Abstract
We examine the mechanism of homomorphic encryptions based on the subgroup membership problem. Using the mechanism, we construct a homomorphic encryption of a direct sum of groups.
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Cramer, R., Gennaro, R., Schoenmakers, B.: A Secure and Optimally Efficient Multi-Authority Election Scheme. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 103–118. Springer, Heidelberg (1997)
Goldwasser, S., Micali, S.: Probabilistic Encryption. Jounal of Computer and System Sciences 28, 270–299 (1984)
Katz, J., Myers, S., Ostrovsky, R.: Cryptographic Counters and Applications to Electronic Voting. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 78–92. Springer, Heidelberg (2001)
Okamoto, T., Uchiyama, S.: A New Public-key Cryptosystem as Secure as Factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)
Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Shoup, V.: Lower Bounds for Discrete Logarithms and Related Problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)
Tsiounis, Y., Yung, M.: On the security of ElGamal based encryption. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol. 1431, pp. 117–134. Springer, Heidelberg (1998)
Yamamura, A., Kurosawa, K.: Generic Algorithms and Key Agreement Protocols Based on Group Actions. In: Eades, P., Takaoka, T. (eds.) ISAAC 2001. LNCS, vol. 2223, pp. 208–218. Springer, Heidelberg (2001)
Yamamura, A., Saito, T.: Private Information Retrieval Based on the Subgroup Membership Problem. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 206–220. Springer, Heidelberg (2001)
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Yamamura, A. (2007). Homomorphic Encryptions of Sums of Groups. In: BoztaÅŸ, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_41
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DOI: https://doi.org/10.1007/978-3-540-77224-8_41
Publisher Name: Springer, Berlin, Heidelberg
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