Converting Cryptographic Schemes from Symmetric to Asymmetric Bilinear Groups
We propose a method to convert schemes designed over symmetric bilinear groups into schemes over asymmetric bilinear groups. The conversion assigns variables to one or both of the two source groups in asymmetric bilinear groups so that all original computations in the symmetric bilinear groups go through over asymmetric groups without having to compute isomorphisms between the source groups. Our approach is to represent dependencies among variables using a directed graph, and split it into two graphs so that variables associated to the nodes in each graph are assigned to one of the source groups. Though searching for the best split is cumbersome by hand, our graph-based approach allows us to automate the task with a simple program. With the help of the automated search, our conversion method is applied to several existing schemes including one that has been considered hard to convert.
KeywordsConversion Symmetric Bilinear Groups Asymmetric Bilinear Groups
Unable to display preview. Download preview PDF.
- 2.Akinyele, J.A., Green, M., Hohenberger, S.: Using SMT solvers to automate design tasks for encryption and signature schemes. In: ACM CCS 2013, pp. 399–410 (2013)Google Scholar
- 3.Barbulescu, R., Gaudry, P., Joux, A., Thomé, E.: A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. IACR ePrint Archive, 2013/400 (2013)Google Scholar
- 4.Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: ACM CCS 1993, pp. 62–73 (1993)Google Scholar
- 7.Boneh, D., Shacham, H.: Group signatures with verifier-local revocation. In: ACM CCS 2004, pp. 168–177 (2004)Google Scholar
- 9.Chatterjee, S., Menezes, A.: On cryptographic protocols employing asymmetric pairings - the role of psi revisited. IACR ePrint Archive, 2009/480 (2009)Google Scholar
- 14.Göloglu, F., Granger, R., McGuire, G., Zumbrägel, J.: On the function field sieve and the impact of higher splitting probabilities: Application to discrete logarithms in f21971. IACR ePrint Archive, 2013/074 (2013)Google Scholar
- 16.Joux, A.: A new index calculus algorithm with complexity l(1/4+o(1)) in very small characteristic. IACR ePrint Archive, 2013/095 (2013)Google Scholar
- 18.Menezes, A.: Asymmetric pairings. Invited Talk in ECC 2009 (2009), http://math.ucalgary.ca/sites/ecc.math.ucalgary.ca/files/u5/Menezes_ECC2009.pdf
- 19.Ramanna, S.C., Chatterjee, S., Sarkar, P.: Variants of waters’ dual-system primitives using asymmetric pairings. IACR ePrint Archive, 2012/024 (2012)Google Scholar