Dr Robert Granger

Lecturer in Secure Systems

MSci (Mathematics), PhD (Computer Science)

+44 (0)1483 683037

r.granger@surrey.ac.uk

15 BB 02

Tuesday 10.00 - 12.00 (please contact me for the zoom meeting details)

Academic and research departments

Faculty of Engineering and Physical Sciences, Department of Computer Science.

About
In the media

Research
Supervision

Teaching

Publications

Biography

Robert Granger holds an MSci from the School of Mathematics, University of Bristol (2002) and a PhD from the Department of Computer Science, University of Bristol (2006). He has held postdoctoral positions at: the Centre for Applied Cryptographic Research, University of Waterloo, Canada; his alma mater, again in the Cryptography and Information Security Group; and at the Claude Shannon Institute, University College Dublin, Ireland. Before joining the University of Surrey as a Lecturer in Secure Systems in December 2018, he was a scientist in the Laboratory for Cryptologic Algorithms, EPFL, Switzerland.

Areas of specialism

Computational number theory and algebraic geometry; Cryptography and cryptanalysis; Algorithm design; Discrete mathematics; Finite field theory

Affiliations and memberships

International Association for Cryptologic Research (IACR)

Member since 2003.

News

16.07.19

Researchers hail the demise of an online security algorithm

In the media

26 May 2014

128-bit crypto scheme allegedly cracked in two hours: Boffins splat 'supersingular curve' crypto

The Register

20 May 2014

Researchers crack unassailable encryption algorithm in two hours

phys.org

20 May 2014

Interviewed live on World Radio Switzerland to talk about breaking an industry-standard ‘128-bit secure’ genus two supersingular curve.

World Radio Switzerland

03 March 2013

Maths whizzes in bits after record code crack

Irish Sunday Times

Research

Research interests

I am a computational number theorist whose main specialism is the number-theoretic assumptions, applications and algorithms underlying public key cryptography. I have over a decade of experience conceiving and leading often groundbreaking research projects in this area, and am an expert in foundational cryptographic security assumptions. In particular, I have designed several highly original discrete logarithm algorithms for various algebraic groups (one receiving the Best Paper Award, CRYPTO 2013) and have set several world records for discrete logarithm computations with my teams. I have a natural passion for attacking interesting and hard problems (in cryptography and elsewhere), combining deep insights with powerful mathematical and computational techniques. In addition to cryptography and cryptanalysis, number theory, algebraic geometry, algorithm design, discrete mathematics and finite field theory, I am interested in various theoretical properties of irreducible polynomials and curves over finite fields.

Supervision

Postgraduate research supervision

Current PhD students:

Bruno Sterner

Previous PhD students (co-supervised):

Benjamin Wesolowski (EPFL 2018)
Naomi Benger (CSI 2010)

My teaching

This year (2020/21) I am teaching

Asymmetric Cryptography (COMM045) in the Information Security MSc,
Foundations of Computing II (COM1033) in the CS BSc and the CIT BSc (jointly with Dr. Yunpeng Li).

I am supervising Professional Projects (COM3001), MSc dissertations (COMM002) and Professional Training placements.

I am also the Examinations Officer for the department.

My publications

Publications

Granger Robert, Scott Michael (2015)Faster ECC over F_2⁵²¹-1, In: Katz Jonathan (eds.), Public-Key Cryptography -- PKC 20159020pp. 539-553 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-662-46447-2_24

Göloğlu Faruk, Granger Robert, McGuire Gary, Zumbrägel Jens (2013)On the Function Field Sieve and the Impact of Higher Splitting Probabilities, In: Advances in Cryptology – CRYPTO 20138043pp. 109-128 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-642-40084-1_7

Granger R., Hess F., Oyono R., Thériault N., Vercauteren F. (2007)Ate Pairing on Hyperelliptic Curves, In: Advances in Cryptology - EUROCRYPT 20074515pp. 430-447 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-540-72540-4_25

Granger Robert, Scott Michael (2010)Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions, In: Public Key Cryptography – PKC 20106056pp. 209-223 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-642-13013-7_13

Granger Robert (2010)On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields, In: Advances in Cryptology - ASIACRYPT 20106477pp. 283-302 International Association for Cryptologic Research

DOI: 10.1007/978-3-642-17373-8_17

Granger Robert, Moss Andrew Generalised Mersenne numbers revisited, In: Mathematics of Computation82(284)pp. 2389-2420 American Mathematical Society

DOI: 10.1090/S0025-5718-2013-02704-4

Granger Robert Could, or should, the ancient Greeks have discovered the Lucas-Lehmer test?, In: The Mathematical Gazette97(539)pp. 242-255 The Mathematical Association

DOI: 10.1017/S0025557200005830

Granger Robert, Jovanovic Philipp, Mennink Bart, Neves Samuel (2016)Improved Masking for Tweakable Blockciphers with Applications to Authenticated Encryption, In: Advances in Cryptology – EUROCRYPT 20169665pp. 263-293 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-662-49890-3_11

Granger R., Page D., Stam M. (2005)Hardware and Software Normal Basis Arithmetic for Pairing-Based Cryptography in Characteristic Three, In: IEEE Transactions on Computers54(7)pp. 852-860 Institute of Electrical and Electronics Engineers (IEEE)

DOI: 10.1109/TC.2005.120

Ahmadi Omran, Granger Robert On isogeny classes of Edwards curves over finite fields, In: Journal of Number Theory132(6)pp. 1337-1358 Elsevier

DOI: 10.1016/j.jnt.2011.12.013

Granger Robert, Page D., Smart N. P. (2006)High Security Pairing-Based Cryptography Revisited, In: Algorithmic Number Theory4076pp. 480-494 Springer, Berlin, Heidelberg

DOI: 10.1007/11792086_34

Granger R., Page D., Stam M. (2006)On Small Characteristic Algebraic Tori in Pairing-Based Cryptography, In: LMS Journal of Computation and Mathematics9pp. 64-85 London Mathematical Society

DOI: 10.1112/S1461157000001194

Granger Robert (2017)Indiscreet discrete logarithms, In: Nieuw Archief voor Wiskunde5/18(3)pp. 176-183 Stichting Mathematisch Centrum

Granger Robert, Kleinjung Thorsten, Zumbrägel Jens (2017)On the discrete logarithm problem in finite fields of fixed characteristic, In: Transactions of the American Mathematical Society370(5)pp. 3129-3145 American Mathematical Society

DOI: 10.1090/tran/7027

Ahmadi Omran, Granger Robert An efficient deterministic test for Kloosterman sum zeros, In: Mathematics of Computation83(285)pp. 347-363 American Mathematical Society

DOI: 10.1090/S0025-5718-2013-02705-6

Göloğlu Faruk, Granger Robert, McGuire Gary, Zumbrägel Jens (2013)Solving a 6120-bit DLP on a Desktop Computer, In: Selected Areas in Cryptography -- SAC 20138282pp. 136-152 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-662-43414-7_7

Ahmadi Omran, Göloğlu Faruk, Granger Robert, McGuire Gary, Yilmaz Emrah Sercan (2016)Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients, In: Finite Fields and Their Applications42pp. 128-164 Elsevier

DOI: 10.1016/j.ffa.2016.07.009

Granger Robert, Kleinjung Thorsten, Zumbrägel Jens (2018)Indiscreet logarithms in finite fields of small characteristic, In: Advances in Mathematics of Communications12(2)pp. 263-286 American Institute of Mathematical Sciences

DOI: 10.3934/amc.2018017

Granger Robert, Kleinjung Thorsten, Zumbrägel Jens (2014)Breaking '128-bit Secure' Supersingular Binary Curves, In: Advances in Cryptology – CRYPTO 20148617pp. 126-145 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-662-44381-1_8

Granger Robert (2019)On the Enumeration of Irreducible Polynomials over GF(q) with Prescribed Coefficients, In: Finite Fields and Their Applications57pp. 156-229 Elsevier

DOI: 10.1016/j.ffa.2019.01.001

Granger Robert, Page D., Stam M. (2004)A Comparison of CEILIDH and XTR, In: Algorithmic Number Theory3076pp. 235-249 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-540-24847-7_17

Granger Robert, Vercauteren F. (2005)On the Discrete Logarithm Problem on Algebraic Tori, In: Advances in Cryptology – CRYPTO 20053621pp. 66-85 Springer, Berlin, Heidelberg

DOI: 10.1007/11535218_5

van Dijk Marten, Granger Robert, Page Dan, Rubin Karl, Silverberg Alice, Stam Martijn, Woodruff David (2005)Practical Cryptography in High Dimensional Tori, In: Advances in Cryptology – EUROCRYPT 20053494pp. 234-250 Springer, Berlin, Heidelberg

DOI: 10.1007/11426639_14

Granger Robert (2003)Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic, In: Cryptography and Coding2898pp. 190-206 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-540-40974-8_16

Smart N. P., Vercauteren F., Granger Robert, Holt A. J., Page D. (2004)Function Field Sieve in Characteristic Three, In: Algorithmic Number Theory3076pp. 223-234 Springer, Berlin, Heidelberg

DOI: 10.1007/978-3-540-24847-7_16

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Dr Robert Granger

Academic and research departments

About

Biography

Areas of specialism

Affiliations and memberships

In the media

News

Researchers hail the demise of an online security algorithm

In the media

Research

Research

Research interests

Supervision

Supervision

Postgraduate research supervision

Teaching

My teaching

Publications

My publications

Publications

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