# Colin Walter - Home Page

For part of my time I am director of the department's Distance Learning MSc. The rest of my time is devoted to research.

## Research

My research interests include extracting key information using side channel leakage from implementations of cryptographic algorithms and counter-measures to reduce this, the general emphasis being on public key crypto-systems and RSA rather than other components; secure and time and/or space efficient hardware and software designs for computer arithmetic, particularly for exponentiation, modular multiplication and other operations used in PKC; and authentication of resource-limited peripheral devices in trusted computing.

## Biography

1968-1972 BSc Maths, 1st class Hons, University of Edinburgh

1972-1976 PhD, Trinity College, University of Cambridge

1976-1984 College Lecturer, Mathematics Dept., University College, Dublin

1984-2002 Senior Lecturer, Computation Dept., UMIST (Manchester)

2002-2008 Head of Cryptography, Comodo Research Lab, Bradford

2009-*present* Director of Distance Learning, ISG, Royal Holloway.

## History

Earlier in my career I spent a number of years looking at class numbers of algebraic number fields and was hoping to apply algebraic geometric techniques to obtain algebraic relationships between class groups for which there were numerical relationships when I became side-tracked into mathematical logic and computability. I briefly looked at developing some polynomial-time algorithms to solve the graph isomorphism problem before moving into program specification and functional programming.

More relevant to today's cryptography, I was trying to prove Fermat's last theorem and generate primes as a school boy (try factorising {x^(p^(n+1))-y^(p^(n+1))}/{x^(p^n)-y^(p^n)} for prime p and integers x,y,n); briefly - and unsuccessfully - looked at lattice type geometry of numbers problems under JWS Cassels, but shared an office with Andrew Wiles; did some consultancy for Plessey-Crypto designing an RSA chip for EFTPOS; and looked into side channel leakage issues for the NatWest Bank's credit/debit cards.

## Contact

Room: McCrea 340 Tel: +44 (0)1784 443089 E-mail: Colin DOT Walter AT rhul.ac.uk

## Publications

Please email me for copies of any of these which you cannot obtain through the given links.

[12B] C. D. Walter, *A Compact Left-to-Right Mixed Base Exponentiation Scheme*, submitted for publication.

[12A] C. D. Walter, *A Duality in Space Usage between Left-to-Right and Right-to-Left Exponentiation*, CT-RSA 2012, Lecture Notes in Computer Science, Springer-Verlag, vol. **7178**, pp. 84-97. PDF Slides

[11A] M. Q. Saeed & C. D. Walter, *A Record Composition/Decomposition Attack on the NDEF Signature Record Type Definition*, 6th Internat. Conf. for Internet Technology and Secured Transactions (ICITST-2011), IEEE, *to appear*.

[10B] C. D. Walter, *Fast Scalar Multiplication for ECC over GF(p) using Division Chains*, 11th International Workshop on Information Security Applications – WISA 2010, Lecture Notes in Computer Science, Springer-Verlag, vol. **6513**, pp 61-75. PDF

[10A] C. D. Walter, *Right-to-Left or Left-to-Right Exponentiation?*, COSADE 2010

[09] W. Schindler, C. Walter, *Optimal Recovery of Secret Keys from Weak Side Channel Traces"*, Cryptography and Coding - IMA 2009, Lecture Notes in Computer Science, Springer-Verlag, vol. **5921**, 2009, pp 446-468.

[08C] C. D. Walter, *Recovering Secret Keys from Weak Side Channel Traces of Differing Lengths*, Cryptographic Hardware and Embedded Systems – CHES 2008, Lecture Notes in Computer Science, Springer-Verlag, vol. **5154**, pp 214-227. PDF

[08B] C. D. Walter, *Randomised Exponentiation Algorithms*, chapter in “*Cryptographic Engineering*”, Çetin Koç (ed), Springer, 2008, pp. 451-473.

[08A] C. D. Walter, *Leakage from Montgomery Multiplication*, chapter in “*Cryptographic Engineering*”, Çetin Koç (ed), Springer, 2008, pp. 431-449.

[07] C. D. Walter, *Longer Randomly Blinded RSA Keys May Be Weaker Than Shorter Ones*, WISA 2007, Lecture Notes in Computer Science, Springer-Verlag, vol. **4867**, 2008, pp 303-316. PDF

[05C] C. D. Walter & D. Samyde, *Data Dependent Power Use in Multipliers*, Proc. 17th IEEE Symposium on Computer Arithmetic, IEEE Press, 2005, pp 4-12.

[05B] S. Contini, Ç. K. Koç & C. D. Walter, *Modular Arithmetic*, Encyclopedia of Cryptography and Security, Henk van Tilborg (ed), Springer 2005.

[05A] Ç. K. Koç & C. D. Walter, *Montgomery Multiplication*, Encyclopedia of Cryptography and Security, Henk van Tilborg (ed), Springer 2005.

[04B] C. D. Walter, *Simple Power Analysis of Unified Code for ECC Double and Add*, Cryptographic Hardware and Embedded Systems – CHES 2004, Lecture Notes in Computer Science, Springer-Verlag, vol. **3156**, pp. 191-204.

[04A] C. D. Walter, *Issues of Security with the Oswald-Aigner Exponentiation Algorithm*, Topics in Cryptology – CT-RSA 2004, Lecture Notes in Computer Science, Springer-Verlag, vol. **2964**, pp. 208-221.

[03F] M. Arnold, T. Bailey, J. Cowles & C. Walter, *Fast Fourier Transforms using the Complex Logarithm Number System*, J. VLSI Signal Proc. **33** (2003) pp. 325-335.

[03E] W. Schindler & C. D. Walter, *More Detail for a Combined Timing and Power Attack against Implementations of RSA*, Proc 9th IMA Internat. Conf. on Cryptography and Coding, Lecture Notes in Computer Science, Springer-Verlag, vol. **2898**, 2003, pp. 245-263.

[03D] C. D. Walter, *Longer Keys may facilitate Side Channel Attacks*, Proc 10th Annual Workshop on Selected Areas in Cryptography – SAC 2003, Lecture Notes in Computer Science, Springer-Verlag, vol. **3006**, pp. 42-57.

[03C] C. D. Walter, *Seeing through Mist Given a Small Fraction of an RSA Private Key*, Topics in Cryptology – CT-RSA 2003, Lecture Notes in Computer Science, vol. **2612**, Springer-Verlag, 2003, pp. 391-402.

[03B] C. D. Walter, *Security Constraints on the Oswald-Aigner Exponentiation Algorithm*, Cryptology ePrint Archive: Report 2003/013, IACR, 22 Jan 2003.

[03A] C. D. Walter, Ç. Koç & C. Paar (editors), *Cryptographic Hardware and Embedded Systems - CHES 2003*, Lecture Notes in Computer Science, vol. **2779**, Springer-Verlag, 2003, 441 pp.

[02D] C. D. Walter, *Breaking the Liardet-Smart Randomized Exponentiation Algorithm*, Proc. CARDIS '02, San Jose, 21-22 Nov 2002, USENIX Assoc, 2002, pp. 59-68.

[02C] C. D. Walter, *Some Security Aspects of the MIST Randomized Exponentiation Algorithm*, Cryptographic Hardware and Embedded Systems – CHES 2002, Lecture Notes in Computer Science, vol. **2523**, Springer-Verlag, 2002, pp. 276-290.

[02B] C. D. Walter, *MIST: An Efficient, Randomized Exponentiation Algorithm for Resisting Power Analysis*, Topics in Cryptology – CT-RSA 2002, Lecture Notes in Computer Science, Springer-Verlag, vol. **2271**, 2001, pp. 53-66. PDF

[02A] C. D. Walter, *Precise Bounds for Montgomery Modular Multiplication and Some Potentially Insecure RSA Moduli*, Topics in Cryptology – CT-RSA 2002, Lecture Notes in Computer Science, vol. **2271**, Springer-Verlag, 2001, pp. 30-39. PDF

[01D] C. D. Walter, *CHES 2001*, Smart Card News, May 2001.

[01C] M. G. Arnold & C. D. Walter, *Unrestricted Faithful Rounding is Good Enough for some LNS Applications*, Proc. 15th IEEE Symposium on Computer Arithmetic, IEEE Press, 2001, pp 237-246.

[01B] C. D. Walter, *Sliding Windows Succumbs to Big Mac Attack*, Cryptographic Hardware and Embedded Systems – CHES 2001, Ç. Koç, D. Naccache & C. Paar, eds, Lecture Notes in Computer Science, vol. **2162**, Springer-Verlag, 2001.

[01A] C. D. Walter & Susan Thompson, *Distinguishing Exponent Digits by Observing Modular Subtractions*, Topics in Cryptology, D. Naccache (editor), Lecture Notes in Computer Science, vol. **2020**, Springer-Verlag, 2001, pp. 192-207.

[00B] C. D. Walter, *Data Integrity in Hardware for Modular Arithmetic*, Cryptographic Hardware and Embedded Systems, Christof Paar & Çetin Koç, eds, Lecture Notes in Computer Science, vol. **1965**, Springer-Verlag, 2000, pp. 204-215.

[00A] C. D. Walter, *Improved Linear Systolic Array for Fast Modular Exponentiation*, IEE Computers and Digital Techniques **147** no. 5 (Sept 2000) pp. 323-328.

[99D] C. D. Walter, *Montgomery Exponentiation Needs No Final Subtractions*, Electronics Letters **35** no. 21 (Oct 1999) pp. 1831-1832.

[99C] N. Nedjah, C. D. Walter & S. E. Eldridge, *Efficient Automata-Driven Pattern Matching for Equational Programs*, Software Practice & Experience **29** no. 9 (1999) pp. 793-813. PDF

[99B] C. D. Walter, *An Overview of Montgomery’s Multiplication Technique: How to make it Smaller and Faster*, Cryptographic Hardware and Embedded Systems, Christof Paar & Çetin Koç, eds, Lecture Notes in Computer Science, vol. **1717**, Springer-Verlag, 1999, pp. 80-93.

[99A] C. D. Walter, *Moduli for Testing Implementations of the RSA Cryptosystem*, Proc. 14th IEEE Symposium on Computer Arithmetic, IEEE Press, 1999, pp. 78-85.

[98C] C. D. Walter, *Techniques for the Hardware Implementation of Modular Multiplication*, Proc. 2nd IMACS Internat. Conf. on Circuits, Systems & Computers, Athens, Oct 1998, vol. **2**, pp. 945-949.

[98B] C. D. Walter, *Techniques for the Hardware Implementation of Modular Multiplication* in "*Recent Advances in Information Science and Technology*", N. Mastorakis editor, World Scientific 1998, pp. 157-161, ISBN 981-02-3657-3.

[98A] C. D. Walter, *Exponentiation using Division Chains*, IEEE Transactions on Computers, **47** no. 7 (July 1998) pp. 757-765. PDF

[97E] C. D. Walter, N. Nedjah & S.E. Eldridge, *More efficient Pattern-Matching Automata for Overlapping Patterns*, Proc. International Workshop on the Implementation of Functional Languages, St Andrews, Sept 1997, pp. 341-350.

[97D] N. Nedjah, C. D. Walter & S. E. Eldridge, *Optimal Left-to-Right Pattern-Matching Automata for Equational Programs*, Proc. ALP97 & HOA97, Lecture Notes in Computer Science, vol. **1298**, Springer-Verlag, 1997, pp. 273-286.

[97C] C. D. Walter, *Exponentiation using Division Chains*, 13th IEEE Symposium on Computer Arithmetic, IEEE Press 1997, pp. 92-98.

[97B] C. D. Walter, *Analysis of Delays in Converting from a Redundant Representation*, IEE Computers & Digital Techniques **144** no. 4 (July 1997) pp. 219-221.

[97A] C. D. Walter, *Space-Time Trade-Offs for Higher Radix Modular Multiplication using Repeated Addition*, IEEE Transactions on Computers **46** no. 2 (1997) pp. 139-141.

[95C] C. D. Walter, *Verification of Hardware combining Multiplication, Division & Square Root*, Microprocessors & Microsystems **19** (1995) pp. 243-245.

[95B] C. D. Walter, *Still Faster Modular Multiplication*, Electronics Letters **31** no 4 (1995) pp. 263-264.

[95A] C. D. Walter, *Optimal Parameters for Fully On-Line Arithmetic*, International J. of Computer Mathematics **56** (1995) pp. 11-18. PDF

[94B] C. D. Walter, *Improving Average Delay for On-Line Algorithms*, Electronics Letters **30** no. 23 (1994) pp. 1925-6.

[94A] C. D. Walter, *Logarithmic Speed Modular Multiplication*, Electronics Letters **30** no. 17 (1994) pp. 1397-1398.

[93B] S. E. Eldridge & C. D. Walter, *Hardware Implementation of Montgomery’s Modular Multiplication Algorithm*, IEEE Trans. on Computers **42** (1993) pp. 693-699. PDF

[93A] C. D. Walter, *Systolic Modular Multiplication*, IEEE Transactions on Computers **42** (1993) pp. 376-378. PDF

[91D] C. D. Walter, *Faster Modular Multiplication by Operand Scaling*, Proc. of CRYPTO 91, Lecture Notes in Computer Science vol. **576**, Springer-Verlag, 1992, pp. 313-323.

[91C] C. D. Walter & S.E. Eldridge, *Formal Specification and Verification of Software*, Concise Encyclopedia of Software Engineering, D. Morris & B. Tamm editors, Pergamon Press, 1991, pp. 331-338, ISBN 0-08-036214-1.

[91B] C. D. Walter, *Formal Methods*, Concise Encyclopedia of Software Engineering, D. Morris & B. Tamm editors, Pergamon Press, 1991, pp. 135-138, ISBN 0-08-036214-1

[91A] C. D. Walter, *Fast Modular Multiplication using 2-Power Radix*, International J. of Computer Mathematics **3** (1991) pp. 21-28.

[90] C. D. Walter & S. E. Eldridge, *A Verification of Brickell’s Fast Modular Multiplication Algorithm*, Internat. J. of Computer Maths **33** (1990) pp. 153-169.

[86C] C. D. Walter, *UMIST OBJ Manual*, version 1.0, UMIST, 1986, 28+iii pp.

[86B] R. Dowsing, V. J. Rayward-Smith & C. D. Walter, *A First Course in Formal Logic and its Applications in Computer Science*, Blackwell Scientific Publications, Oxford, 1986 (265pp + vi).

[86A] C. D. Walter, *Adjacency Matrices*, SIAM J. on Algebraic & Discrete Methods **7** (1986) pp. 18-29.

[84] C. D. Walter, *Computers in the Teaching of Mathematics at UCD*, Bull Irish Mathematical Society **10** (1984) pp. 83-88.

[83] C. D. Walter, *Intersection Numbers for Coherent Configurations and the Spectrum of a Graph*, J. of Combinatorial Theory (B) **35** (1983) pp. 201-204.

[80] C. D. Walter, *Pure fields of degree 9 with class number prime to 3*, Annales de l’Institut Fourier, Grenoble **30** (1980) pp. 1-16.

[79C] C. D. Walter, *The ambiguous class group and the genus group of certain non-normal extensions*, Mathematika, **26** (1979) pp. 113-124.

[79B] C. D. Walter, *Kuroda’s class number relation*, Acta Arithmetica **35** (1979) pp. 41-51.

[79A] C. D. Walter, *Brauer’s class number relation*, Acta Arithmetica **35** (1979) pp. 33-40.

[77B] C. D. Walter, *A class number relation in Frobenius extensions of number fields*, Mathematika **24** (1977) pp. 216-225.

[77A] C. J. Parry & C. D. Walter, *The class number of pure fields of prime degree*, Mathematika **23** (1976) pp. 220 - 226, and Mathematika **24** (1977) p. 122.

[76] C. D. Walter, *Class Number Relations in Algebraic Number Fields*, PhD thesis, Univ. of Cambridge, April 1976, x+101pp.