Cryptanalysis via Algebraic Spans
We introduce a method for obtaining provable polynomial time solutions of problems in nonabelian algebraic cryptography. This method is widely applicable, easier to apply, and more efficient than earlier methods. After demonstrating its applicability to the major classic nonabelian protocols, we use this method to cryptanalyze the Triple Decomposition key exchange protocol, the only classic group theory based key exchange protocol that could not be cryptanalyzed by earlier methods.
We thank Avraham (Rami) Eizenbud and Craig Gentry for intriguing discussions. A part of this work was carried out while the third named author was on Sabbatical at the Weizmann Institute of Science. This author thanks his hosts for their kind hospitality. The research of the first and third named authors was partially supported by the European Research Council under the ERC starting grant n. 757731 (LightCrypt), and by the BIU Center for Research in Applied Cryptography and Cyber Security, in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office.
- 1.Andrecut, M.: A matrix public key cryptosystem, arXiv eprint 1506.00277 (2015)Google Scholar
- 9.Gilman, R., Myasnikov, A., Myasnikov, A., Ushakov, A.: New developments in commutator key exchange. In: Proceedings of the First International Conference on Symbolic Computation and Cryptography, Beijing, pp. 146–150 (2008). http://www-calfor.lip6.fr/~jcf/Papers/scc08.pdf
- 11.Holt, D.: Answer to MathOverflow question. http://mathoverflow.net/questions/154761
- 14.Kurt, Y.: A new key exchange primitive based on the triple decomposition problem, IACR eprint 2006/378Google Scholar
- 15.Peker, Y.K.: A new key agreement scheme based on the triple decomposition problem. Int. J. Netw. Secur. 16, 340–350 (2014)Google Scholar
- 19.Roman’kov, V.: Algebraic Cryptography. Omsk State Dostoevsky University, Omsk (2013). (In Russian)Google Scholar
- 20.Roman’kov, V.: Cryptanalysis of some schemes applying automorphisms. Prikladnaya Discretnaya Matematika 3, 35–51 (2013). (In Russian)Google Scholar
- 25.Shpilrain, V., Ushakov, A.: A new key exchange protocol based on the decomposition problem. In: Gerritzen, L., Goldfeld, D., Kreuzer, M., Rosenberger, G., Shpilrain, V. (eds.) Algebraic Methods in Cryptography. Contemporary Mathematics, vol. 418, pp. 161–167 (2006)Google Scholar
- 26.Stickel, E.: A new method for exchanging secret keys. In: Proceedings of the Third International Conference on Information Technology and Applications (ICITA 2005), pp. 426–430 (2005)Google Scholar
- 27.Tsaban, B.: The Conjugacy Problem: cryptoanalytic approaches to a problem of Dehn. minicourse, Düsseldorf University, Germany, July–August 2012. http://reh.math.uni-duesseldorf.de/~gcgta/slides/Tsaban_minicourses.pdf