127,423 research outputs found
Non-Malleable Extractors and Non-Malleable Codes: Partially Optimal Constructions
Full text linkThe recent line of study on randomness extractors has been a great success, resulting in exciting new techniques, new connections, and breakthroughs to long standing open problems in several seemingly different topics. These include seeded non-malleable extractors, privacy amplification protocols with an active adversary, independent source extractors (and explicit Ramsey graphs), and non-malleable codes in the split state model. Previously, the best constructions are given in [Xin Li, 2017]: seeded non-malleable extractors with seed length and entropy requirement O(log n+log(1/epsilon)log log (1/epsilon)) for error epsilon; two-round privacy amplification protocols with optimal entropy loss for security parameter up to Omega(k/log k), where k is the entropy of the shared weak source; two-source extractors for entropy O(log n log log n); and non-malleable codes in the 2-split state model with rate Omega(1/log n). However, in all cases there is still a gap to optimum and the motivation to close this gap remains strong.
In this paper, we introduce a set of new techniques to further push the frontier in the above questions. Our techniques lead to improvements in all of the above questions, and in several cases partially optimal constructions. This is in contrast to all previous work, which only obtain close to optimal constructions. Specifically, we obtain:
1) A seeded non-malleable extractor with seed length O(log n)+log^{1+o(1)}(1/epsilon) and entropy requirement O(log log n+log(1/epsilon)), where the entropy requirement is asymptotically optimal by a recent result of Gur and Shinkar [Tom Gur and Igor Shinkar, 2018];
2) A two-round privacy amplification protocol with optimal entropy loss for security parameter up to Omega(k), which solves the privacy amplification problem completely;
3) A two-source extractor for entropy O((log n log log n)/(log log log n)), which also gives an explicit Ramsey graph on N vertices with no clique or independent set of size (log N)^{O((log log log N)/(log log log log N))}; and
4) The first explicit non-malleable code in the 2-split state model with constant rate, which has been a major goal in the study of non-malleable codes for quite some time. One small caveat is that the error of this code is only (an arbitrarily small) constant, but we can also achieve negligible error with rate Omega(log log log n/log log n), which already improves the rate in [Xin Li, 2017] exponentially.
We believe our new techniques can help to eventually obtain completely optimal constructions in the above questions, and may have applications in other settings
Guo li zhong yang da xue jiao yu xue yuan xin li xue xi gai kuang.
No full textCover title.; Special collection from London Missionary Society.; Also available in an electronic version via the Internet at http://nla.gov.au/nla.gen-vn1973394
Li Xin
Full text linkAutant peintre calligraphe que dessinateur, Li Xin fait voyager le spectateur dans un univers à la fois poétique et mystérieux où les couleurs d’origine naturelle et le gris se dégradent dans toutes leurs subtilités. L’artiste affectionne l’encre, un médium pictural de la culture chinoise mais aussi, plus récemment, la peinture à l’huile. À mi-chemin entre les préoccupations traditionnelles et la peinture minimaliste contemporaine, Li Xin emploie l’encre pure, se diluant en parcimonie sur la ..
Xin li xue yu jiao yu xin li xue /
No full textCover title.; Special collection from London Missionary Society.; 880-03 Bian zhu zhong zhi jiao yu xin li xue di yi zhang.; Also available in an electronic version via the Internet at http://nla.gov.au/nla.gen-vn455089
Zeng Guofan mi chuan Li Hongzhang 72 xin fa
No full textBen shu bian zhu zhe sou luo le jin dai yi bai duo zhong bi ji, zhui xun chu qi zhong de xuan miao zhi chu, jie he zeng guo fan li hong zhang er ren de shu bai feng mi xin, yi ji bi jiao ta men de chu shi mou lue, jin xing le jing xin de tan jiu, zong jie chu le 72 ge cheng gong xin fa, yi hui wei li shi, xi qu ren sheng zhi hu
Zeng Guofan mi chuan Li Hongzhang 72 xin fa
No full textBen shu bian zhu zhe sou luo le jin dai yi bai duo zhong bi ji, zhui xun chu qi zhong de xuan miao zhi chu, jie he zeng guo fan li hong zhang er ren de shu bai feng mi xin, yi ji bi jiao ta men de chu shi mou lue, jin xing le jing xin de tan jiu, zong jie chu le 72 ge cheng gong xin fa, yi hui wei li shi, xi qu ren sheng zhi hu
Two-Source and Affine Non-Malleable Extractors for Small Entropy
Full text linkNon-malleable extractors are generalizations and strengthening of standard randomness extractors, that are resilient to adversarial tampering. Such extractors have wide applications in cryptography and have become important cornerstones in recent breakthroughs of explicit constructions of two-source extractors and affine extractors for small entropy. However, explicit constructions of non-malleable extractors appear to be much harder than standard extractors. Indeed, in the well-studied models of two-source and affine non-malleable extractors, the previous best constructions only work for entropy rate > 2/3 and 1-γ for some small constant γ > 0 respectively by Li (FOCS' 23).
In this paper, we present explicit constructions of two-source and affine non-malleable extractors that match the state-of-the-art constructions of standard ones for small entropy. Our main results include:
- Two-source and affine non-malleable extractors (over ₂) for sources on n bits with min-entropy k ≥ log^C n and polynomially small error, matching the parameters of standard extractors by Chattopadhyay and Zuckerman (STOC' 16, Annals of Mathematics' 19) and Li (FOCS' 16).
- Two-source and affine non-malleable extractors (over ₂) for sources on n bits with min-entropy k = O(log n) and constant error, matching the parameters of standard extractors by Li (FOCS' 23).
Our constructions significantly improve previous results, and the parameters (entropy requirement and error) are the best possible without first improving the constructions of standard extractors. In addition, our improved affine non-malleable extractors give strong lower bounds for a certain kind of read-once linear branching programs, recently introduced by Gryaznov, Pudlák, and Talebanfard (CCC' 22) as a generalization of several well studied computational models. These bounds match the previously best-known average-case hardness results given by Chattopadhyay and Liao (CCC' 23) and Li (FOCS' 23), where the branching program size lower bounds are close to optimal, but the explicit functions we use here are different. Our results also suggest a possible deeper connection between non-malleable extractors and standard ones
Ren zhi xin li xue
No full textBen shu jie shao le ren zhi xin li xue de ji ben yuan ze he fang fa, yi ji dui ge zhong zhong yao ren zhi guo cheng de yan jiu, bao gua zhi jue, zhu yi, ji yi, biao xiang, si wei he yu yan den
A new species and key to all known species of Confusacris Yin & Li, 1987 (Orthoptera: Acrididae) from China
No full textJi, Li-Li, Zhi, Yong-Chao, Li, Xin-Jiang (2019): A new species and key to all known species of Confusacris Yin & Li, 1987 (Orthoptera: Acrididae) from China. Zootaxa 4555 (4): 595-599, DOI: 10.11646/zootaxa.4555.4.1
Zhou yi lüe li
No full text王弼, 韓康伯注 ; 孔穎達正義.綫裝, 1函.框19.7x13.1公分, 9行21字, 小字雙行同. 白口, 無魚尾, 四周單邊. 版心中鐫"易疏"及卷次, 下記刻工.分上,下經 ; 卷一至三為上經, 卷四至九為下經.出版項據《明代版本圖錄初編》推定.卷一至六由王弼注, 卷七至九由韓康伯注.With: 經典釋文 : 周易音義 / 陸德明撰 -- 周易略例 / 王弼撰.鈐有"呂氏樂房藏書", "得良館藏書記"印.Xian zhuang, 1 han.Kuang 19.7 x 13.1 gong fen, 9 hang 21 zi, xiao zi shuang hang tong. Bai kou, wu yu wei, si zhou dan bian. Ban xin zhong juan "Yi shu" ji juan ci, xia ji ke gong.Fen shang, xia jing ; juan yi zhi san wei shang jing, juan si zhi jiu wei xia jing.Chu ban xiang ju "Ming dai ban ben tu lu chu bian" tui ding.Juan yi zhi liu you Wang Bi zhu, juan qi zhi jiu you Han Kangbo zhu.Wang Bi, Han Kangbo zhu ; Kong Yingda zheng yi.With: Jing dian shi wen : Zhou yi yin yi / Lu Deming zhuan -- Zhou yi lüe li / Wang Bi zhuan.Qian you "Lü shi Le fang cang shu", "De liang guan cang shu ji" yin
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