Gee Law’s Blog

Two (equivalent) definitions of computational indistinguishability, two (isomorphic) ways of doing hybrids

It wasn’t until recently did I realise there are two isomorphic ways (different styles) of writing hybrid proofs. They actually correspond to the two equivalent definitions of computational indistinguishability — one based on guessing and the other based on distinguishing. Actually, I’ve been writing both kinds of proofs subconciously.

Two (equivalent) definitions of computational indistinguishability, two (isomorphic) ways of doing hybrids

A note on (non-)uniform reductions

I learnt how to write uniform hybrid reductions in my rudimentary cryptography course, which are beasty beauties that wrap an adversary, trying break each of the many underlying cryptographic assumptions simultaneously. However, those constructions are less easy to write and read than using the transitivity of computational indistinguishability up to polynomially many times. The latter involves writing out the (perhaps polynomially many) hybrids and arguing that adjacent hybrids are indistinguishable. I also learnt non-uniform reductions, noticeably the technique to only work with deterministic adversaries. I’m writing a proof using hybrid argument lately, and I asked my advisor about whether I should write the beast or just the hybrids…

A note on (non-)uniform reductions

《悲惨世界》概念版歌词计划 13

本系列旨在忠实提供 1980 版的《悲惨世界》概念版音乐剧的歌词。第十二篇记录的是 Voilà le soir qui tombe !、L'un vers l'autre 和 Le cœur au bonheur 的歌词,这一段是经典的白学现场。

《悲惨世界》概念版歌词计划 13

[KW19] 标准假设下适用于 NC¹ 策略的紧凑、适应性安全的属性加密

Kowalczyk 和 Wee 在 EUROCRYPT 2019(欧密会)上发表的文章 Compact Adaptively Secure ABE for NC¹ from 𝑘-Lin 可以说是彻底解决了 NC¹ 访问策略的属性加密问题。我在最近的密码学读书会上将讲述该文,这篇博文算是我用母语对该文章的总结(感觉我脑内思考语言仍然是汉语),也算是在中文密码学社区里传播知识。

[KW19] 标准假设下适用于 NC¹ 策略的紧凑、适应性安全的属性加密

Blogging my blog

A meta-blog that keeps the trace of my blog site. Some renovations are happening in April. Check them out!

《悲惨世界》概念版歌词计划 12

本系列旨在忠实提供 1980 版的《悲惨世界》概念版音乐剧的歌词。第十二篇记录的是 Te souviens-tu du premier jour ?、Cosette : Dans la vie 和 Marius : Dans la vie 的歌词,这一段是 Marius 在 Éponine 的帮助下找到了 Cosette 的住处,两个互相暗恋的人终于重逢的情节。

《悲惨世界》概念版歌词计划 12

谈“理想”和其他

理想(ideal)是出现在抽象代数(更特别地,环论)中的一类对象,其命名很有渊源。之前我只知道这个名字来源于一位数学家研究惟一分解时引入的“理想数”(该研究的思路和一般化最终形成了现代数学语言中“理想”的定义),但是具体的细节不是很明白;最近在阅读基于格(lattice)的密码学的内容,其中提到了环上的格(ring lattice),其中提到了理想格(环的一个子集,同时满足格和理想的要求),好奇心一发不可收拾,读了一些数学历史故事,对“理想数”加深了认识,记录下来以飨观众。文章最后讨论了“理想数”这个翻译的不达意之处。