M. Anokhin, Constructing a pseudo-free family of finite computational groups under the general integer factoring intractability assumption, Groups Complex. Cryptol. 5 (2013), no. 1, 53–74. Google Scholar
K. Azimian, Breaking Diffie–Hellman is no easier than root finding, Electronic Colloquium on Computational Complexity ECCC TR05-124, 2005, https://eccc.weizmann.ac.il/.
Y. Dodis, S. Goldwasser, Y. T. Kalai, C. Peikert and V. Vaikuntanathan, Public-key encryption schemes with auxiliary inputs, Proceedings of the 7th Theory of Cryptography Conference (TCC 2010), Lecture Notes in Comput. Sci. 5978, Springer, Berlin (2010), 361–381. Google Scholar
M. Fukumitsu, Pseudo-free groups and cryptographic assumptions, Ph.D. thesis, Tohoku University, 2014. Google Scholar
O. Goldreich, Foundations of Cryptography. Volume 1: Basic Tools, Cambridge University Press, Cambridge, 2001. Google Scholar
S. Goldwasser and M. Bellare, Lecture notes on cryptography, lecture notes (2008), http://cseweb.ucsd.edu/~mihir/papers/gb.html.
S. R. Hohenberger, The cryptographic impact of groups with infeasible inversion, Master’s thesis, Massachusetts Institute of Technology, 2003. Google Scholar
R. Impagliazzo and M. Naor, Efficient cryptographic schemes provably as secure as subset sum, J. Cryptology 9 (1996), no. 4, 199–216. Google Scholar
M. Luby, Pseudorandomness and Cryptographic Applications, Princeton University Press, Princeton, 1996. Google Scholar
D. Micciancio and P. Mol, Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions, Advances in Cryptology – Crypto 2011, Lecture Notes in Comput. Sci. 6841, Springer, Berlin (2011), 465–484. Google Scholar
R. L. Rivest, On the notion of pseudo-free groups, Proceedings of the 1st Theory of Cryptography Conference (TCC 2004), Lecture Notes in Comput. Sci. 2951, Springer, Berlin (2004), 505–521. Google Scholar
R. L. Rivest, On the notion of pseudo-free groups, presentation (2004), https://people.csail.mit.edu/rivest/pubs/Riv04e.slides.pdf.
Z. Shmuely, Composite Diffie–Hellman public-key generating systems are hard to break, Technical Report 356, Technion – Israel Institute of Technology, Haifa, 1985. Google Scholar
V. Shoup, A Computational Introduction to Number Theory and Algebra, 2nd ed., Cambridge University Press, Cambridge, 2008. Google Scholar
About the article
Published Online: 2017-04-19
Published in Print: 2017-05-01
Funding Source: Russian Foundation for Basic Research
Award identifier / Grant number: 13-01-00183
This research was supported in part by the Russian Foundation for Basic Research (13-01-00183).