MarriageTheoremのこと

_ IACR ePrint 2015/135まで確認済み、ECCC 2003年分まで確認済み

_ 気になった論文１：Self-bilinear Map on Unknown Order Groups from Indistinguishability Obfuscation and Its Applications, Takashi Yamakawa and Shota Yamada and Goichiro Hanaoka and Noboru Kunihiro, http://eprint.iacr.org/2015/128

A self-bilinear map is a bilinear map where the domain and target groups are identical. In this paper, we introduce a self-bilinear map with auxiliary information which is a weaker variant of a self-bilinear map, construct it based on indistinguishability obfuscation and prove that a useful hardness assumption holds with respect to our construction under the factoring assumption. From our construction, we obtain a multilinear map with interesting properties: the level of multilinearity is not bounded in the setup phase, and representations of group elements are compact, i.e., their size is independent of the level of multilinearity. This is the first construction of a multilinear map with these properties. Note, however, that to evaluate the multilinear map, auxiliary information is required. As applications of our multilinear map, we construct multiparty non-interactive key-exchange and distributed broadcast encryption schemes where the maximum number of users is not fixed in the setup phase. Besides direct applications of our self-bilinear map, we show that our technique can also be used for constructing somewhat homomorphic encryption based on indistinguishability obfuscation and the Phi-hiding assumption.

_ 気になった論文２：Homomorphic Computation of Edit Distance, Jung Hee Cheon and Miran Kim and Kristin Lauter, http://eprint.iacr.org/2015/132

These days genomic sequence analysis provides a key way of understanding the biology of an organism. However, since these sequences contain much private information, it can be very dangerous to reveal any part of them. It is desirable to protect this sensitive information when performing sequence analysis in public. As a first step in this direction, we present a method to perform the edit distance algorithm on encrypted data to obtain an encrypted result. In our approach, the genomic data owner provides only the encrypted sequence, and the public commercial cloud can perform the sequence analysis without decryption. The result can be decrypted only by the data owner or designated representative holding the decryption key.

In this paper, we describe how to calculate edit distance on encrypted data with a somewhat homomorphic encryption scheme and analyze its performance. More precisely, given two encrypted sequences of lengths $n$ and $m$, we show that a somewhat homomorphic scheme of depth $\bigo((n+m) \log\log (n+m))$ can evaluate the edit distance algorithm in $\bigo(nm \log (n+m))$ homomorphic computations. In the case of $n=m$, the depth can be brought down to $\bigo(n)$ using our optimization technique. Finally, we present the estimated performance of the edit distance algorithm and verify it by implementing it for short DNA sequences.

_ 気になった論文３：Private Computation on Encrypted Genomic Data, Kristin Lauter and Adriana Lopez-Alt and Michael Naehrig, http://eprint.iacr.org/2015/133

A number of databases around the world currently host a wealth of genomic data that is invaluable to researchers conducting a variety of genomic studies. However, patients who volunteer their genomic data run the risk of privacy invasion. In this work, we give a cryptographic solution to this problem: to maintain patient privacy, we propose encrypting all genomic data in the database. To allow meaningful computation on the encrypted data, we propose using a homomorphic encryption scheme.

Specifically, we take basic genomic algorithms which are commonly used in genetic association studies and show how they can be made to work on encrypted genotype and phenotype data. In particular, we consider the Pearson Goodness-of-Fit test, the D' and r^2-measures of linkage disequilibrium, the Estimation Maximization (EM) algorithm for haplotyping, and the Cochran-Armitage Test for Trend. We also provide performance numbers for running these algorithms on encrypted data.