M. Abramowitz and I. Stegun, Stirling Numbers of the Second Kind, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1972.

I. Ajzen, The theory of planned behavior, Theories of Cognitive Self-Regulation, pp.179-211, 1991.
DOI : 10.1016/0749-5978(91)90020-T

A. J. Aviv, K. L. Gibson, E. Mossop, M. Blaze, and J. M. Smith, Smudge attacks on smartphone touch screens, 4th USENIX Workshop on Offensive Technologies, WOOT '10, 2010.

A. Baddeley, Working Memory: Theories, Models, and Controversies, Annual Review of Psychology, vol.63, issue.1, pp.1-29, 2012.
DOI : 10.1146/annurev-psych-120710-100422

A. Bianchi, I. Oakley, V. Kostakos, and D. S. Kwon, The phone lock, Proceedings of the fifth international conference on Tangible, embedded, and embodied interaction, TEI '11, pp.197-200, 2011.
DOI : 10.1145/1935701.1935740

R. Biddle, S. Chiasson, and P. C. Van-oorschot, Graphical passwords, ACM Computing Surveys, vol.44, issue.4, pp.1-1941, 2012.
DOI : 10.1145/2333112.2333114

N. Cowan, The Magical Mystery Four, Current Directions in Psychological Science, vol.19, issue.1, pp.51-57, 2010.
DOI : 10.1038/nature04171

D. Davis, F. Monrose, and M. K. Reiter, On user choice in graphical password schemes, Proceedings of the 13th USENIX Security Symposium, pp.151-164, 2004.

F. D. Davis, Perceived Usefulness, Perceived Ease of Use, and User Acceptance of Information Technology, MIS Quarterly, vol.13, issue.3, pp.319-340, 1989.
DOI : 10.2307/249008

R. Dhamija and A. Perrig, Deja vu-a user study: Using images for authentication, 9th USENIX Security Symposium, 2000.

L. N. Evangelin, A. L. Fred, R. Hayashi, N. Dhamija, A. Christin et al., Biometric authentication of physical characteristics recognition using artificial neural network with PSO algorithm, Proceedings of the 4th Symposium on Usable Privacy and Security, SOUPS '08, pp.219-229, 2008.
DOI : 10.1504/IJCAT.2017.088196

S. Higashikawa, T. Kosugi, S. Kitajima, and M. Mambo, Shouldersurfing resistant authentication using pass pattern of pattern lock, IEICE Transactions, vol.101, issue.1, pp.45-52, 2018.

I. Jermyn, A. Mayer, F. Monrose, M. K. Reiter, and A. D. Rubin, The design and analysis of graphical passwords, Proceedings of the 8th Conference on USENIX Security Symposium - SSYM'99, pp.1-1, 1999.

D. E. Knuth, Two Notes on Notation, The American Mathematical Monthly, vol.90, issue.25, pp.403-422, 1992.
DOI : 10.1017/S0013091500035367

T. Kwon and S. Na, TinyLock: Affordable defense against smudge attacks on smartphone pattern lock systems, Computers & Security, vol.42, pp.137-150, 2014.
DOI : 10.1016/j.cose.2013.12.001

M. Lee, Security Notions and Advanced Method for Human Shoulder-Surfing Resistant PIN-Entry, IEEE Transactions on Information Forensics and Security, vol.9, issue.4, pp.695-708, 2014.
DOI : 10.1109/TIFS.2014.2307671

A. Mahfouz, T. M. Mahmoud, and A. S. Eldin, A survey on behavioral biometric authentication on smartphones, Journal of Information Security and Applications, vol.37, pp.28-37, 2017.
DOI : 10.1016/j.jisa.2017.10.002

N. Malkin, M. Harbach, A. De-luca, and S. Egelman, THE ANATOMY OF SMARTPHONE UNLOCKING, GetMobile: Mobile Computing and Communications, vol.20, issue.3, pp.42-46, 2017.
DOI : 10.1109/ICNP.2014.43

K. Mowery, S. Meiklejohn, and S. Savage, Heat of the moment: Characterizing the efficacy of thermal camera-based attacks, 5th USENIX Workshop on Offensive Technologies, pp.46-53, 2011.

S. J. Murdoch, S. Drimer, R. J. Anderson, and M. Bond, Chip and PIN is Broken, 2010 IEEE Symposium on Security and Privacy, pp.433-446, 2010.
DOI : 10.1109/SP.2010.33

. Nielsen, Usability Engineering, 1993.

A. Papadopoulos, T. Nguyen, E. Durmus, and N. Memon, IllusionPIN: Shoulder-Surfing Resistant Authentication Using Hybrid Images, IEEE Transactions on Information Forensics and Security, vol.12, issue.12, pp.2875-2889, 2017.
DOI : 10.1109/TIFS.2017.2725199
URL : http://arxiv.org/pdf/1708.06508

M. and R. Everett, Diffusion of innovations, 1995.

V. Roth, K. Richter, and R. Freidinger, A PIN-entry method resilient against shoulder surfing, Proceedings of the 11th ACM conference on Computer and communications security , CCS '04, pp.236-245, 2004.
DOI : 10.1145/1030083.1030116

F. Schaub, M. Walch, B. Könings, and M. Weber, Exploring the design space of graphical passwords on smartphones, Proceedings of the Ninth Symposium on Usable Privacy and Security, SOUPS '13, pp.1-11, 2013.
DOI : 10.1145/2501604.2501615

P. Shi, B. Zhu, and A. Youssef, A PIN Entry Scheme Resistant to Recording-Based Shoulder-Surfing, 2009 Third International Conference on Emerging Security Information, Systems and Technologies, pp.237-241, 2009.
DOI : 10.1109/SECURWARE.2009.43

Z. Sun, Y. Wang, G. Qu, and Z. Zhou, A 3-d hand gesture signature based biometric authentication system for smartphones, pp.1359-1373, 2016.

E. Von-zezschwitz, A. D. Luca, B. Brunkow, and H. Hussmann, SwiPIN, Proceedings of the 33rd Annual ACM Conference on Human Factors in Computing Systems, CHI '15, pp.1403-1406, 2015.
DOI : 10.1145/1030083.1030116

S. Wiedenbeck, J. Waters, L. Sobrado, and J. Birget, Design and evaluation of a shoulder-surfing resistant graphical password scheme, Proceedings of the working conference on Advanced visual interfaces , AVI '06, pp.177-184, 2006.
DOI : 10.1145/1133265.1133303