Dr Robert Granger


Lecturer in Secure Systems
MSci (Mathematics), PhD (Computer Science)
+44 (0)1483 683037
15 BB 02
Tuesday 10.00 - 12.00 (please contact me for the zoom meeting details)

Biography

Areas of specialism

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

News

In the media

Interviewed live on World Radio Switzerland to talk about breaking an industry-standard ‘128-bit secure’ genus two supersingular curve.
World Radio Switzerland
Maths whizzes in bits after record code crack
Irish Sunday Times

Research

Research interests

Supervision

Postgraduate research supervision

My teaching

My publications

Publications

Granger Robert, Scott Michael (2015)Faster ECC over F2521-1, In: Katz Jonathan (eds.), Public-Key Cryptography -- PKC 20159020pp. 539-553 Springer, Berlin, Heidelberg
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
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
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
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
Granger Robert, Moss Andrew Generalised Mersenne numbers revisited, In: Mathematics of Computation82(284)pp. 2389-2420 American Mathematical Society
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
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
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)
Ahmadi Omran, Granger Robert On isogeny classes of Edwards curves over finite fields, In: Journal of Number Theory132(6)pp. 1337-1358 Elsevier
Granger Robert, Page D., Smart N. P. (2006)High Security Pairing-Based Cryptography Revisited, In: Algorithmic Number Theory4076pp. 480-494 Springer, Berlin, Heidelberg
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
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
Ahmadi Omran, Granger Robert An efficient deterministic test for Kloosterman sum zeros, In: Mathematics of Computation83(285)pp. 347-363 American Mathematical Society
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
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
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
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
Granger Robert (2019)On the Enumeration of Irreducible Polynomials over GF(q) with Prescribed Coefficients, In: Finite Fields and Their Applications57pp. 156-229 Elsevier
Granger Robert, Page D., Stam M. (2004)A Comparison of CEILIDH and XTR, In: Algorithmic Number Theory3076pp. 235-249 Springer, Berlin, Heidelberg
Granger Robert, Vercauteren F. (2005)On the Discrete Logarithm Problem on Algebraic Tori, In: Advances in Cryptology – CRYPTO 20053621pp. 66-85 Springer, Berlin, Heidelberg
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
Granger Robert (2003)Estimates for Discrete Logarithm Computations in Finite Fields of Small Characteristic, In: Cryptography and Coding2898pp. 190-206 Springer, Berlin, Heidelberg
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