Cryptology ePrint Archive: Report 2019/1375

New ideas to build noise-free homomorphic cryptosystems

Gérald Gavin and Sandrine Tainturier

Abstract: We design a very simple private-key encryption scheme whose decryption function is a rational function. This scheme is not born naturally homomorphic. To get homomorphic properties, a nonlinear additive homomorphic operator is specifically developed. The security analysis is based on symmetry considerations and we prove some formal results under the factoring assumption. In particular, we prove IND-CPA security in the generic ring model. Even if our security proof is not complete, we think that it is convincing and that the technical tools considered in this paper are interesting by themselves. Moreover, the factoring assumption is just needed to ensure that solving nonlinear equations or finding non-null polynomials with many roots is difficult. Consequently, the ideas behind our construction could be re-used in rings satisfying these properties. As motivating perspectives, we then propose to develop a simple multiplicative operator. To achieve this, randomness is added in our construction giving hope to remove the factoring assumption in order to get a pure multivariate encryption scheme.

Category / Keywords: public-key cryptography / Homomorphic cryptosystem, Multivariate encryption scheme, Generic ring model

Date: received 29 Nov 2019, last revised 2 Dec 2019

Contact author: gerald gavin at univ-lyon1 fr

Available format(s): PDF | BibTeX Citation

Version: 20191202:072416 (All versions of this report)

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