Abstract
We propose a new fully homomorphic cryptosystem called Symmetric Polly Cracker (SymPC) and we prove its security in the information theoretical settings. Namely, we prove that SymPC approaches perfect secrecy in bounded CPA model as its security parameter grows (which we call approximate perfect secrecy).
In our construction, we use a Gröbner basis to generate a polynomial factor ring of ciphertexts and use the underlying field as the plaintext space. The Gröbner basis equips the ciphertext factor ring with a multiplicative structure that is easily algorithmized, thus providing an environment for a fully homomorphic cryptosystem.
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References
Fellows, M., Koblitz, N.: Combinatorial cryptosystems galore! In: Mullen, G.L., Shiue, P.J.-S. (eds.) Finite Fields: Theory, Applications, and Algorithms. Contemporary Mathematics, vol. 168, pp. 51–61. AMS (1994)
Steinwandt, R., Geiselmann, W., Endsuleit, R.: Attacking a polynomial-based cryptosystem: Polly cracker. International Journal of Information Security 1(3), 143–148 (2002)
Caboara, M., Caruso, F., Traverso, C.: Lattice polly cracker cryptosystems. J. Symb. Comput., 534–549 (2011)
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) STOC, pp. 169–178. ACM (2009)
Gentry, C., Halevi, S., Smart, N.P.: Fully Homomorphic Encryption with Polylog Overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. Springer, Heidelberg (2012)
Brakerski, Z., Gentry, C., Vaikuntanathan, V. (leveled) fully homomorphic encryption without bootstrapping. In: Goldwasser, S. (ed.) ITCS, pp. 309–325. ACM (2012)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. Journal of the ACM 56(6) (2009)
Albrecht, M.R., Farshim, P., Faugère, J.-C., Perret, L.: Polly Cracker, Revisited. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 179–196. Springer, Heidelberg (2011)
Herold, G.: Polly Cracker, Revisited, Revisited. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 17–33. Springer, Heidelberg (2012)
Cox, D.A., Little, J., O’Shea, D.: Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra, 2nd edn. Undergraduate texts in mathematics, pp. 1–536. Springer (1997)
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Hojsík, M., Půlpánová, V. (2013). A Fully Homomorphic Cryptosystem with Approximate Perfect Secrecy. In: Dawson, E. (eds) Topics in Cryptology – CT-RSA 2013. CT-RSA 2013. Lecture Notes in Computer Science, vol 7779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36095-4_24
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DOI: https://doi.org/10.1007/978-3-642-36095-4_24
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