.0, 25 January, 2001.
- An FPGA-Based Performance Evaluation of the AES Block Cipher Candidate Algorithm Finalists, A. Elbirt, W. Yip, B. Chetwynd, C. Paar, To Appear in the IEEE Transactions on VLSI.

**Related Encryption Implementation Resources**

- Elliptic Curves: Implementation by Helger Lipmaa.
- Cryptographic Research at the University of Waterloo.
- Secure Coprocessing at IBM.