Patents

1. 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.   PDF
2. C. K. Koc and A. F. Tenca. A scalable architecture for Montgomery multiplication. US Patent Nr. 7,046,800. May 16, 2006.   PDF
3. C. K. Koc and E. Savas. Cryptographic methods and apparatus using word-wise Montgomery multiplication. US Patent Nr. 7,050,579. May 23, 2006.   PDF
4. C. K. Koc, T. Yanik, and E. Savas. Methods and apparatus for incomplete modular arithmetic. US Patent Nr. 7,080,109. July 18, 2006.   PDF
5. C. K. Koc, A. F. Tenca, and G. Todorov. Methods and apparatus for variable radix scalable modular multiplication. US Patent Nr. 7,174,015. February 6, 2007.   PDF
6. C. K. Koc, E. Savas, and A. F. Tenca. Scalable and unified multiplication methods and apparatus. US Patent Nr. 7,240,204. July 3, 2007.   PDF
7. C. K. Koc and S. S. Erdem. Multiplication of multi-precision numbers having a size of a power of two. US Patent Nr. 7,401,109. July 15, 2008.   PDF
8. C. K. Koc and S. S. Erdem. Lean multiplication of multi-precision numbers over GF(2^m). US Patent Nr. 7,447,310. November 4, 2008.   PDF
9. C. K. Koc. Systems and methods for providing security for computer systems. US Patent Nr. 8,090,934. January 3, 2012.   PDF

Patent Applications

1. C. K. Koc and G. Saldamli. Spectral modular arithmetic method and apparatus. US Patent Application Nr. 11/413,686. April 28, 2005.
2. G. Hammouri, K. Akdemir, B. Sunar, and C. K. Koc. Computing system identifier using software extraction of manufacturing variability. US Patent Application Nr. 12/838,021. July 16, 2010.
3. G. Hammouri, B. Sunar, and C. K. Koc. Mobile phone aided cryptographic operations system and method. US Patent Application Nr. 12/838,253. July 16, 2010.