_ IACR ePrint 2014/534まで確認済み、ECCC 2003年分まで確認済み
_ 気になった論文:Groups With Two Generators Having Unsolvable Word Problem And Presentations of Mihailova Subgroups
, Xiaofeng Wang and Chen Xu and Guo Li and Hanling Lin, http://eprint.iacr.org/2014/528
A presentation of a group with two generators having unsolvable word problem and an explicit countable presentation of Mihailova subgroup of F_2×F_2 with finite number of generators are given. Where Mihailova subgroup of F_2×F_2 enjoys the unsolvable subgroup membership problem.One then can use the presentation to create entities' private key in a public key cryptsystem.
_ (7/16記:査読者からコメントが送られてきていた論文修正を済ませて再投稿するなど。修正分量は少なかったのに、内容的には今までの論文修正で一番しんどかった気がする。よい結果になるといいなぁ。)
_ IACR ePrint 2014/537まで確認済み、ECCC 2003年分まで確認済み
_ 気になった論文:On Key Recovery Attacks against Existing Somewhat Homomorphic Encryption Schemes
, Massimo Chenal and Qiang Tang, http://eprint.iacr.org/2014/535
In his seminal paper at STOC 2009, Gentry left it as a future work to investigate (somewhat) homomorphic encryption schemes with IND-CCA1 security. At SAC 2011, Loftus et al. showed an IND-CCA1 attack against the somewhat homomorphic encryption scheme presented by Gentry and Halevi at Eurocrypt 2011. At ISPEC 2012, Zhang, Plantard and Susilo showed an IND-CCA1 attack against the somewhat homomorphic encryption scheme developed by van Dijk et al. at Eurocrypt 2010. Both attacks recover the secret key of the encryption schemes.
In this paper, we continue this line of research and show that most existing somewhat homomorphic encryption schemes are not IND-CCA1 secure. In fact, we show that these schemes suffer from key recovery attacks (stronger than a typical IND-CCA1 attack), which allow an adversary to recover the private keys through a number of decryption oracle queries. The schemes, that we study in detail, include those by Brakerski and Vaikuntanathan at Crypto 2011 and FOCS 2011, and that by Gentry, Sahai and Waters at Crypto 2013. We also develop a key recovery attack that applies to the somewhat homomorphic encryption scheme by van Dijk et al., and our attack is more efficient and conceptually simpler than the one developed by Zhang et al.. Our key recovery attacks also apply to the scheme by Brakerski, Gentry and Vaikuntanathan at ITCS 2012, and we also describe a key recovery attack for the scheme developed by Brakerski at Crypto 2012.
_ (8/8記:暗号分野の某先生が来日してNTTの研究所に滞在しているということで、公開講座が開かれることになった。その初日。この日は午後から開始だったのでよかったが、翌日からは開始時間が早い(本人比)ので大変そうだなぁと思っていた。)
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