Journal Papers

• C. K. Koc and S. Johnson. Multiplication of signed-digit numbers. Electronics Letters, 30(11):840-841, 26th May 1994.   Abstract   Paper
• O. Egecioglu and C. K. Koc. Exponentiation using canonical recoding. Theoretical Computer Science, 129(2):407-417, 1994.   Abstract   Paper
• C. K. Koc. Montgomery reduction with even modulus. IEE Proceedings - Computers and Digital Techniques, 141(5):314-316, September 1994.   Abstract   Paper
• C. K. Koc. Analysis of sliding window techniques for exponentiation. Computers and Mathematics with Applications, 30(10):17-24, 1995.   Abstract   Paper
• C. K. Koc, T. Acar, and B. S. Kaliski Jr. Analyzing and comparing Montgomery multiplication algorithms. IEEE Micro, 16(3):26-33, June 1996.   Abstract   Paper
• C. K. Koc. Parallel canonical recoding. Electronics Letters, 32(22):2063-2065, 24th October 1996.   Abstract   Paper
• C. K. Koc and B. Sunar. Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields. IEEE Transactions on Computers, 47(3):353-356, March 1998.   Abstract   Paper
• C. K. Koc and T. Acar. Montgomery multiplication in GF(2^k). Designs, Codes and Cryptography, 14(1):57-69, April 1998.   Abstract   Paper
• C. K. Koc and C. Y. Hung. Fast algorithm for modular reduction. IEE Proceedings - Computers and Digital Techniques, 145(4):265-271, July 1998.   Abstract   Paper
• B. Sunar and C. K. Koc. Mastrovito multiplier for all trinomials. IEEE Transactions on Computers, 48(5):522-527, July 1999.   Abstract   Paper
• A. Halbutogullari and C. K. Koc. Mastrovito multiplier for general irreducible polynomials. IEEE Transactions on Computers, 49(5):503-518, May 2000.   Abstract   Paper
• A. Halbutogullari and C. K. Koc. Parallel multiplication in GF(2^k) using polynomial residue arithmetic. Designs, Codes and Cryptography, 20(2):155-173, June 2000.   Abstract   Paper
• E. Savas and C. K. Koc. The Montgomery modular inverse - revisited. IEEE Transactions on Computers, 49(7):763-766, July 2000.   Abstract   Paper
• B. Sunar and C. K. Koc. An efficient optimal normal basis type II multiplier. IEEE Transactions on Computers, 50(1):83-87, January 2001.   Abstract   Paper
• A. Levi and C. K. Koc. Risks in email security. Communications of the ACM, 44(8):112-112, August 2001.   Abstract   Paper
• M. Aydos, T. Yanik, and C. K. Koc. High-speed implementation of an ECC-based wireless authentication protocol on an ARM microprocessor. IEE Proceedings - Communications, 148(5):273-279, October 2001.   Abstract   Paper
• T. Yanik, E. Savas, and C. K. Koc. Incomplete reduction in modular arithmetic. IEE Proceedings - Computers and Digital Techniques, 149(2):46-52, March 2002.   Abstract   Paper
• C. K. Koc and C. Paar. Guest editors' introduction to special section on cryptographic hardware and embedded systems. IEEE Transactions on Computers, 52(4):401-402, April 2003.   Abstract   Paper
• A. F. Tenca and C. K. Koc. A scalable architecture for modular multiplication based on Montgomery's algorithm. IEEE Transactions on Computers, 52(9):1215-1221, September 2003.   Abstract   Paper
• B. Sunar, E. Savas, and C. K. Koc. Constructing composite field representations for efficient conversion. IEEE Transactions on Computers, 52(11):1391-1398, November 2003.   Abstract   Paper
• F. Rodriguez-Henriquez and C. K. Koc. Parallel multipliers based on special irreducible pentanomials. IEEE Transactions on Computers, 52(12):1535-1542, December 2003.   Abstract   Paper
• A. Levi, M. U. Caglayan, and C. K. Koc. Use of nested certificates for efficient, dynamic and trust preserving public key infrastructure. ACM Transactions on Information and System Security, 7(1):21-59, February 2004.   Abstract   Paper
• E. Savas, A. F. Tenca, M. E. Ciftcibasi, and C. K. Koc. Novel multiplier architectures for GF(p) and GF(2^n). IEE Proceedings - Computers and Digital Techniques, 151(2):147-160, March 2004.   Abstract   Paper
• T. Wollinger, J. Pelzl, V. Wittelsberger, C. Paar, G. Saldamli, and C. K. Koc. Elliptic and hyperelliptic curves on embedded µP. ACM Transactions on Embedded Computing Systems, 3(3):509-533, August 2004.   Abstract   Paper
• A. F. Tenca, E. Savas, and C. K. Koc. A design framework for scalable and unified architectures that perform multiplication in GF(p) and GF(2^m). International Journal of Computer Research, 13(1):68-83, 2004.   Abstract   Paper
• E. Savas, M. Naseer, A. A.-A. Gutub, and C. K. Koc. Efficient unified Montgomery inversion with multibit shifting. IEE Proceedings - Computers and Digital Techniques, to appear, 2004.   Abstract   Paper
• L. A. Tawalbeh, A. F. Tenca, and C. K. Koc. A radix-4 design of a scalable modular multiplier with recoding techniques. IEEE Potentials, to appear, 2005.   Abstract   Paper

Conference Papers

• C. K. Koc and T. Acar. Montgomery multiplication in GF(2^k). Proceedings of Third Annual Workshop on Selected Areas in Cryptography, pages 95-106, Queen's University, Kingston, Ontario, Canada, August 15-16, 1996.   Abstract   Paper
• C. K. Koc and T. Acar. Fast software exponentiation in GF(2^k). Proceedings, 13th Symposium on Computer Arithmetic, T. Lang, J.-M. Muller, and N. Takagi, editors, pages 225-231, Asilomar, California, July 6-9, 1997, Los Alamitos, CA: IEEE Computer Society Press.   Abstract   Paper
• C. K. Koc and B. Sunar. Low-complexity bit-parallel canonical and normal basis multipliers for a class of finite fields. Proceedings of 1998 IEEE International Symposium on Information Theory, pages 294-294, MIT, Cambridge, Massachusetts, August 16-21, 1998.   Abstract   Paper
• M. Aydos, E. Savas, and C. K. Koc. Implementing network security protocols based on elliptic curve cryptography. Proceedings of the Fourth Symposium on Computer Networks, pages 130-139, Istanbul, Turkey, May 20-21, 1999.   Abstract   Paper
• A. F. Tenca and C. K. Koc. A scalable architecture for Montgomery multiplication. Cryptographic Hardware and Embedded Systems, C. K. Koc and C. Paar, editors, First International Workshop, Worcester, MA, USA, pages 94-108, Springer Verlag, LNCS Nr. 1717, August 12-13, 1999. Abstract   Paper
• A. Halbutogullari and C. K. Koc. Mastrovito multiplier for general irreducible polynomials. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, M. Fossorier, H. Imai, S. Lin, and A. Poli, editors, 13th International Symposium, Honolulu, Hawaii, USA, pages 498-507, Springer Verlag, LNCS Nr. 1719, November 15-19, 1999. Abstract   Paper
• E. Savas, A. F. Tenca, and C. K. Koc. A scalable and unified multiplier architecture for finite fields GF(p) and GF(2^m). Cryptographic Hardware and Embedded Systems - CHES 2000, C. K. Koc and C. Paar, editors, Second International Workshop, Worcester, MA, USA, pages 277-292, Springer Verlag, LNCS Nr. 1965, August 17-18, 2000. Abstract   Paper
• M. Aydos, T. Yanik, and C. K. Koc. High-speed implementation of an ECC-based wireless authentication protocol on an ARM microprocessor. Proceedings, The 16th Annual Computer Security Applications Conference, pages 401-409, New Orleans, Louisiana, IEEE Computer Society Press, Los Alamitos, California, December 11-15, 2000.   Abstract   Paper
• E. Savas, T. A. Schmidt, and C. K. Koc. Generating elliptic curves of known order. Cryptographic Hardware and Embedded Systems - CHES 2001, C. K. Koc, D. Naccache, and C. Paar, editors, Third International Workshop, Paris, France, pages 142-158, Springer Verlag, LNCS Nr. 2162, May 14-16, 2001. Abstract Paper
• A. F. Tenca, G. Todorov, and C. K. Koc. High-radix design of a scalable modular multiplier. Cryptographic Hardware and Embedded Systems - CHES 2001, C. K. Koc, D. Naccache, and C. Paar, editors, Third International Workshop, Paris, France, pages 185-201, Springer Verlag, LNCS Nr. 2162, May 14-16, 2001. Abstract Paper
• A. Levi and C. K. Koc. Reducing certificate revocation cost using NPKI. Trusted Information, The New Decade Challenge, IFIP TC11 16th International Conference on Information Security, pages 51-59, M. Dupuy and P. Paradinas, editors, Kluwer Academic Publishers, Boston, MA, June 11-13, 2001.   Abstract   Paper
• A. Levi and C. K. Koc. CONSEPP: Convenient and secure electronic payment protocol based on X9.59. Proceedings, The 17th Annual Computer Security Applications Conference, pages 286-295, New Orleans, Louisiana, IEEE Computer Society Press, Los Alamitos, California, December 10-14, 2001.   Abstract   Paper
• A. A.-A. Gutub, A. F. Tenca, and C. K. Koc. Scalable VLSI architecture for GF(p) Montgomery modular inverse computation. IEEE Computer Society Annual Symposium on VLSI, pages 53--58, Pittsburgh, Pennsylvania, IEEE Computer Society Press, Los Alamitos, California, April 25-26, 2002.   Abstract   Paper
• A. A.-A. Gutub, A. F. Tenca, E. Savas, and C. K. Koc. Scalable and unified hardware to compute Montgomery inverse in GF(p) and GF(2^n). Cryptographic Hardware and Embedded Systems - CHES 2002, B. S. Kaliski Jr., C. K. Koc, and C. Paar, editors, 4th International Workshop, Redwood Shores, CA, USA, pages 484-499, Springer Verlag, LNCS Nr. 2523, August 13-15, 2002.   Abstract   Paper
• E. Savas and C. K. Koc. Architectures for unified field inversion with applications in elliptic curve cryptography. The 9th IEEE International Conference on Electronics, Circuits and Systems - ICECS 2002, to appear, Dubrovnik, Croatia, September 15-18, 2002.   Abstract   Paper
• C. van Dyke and C. K. Koc. On ubiquitous network security and anomaly detection. 2003 Symposium on Applications and Internet - Workshop on Security and Assurance in Ad hoc Networks, pages 374-378, Orlando, Florida, January 27-31, 2003.   Abstract   Paper
• F. Rodriguez-Henriquez and C. K. Koc. On fully parallel Karatsuba multipliers for GF(2^m). Proceedings of the International Conference on Computer Science and Technology - CST 2003, pages 405-410, Acta Press, Cancun, Mexico, May 19-21, 2003.   Abstract   Paper
• S. S. Erdem and C. K. Koc. A less recursive variant of Karatsuba-Ofman algorithm for multiplying operands of size a power of two. Proceedings, 16th IEEE Symposium on Computer Arithmetic, J.-C. Bajard and M. Schulte, editors, pages 28-35, IEEE Computer Society Press, Santiago de Compostela, Spain, June 15-18, 2003.   Abstract   Paper
• E. Savas, A. F. Tenca, and C. K. Koc. Dual-field multiplier architecture for cryptographic applications Thirty-Seventh Asilomar Conference on Signals, Systems, and Computers, pages 374-378, IEEE Press, Pacific Grove, California, November 9-12, 2003.   Abstract   Paper
• A. Levi, E. Cetintas, M. Aydos, C. K. Koc, and M. U. Caglayan. Relay attacks on Bluetooth authentication and solutions. Computer and Information Sciences - ISCIS 2004, C. Aykanat et al, editors, 19th International Symposium, Kemer-Antalya, Turkey, pages 278-288, Springer Verlag, LNCS Nr. 3280, October 27-29, 2004.   Abstract   Paper
• A. F. Tenca, L. A. Tawalbeh, S. Park, and C. K. Koc. A dual-field modular division algorithm and architecture for application specific hardware. Thirty-Eighth Asilomar Conference on Signals, Systems, and Computers, to appear, IEEE Press, Pacific Grove, California, November 7-10, 2004.   Abstract   Paper

Conference Presentations

• M. Aydos, B. Sunar, and C. K. Koc. An elliptic curve cryptography based authentication and key agreement protocol for wireless communication. 2nd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, Dallas, Texas, October 30, 1998.   Abstract   Paper

Books

• C. K. Koc and C. Paar, editors. Cryptographic Hardware and Embedded Systems. First International Workshop, Worcester, MA, USA. Springer Verlag, LNCS Nr. 1717, August 12-13, 1999.   Cover
• C. K. Koc and C. Paar, editors. Cryptographic Hardware and Embedded Systems - CHES 2000. Second International Workshop, Worcester, MA, USA. Springer Verlag, LNCS Nr. 1965, August 17-18, 2000.   Cover
• C. K. Koc, D. Naccache, and C. Paar, editors. Cryptographic Hardware and Embedded Systems - CHES 2001. Third International Workshop, Paris, France. Springer Verlag, LNCS Nr. 2162, May 14-16, 2001.   Cover
• B. S. Kaliski Jr., C. K. Koc, and C. Paar, editors. Cryptographic Hardware and Embedded Systems - CHES 2002. 4th International Workshop, Redwood Shores, CA, USA. Springer Verlag, LNCS Nr. 2523, August 13-15, 2002.   Cover
• C. D. Walter, C. K. Koc, and C. Paar, editors. Cryptographic Hardware and Embedded Systems - CHES 2003. 5th International Workshop, Cologne, Germany. Springer Verlag, LNCS Nr. 2779, September 7-10, 2003.   Cover

Patents and Patent Applications

• C. K. Koc and B. Sunar. Methods and Apparatus for Multiplication in a Galois Field GF(2^m), and Encoders and Decoders using Same. US Patent Nr. 6,343,305. January 29, 2002.   Abstract
• C. K. Koc. Transformation Methods for Optimizing Elliptic Curve Cryptographic Computations. US Patent Application, December 5, 1997.   Abstract
• C. K. Koc and A. F. Tenca. A Scalable Architecture for Montgomery Multiplication. US Patent Application, April 29, 1999.   Abstract
• C. K. Koc and E. Savas. Cryptographic Methods and Apparatus using Word-Wise Montgomery Multiplication. US Patent Application, August 17, 1999.   Abstract
• C. K. Koc, E. Savas, A. F. Tenca. A Scalable and Unified Multiplier for Finite Fields. US Patent Application, February 29, 2000.   Abstract
• C. K. Koc, T. Yanik, and E. Savas. Incomplete Modular Arithmetic. US Patent Application, June 20, 2000.   Abstract
• C. K. Koc, A. F. Tenca, and G. Todorov. An High-Radix Scalable Modular Multiplier. US Patent Application, April 25, 2001.   Abstract
• C. K. Koc and S. S. Erdem. A Less Recursive Variant of Karatsuba-Ofman Algorithm for Multiplying Operands of Size a Power of Two. US Patent Application, January 25, 2002.   Abstract
• C. K. Koc and S. S. Erdem. Improved Karatsuba-Ofman Multiplication in GF(2^m). US Patent Application, January 25, 2002.   Abstract

Technical Reports

• C. K. Koc. High-Speed RSA Implementation. TR 201, RSA Laboratories, 73 pages, November 1994.   Abstract   Report   (Also available from RSA Laboratories)
• C. K. Koc. RSA Hardware Implementation. TR 801, RSA Laboratories, 30 pages, April 1996.   Abstract   Report   (Also available from RSA Laboratories)
• C. K. Koc. Analysis of MMX Technology for Implementing Number-Theoretic Cryptosystems. Technical Report, Intel Corporation, 24 pages, February 1997.   Abstract
• C. K. Koc and T. Acar. A Methodology for High-Speed Software Implementations of Number-Theoretic Cryptosystems. Technical Report, Electrical and Computer Engineering, Oregon State University, 12 pages, May 1997.   Abstract Report
• C. K. Koc and A. Halbutogullari. A Reduction Method for Multiplication in Finite Fields. Technical Report, Electrical and Computer Engineering, Oregon State University, 16 pages, August 1998.   Abstract Report
• C. K. Koc. Recommended Test Plan for Arithmetic and Cryptographic Operations in DTCP Signing Facility. Technical Report, Intel Corporation, 9 pages, October 1998.   Abstract
• E. Savas and C. K. Koc. Efficient methods for composite field arithmetic. Technical Report, Electrical and Computer Engineering, Oregon State University, 19 pages, December 1999.   Abstract Report
• C. K. Koc. A Tutorial on p-adic Arithmetic. Technical Report, Electrical and Computer Engineering, Oregon State University, 13 pages, April 2002.   Abstract   Report

Theses

• T. Acar. High-Speed Algorithms & Architectures For Number-Theoretic Cryptosystems. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, December 4, 1997.   Abstract   Thesis
• A. Halbutogullari. Fast Bit-Level, Word-Level and Parallel Arithmetic in Finite Fields for Elliptic Curve Cryptosystems. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, November 2, 1998.   Abstract   Thesis
• B. Sunar. Fast Galois Field Arithmetic for Elliptic Curve Cryptography and Error Control Codes. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, November 6, 1998.   Abstract   Thesis
• J. B. Sessions. Fast Software Implementations of Block Ciphers. M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, November 23, 1998.   Abstract   Thesis
• M. Aydos. Efficient Wireless Security Protocols based on Elliptic Curve Cryptography. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 13, 2000.   Abstract   Thesis
• E. Savas. Implementation Aspects of Elliptic Curve Cryptography. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 20, 2000.   Abstract   Thesis
• M. Musa. Improved Montgomery Algorithms Using Special Primes and Impact on Elliptic Curve Digital Signature. M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 21, 2000.   Abstract   Thesis
• F. Rodriguez-Henriquez. New Algorithms and Architectures for Arithmetic in GF(2^m) Suitable for Elliptic Curve Cryptography. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 7, 2000.   Abstract   Thesis
• G. Todorov. ASIC Design, Implementation and Analysis of a Scalable High-Radix Montgomery Multiplier. M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, December 27, 2000.   Abstract   Thesis
• E. Turan. ECDSA Optimizations on an ARM Processor for a NIST Curve Over GF(2^k). M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 15, 2001.   Abstract   Thesis
• H. K. Tanik. ECDSA Optimizations on an ARM Processor for a NIST Curve Over GF(p). M.S. Thesis, Department of Computer Science, Oregon State University, June 19, 2001.   Abstract   Thesis
• S. S. Erdem. Improving the Karatsuba-Ofman Multiplication Algorithm for Special Applications. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, November 8, 2001.   Abstract
• T. Yanik. New Methods for Finite Field Arithmetic. Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, November 21, 2001.   Abstract   Thesis
• A. A.-A. Gutub. New Hardware Algorithms and Designs for Montgomery Modular Inverse Computation in Galois Fields GF(p) and GF(2^n). Ph.D. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 11, 2002.   Abstract   Thesis
• M. Khaldoon. Prototyping of Scalable Montgomery Multiplier using Field Programmable Gate Arrays (FPGAs). M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, July 23, 2002.   Abstract   Thesis
• B. Kurniawan. ASIC Design and Implementation of A Parallel Exponentiation Algorithm using Optimized Scalable Montgomery Multipliers. M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, July 23, 2002.   Abstract   Thesis
• A. W. Montville. Random Number Generation on Handheld Devices for Cryptographic Applications. M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, May 21, 2003.   Abstract   Thesis
• S. Almanei. Secure Instant Messaging: The Jabber Protocol. M.S. Thesis, Department of Electrical & Computer Engineering, Oregon State University, June 3, 2003.   Abstract   Thesis
• U. Banerjee. Hardware Encryption Using the MPC180 Security Co-Processor. M.S. Thesis, School of of Electrical Engineering & Computer Science, Oregon State University, December 4, 2003.   Abstract   Thesis
• P. Godbole. Optimizing the Advanced Encryption Standard on Intel's SIMD Architecture. M.S. Thesis, School of Electrical Engineering and Computer Science, Oregon State University, January 15, 2004.   Abstract   Thesis
• C. van Dyke. An In-Depth Analysis of Common Software Vulnerabilities and their Solutions. M.S. Thesis, School of Electrical Engineering and Computer Science, Oregon State University, May 11, 2004.   Abstract
• O. Aciicmez. Fast Hashing on Pentium SIMD Architecture. M.S. Thesis, School of Electrical Engineering and Computer Science, Oregon State University, May 11, 2004.   Abstract
• L. Tawalbeh. A Novel Unified Algorithm and Hardware Architecture for Integrated Modular Division and Multiplication in GF(p) and GF(2n) Suitable for Public-Key Cryptography. Ph.D. Thesis, School of Electrical Engineering & Computer Science, Oregon State University, October 28, 2004   Abstract   Thesis