暗号プラットフォーム研究の展望 · 2020. 8. 6. ·...
TRANSCRIPT
暗号プラットフォーム研究の展望
Nuttapong (Nuts) Attrapadung
CPSEC symposium 2018.12.17
On Cryptography Platform: Attribute-based Encryption and More
Nuttapong (Nuts) Attrapadung
CPSEC symposium 2018.12.17
About Myself
3
Nuttapong Attrapadung (Nut/Nuts/Nattsu/ナッツ)
1997-2001 Thailand
Chulalongkorn University Bachelor Engineering
2001-2007 Japan
University of Tokyo Master, Ph.D. (Info.Science&Tech)
2007-now Japan
AIST researcher
International Math Olympiad 1997 Argentina
2012-2013 France
École normale supérieure, Paris visiting researcher
暗号プラットフォーム研究チームの紹介
4
本研究チーム:暗号技術を応用し、システムの様々なレイヤでセキュアプラットフォーム・フレームワークを設計・開発
設計した汎用的フレームワークの中で、ニーズに沿った応用機能を提供
権威ある国際学会・ジャーナルへの論文採録による安全性保証
外部企業・機関
共同研究先:三菱電機、パナソニック、NTT、日立、KDDI研究所
ナッツ 村上 照屋 須崎 塚本
研究プロジェクト• JST CREST
• 他 (調整中)• JST ACT-i• Kakenhi
他チーム@
5
Big Data
Utility
health care, marketing, financial, machine learning …
6
Big Data
Privacy
Problem: traditional encryption is all-or-nothing
+ ?
7
Big Data
Utility Privacy
encryption with access control
Q.
8
(handsome rich)<̂latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">AAAC2XichVG/T9tQEP5wS5umUAIslVisRiAm6+JCMZ1QuzDyKwEpIGQ7j+DiX7JfIqVRhm6IqVIHBEwgMaD+GSz8AwxMnREjlVgYODuuKobAWc/v3r37vvfdnRW6TiyJrvqUFy/7X73Ovcm/HRh8N1QYHqnEQSOyRdkO3CBas8xYuI4vytKRrlgLI2F6litWrZ2vyf1qU0SxE/grshWKDc+s+86WY5uSQ5V11/Rr+c1CkTSdPs7qukra9OwnmjHYMaYNQ59SSxqlVkRmC0HhD9ZRQwAbDXgQ8CHZd2Ei5q+KEgghxzbQ5ljEnpPeC3SQZ2yDswRnmBzd4X+dT9Us6vM54YxTtM2vuLwiRqoYp0s6o1u6oN90Tfc9udopR6KlxbvVxYpwc2jv/fLdsyiPd4nt/6gnNUtswUi1Oqw9TCNJFXYX3/y+f7v8eWm8PUEndMP6j+mKzrkCv/nXPl0US0dP6ImZy0s72OJV6zLye0k/VK4ryvIF5/VmsdMeRKyvzlVJdHjg/6aq9nYqulYirbQ4VZz7ko0+hzF8wCTPdwZzmMcCysz+DT9xgEOlqvxQdpW9bqrSl2FG8ciUXw9QoaOq</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit>
_<latexit sha1_base64="8TkXZPRElY7xQ5n6QhSDQ3TIp3E=">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</latexit><latexit sha1_base64="8TkXZPRElY7xQ5n6QhSDQ3TIp3E=">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</latexit><latexit sha1_base64="8TkXZPRElY7xQ5n6QhSDQ3TIp3E=">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</latexit><latexit sha1_base64="8TkXZPRElY7xQ5n6QhSDQ3TIp3E=">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</latexit>
(aist crypto)<̂latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit>
profile
• 2015: infamous leak incident on a matchmaker service Ashley Madison
This application example is inspired by Hoeteck Wee’s Asiacrypt 2016 talk.
aist, crypto
profile
http://www.businessinsider.com/cheating-affair-website-ashley-madison-hacked-user-data-leaked-2015-7
Example: Matchmaker Application
Attribute Based Encryption
9
aist, crypto
aist, AI
phd, crypto
M<latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit>
(aist crypto)<̂latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">AAAC2XichVG/T9tQEP5wS5umUAIslVisRiAm6+JCMZ1QuzDyKwEpIGQ7j+DiX7JfIqVRhm6IqVIHBEwgMaD+GSz8AwxMnREjlVgYODuuKobAWc/v3r37vvfdnRW6TiyJrvqUFy/7X73Ovcm/HRh8N1QYHqnEQSOyRdkO3CBas8xYuI4vytKRrlgLI2F6litWrZ2vyf1qU0SxE/grshWKDc+s+86WY5uSQ5V11/Rr+c1CkTSdPs7qukra9OwnmjHYMaYNQ59SSxqlVkRmC0HhD9ZRQwAbDXgQ8CHZd2Ei5q+KEgghxzbQ5ljEnpPeC3SQZ2yDswRnmBzd4X+dT9Us6vM54YxTtM2vuLwiRqoYp0s6o1u6oN90Tfc9udopR6KlxbvVxYpwc2jv/fLdsyiPd4nt/6gnNUtswUi1Oqw9TCNJFXYX3/y+f7v8eWm8PUEndMP6j+mKzrkCv/nXPl0US0dP6ImZy0s72OJV6zLye0k/VK4ryvIF5/VmsdMeRKyvzlVJdHjg/6aq9nYqulYirbQ4VZz7ko0+hzF8wCTPdwZzmMcCysz+DT9xgEOlqvxQdpW9bqrSl2FG8ciUXw9QoaOq</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit>
Attribute Based Encryption (naively)
10
aist, crypto
aist, AI
phd, crypto
M<latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit>
(aist crypto)<̂latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit>
Rphd<latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit><latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit><latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit><latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit>
Raist<latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit>
Rcrypto<latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit>
RAI<latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit><latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit><latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit><latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit>
Raist<latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">AAAC5HichVI9bxNBEH05vkL4sIEGicbCCqKy5o6gGKoIGsrEwUmkJLLuLmtzyn3pbm1hTv4DiA4hikhIIFIgfgYNf4AiFTWiDBINBe/WhxCFw5z2dnZ23sybmfXSMMi1yNGcder0mbPn5s8vXLh46XKtfuXqRp4MM191/SRMsi3PzVUYxKqrAx2qrTRTbuSFatPbf1jeb45UlgdJ/FiPU7UbuYM46Ae+q2nq1WudXrGj1VNduEw2mfTqTWnZ7buy1G5QuefcEYeKs+zYVOyWGGmiktWk/hU72EMCH0NEUIihqYdwkfPbhg1BStsuCtoyaoG5V5hggdghvRQ9XFr3+R/wtF1ZY57LmLlB+8wScmVENrAoX+SDHMtn+Sjf5NfMWIWJUXIZc/emWJX2as+vr//8LyrirvHkL+pEzhp9tA3XgNxTYymr8Kf40bPXx+v3O4vFLXkn38n/rRzJJ1YQj374h2uqc3ACn5yxItPBMdfeNCLzlf1osK6s8lf0mx3FNz3IyG/AqjTKgf+ZamO2suG0bD6HtaXmyoNq9PO4gZu4zfkuYwWPsIqueQMHeI9Dq2+9sF5ar6au1lyFuYZ/xHrzG+ObqIQ=</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit>
Rcrypto<latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit>
C = M � Raist � Rcrypto<latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">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</latexit><latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">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</latexit><latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">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</latexit><latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">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</latexit>
C � Raist � Rcrypto ) M<latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit><latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit><latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit><latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit>
Attribute Based Encryption (naively)
11
aist, crypto
aist, AI
phd, crypto
M<latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit>
(aist crypto)<̂latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit><latexit sha1_base64="QD9iyHdLulzl3FodFkMUTg9XI8M=">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</latexit>
Rphd<latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit><latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit><latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit><latexit sha1_base64="h1ccpxgFswC1K9VZcHHqqAJaWlg=">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</latexit>
Raist<latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">AAAC5HichVI9bxNBEH05vkL4sIEGicbCCqKy5o6gGKoIGsrEwUmkJLLuLmtzyn3pbm1hTv4DiA4hikhIIFIgfgYNf4AiFTWiDBINBe/WhxCFw5z2dnZ23sybmfXSMMi1yNGcder0mbPn5s8vXLh46XKtfuXqRp4MM191/SRMsi3PzVUYxKqrAx2qrTRTbuSFatPbf1jeb45UlgdJ/FiPU7UbuYM46Ae+q2nq1WudXrGj1VNduEw2mfTqTWnZ7buy1G5QuefcEYeKs+zYVOyWGGmiktWk/hU72EMCH0NEUIihqYdwkfPbhg1BStsuCtoyaoG5V5hggdghvRQ9XFr3+R/wtF1ZY57LmLlB+8wScmVENrAoX+SDHMtn+Sjf5NfMWIWJUXIZc/emWJX2as+vr//8LyrirvHkL+pEzhp9tA3XgNxTYymr8Kf40bPXx+v3O4vFLXkn38n/rRzJJ1YQj374h2uqc3ACn5yxItPBMdfeNCLzlf1osK6s8lf0mx3FNz3IyG/AqjTKgf+ZamO2suG0bD6HtaXmyoNq9PO4gZu4zfkuYwWPsIqueQMHeI9Dq2+9sF5ar6au1lyFuYZ/xHrzG+ObqIQ=</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit>
Rcrypto<latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">AAAC5nichVI9b9RAEH0xXyF85AINEs2JUxDVaewE5aCKoKFMLlwSKYlO9mZzseIv2XsHh3V/gIIOpUBIgAQI8TNo+AMUqagRZZBoKHj2GSGKC2utd3Z23ts3M+slgZ8ZkaMp69TpM2fPTZ+fuXDx0uXZ2tyV9Szup0p3VBzE6abnZjrwI90xvgn0ZpJqN/QCveEd3C/ONwY6zfw4emiGid4J3V7k7/nKNXR1a3Ptbr5t9GOTq3SYmHg06tYa0rRbt2WxVadxx1kQh4az5Ng07KaUo4FqrMS1r9jGLmIo9BFCI4KhHcBFxm8LNgQJfTvI6Utp+eW5xggzxPYZpRnh0nvAf4+7rcobcV9wZiVa8ZaAMyWyjnn5Ih/kWD7LR/kmvyZy5SVHoWXI1RtjddKdfXpt7ed/USFXg/2/qBM1G+yhVWr1qT0pPUUWaowfPDk8Xrvbns9vyhv5Tv2v5Ug+MYNo8EO9XdXtFyfoycgVlhUccu6OGXlfUY8680qreM24ySyqrEFKfT1mZVA0/E9X65ONdadp8zmsLjaW71Wtn8Z13MAt9ncJy3iAFXTI/ggv8Q7vrX3rmfXcOhyHWlMV5ir+Gdar34ZeqYg=</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">AAAC5nichVI9b9RAEH0xXyF85AINEs2JUxDVaewE5aCKoKFMLlwSKYlO9mZzseIv2XsHh3V/gIIOpUBIgAQI8TNo+AMUqagRZZBoKHj2GSGKC2utd3Z23ts3M+slgZ8ZkaMp69TpM2fPTZ+fuXDx0uXZ2tyV9Szup0p3VBzE6abnZjrwI90xvgn0ZpJqN/QCveEd3C/ONwY6zfw4emiGid4J3V7k7/nKNXR1a3Ptbr5t9GOTq3SYmHg06tYa0rRbt2WxVadxx1kQh4az5Ng07KaUo4FqrMS1r9jGLmIo9BFCI4KhHcBFxm8LNgQJfTvI6Utp+eW5xggzxPYZpRnh0nvAf4+7rcobcV9wZiVa8ZaAMyWyjnn5Ih/kWD7LR/kmvyZy5SVHoWXI1RtjddKdfXpt7ed/USFXg/2/qBM1G+yhVWr1qT0pPUUWaowfPDk8Xrvbns9vyhv5Tv2v5Ug+MYNo8EO9XdXtFyfoycgVlhUccu6OGXlfUY8680qreM24ySyqrEFKfT1mZVA0/E9X65ONdadp8zmsLjaW71Wtn8Z13MAt9ncJy3iAFXTI/ggv8Q7vrX3rmfXcOhyHWlMV5ir+Gdar34ZeqYg=</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit>
RAI<latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit><latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit><latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit><latexit sha1_base64="vgezhLNNPqfkNH4FBLjFklAN2XE=">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</latexit>
Raist<latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit>
Rcrypto<latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit><latexit sha1_base64="l+hzjjB/YoAh0Zo1GjvAl/ZWCoM=">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</latexit>
C = M � Raist � Rcrypto<latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">AAADCHichVJNa9RQFL2NH6212lE3QjfBocXVcJO2dCwIxW66KbRTpy10ypC8vk5D88XLm6FjyB/oHxBxZcGFuHEnrgTd1B/goivX4rKCGxeeZCIiMvWF5N133j3nnftu3Nj3Es18NmJcunzl6ujYtfHrEzduTlZu3d5Moq4SsikiP1LbrpNI3wtlU3val9uxkk7g+nLLPVzO97d6UiVeFD7W/VjuBk4n9PY94WhA7crs8sNVsxXFfjcxG+20peWRTh2cm2X/wEL1Yx1lWbtS5ZpVn+e5uonggT3LNgJ7wbYQWDUuRpXKsRZVvlCL9igiQV0KSFJIGrFPDiV4dsgiphjYLqXAFCKv2JeU0Ti4XWRJZDhAD/HtYLVToiHWuWZSsAVO8fEqME2a5s/8is/5lF/zV/45VCstNHIvfczugCvj9uTx3Y0f/2UFmDUd/GFd6FnTPtULrx68xwWSVyEG/N6Tp+cbi43pdIZP+Bv8v+Az/ogKwt538XJdNp5f4CeBVlDcYB/v3kAR5+X3YaIuVeZL5A1XEcUdKPjroCpNecN/d9UcHmzaNQu/w/pcdelR2foxmqJ7dB/9XaAlWqE1akL9Gb2nU/pkHBtvjLfGu0GqMVJy7tBfw/jwC572t7o=</latexit><latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">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</latexit><latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">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</latexit><latexit sha1_base64="nXnm0j3Z1ea0AVk8toZCba5FOgw=">AAADCHichVJNa9RQFL2NH6212lE3QjfBocXVcJO2dCwIxW66KbRTpy10ypC8vk5D88XLm6FjyB/oHxBxZcGFuHEnrgTd1B/goivX4rKCGxeeZCIiMvWF5N133j3nnftu3Nj3Es18NmJcunzl6ujYtfHrEzduTlZu3d5Moq4SsikiP1LbrpNI3wtlU3val9uxkk7g+nLLPVzO97d6UiVeFD7W/VjuBk4n9PY94WhA7crs8sNVsxXFfjcxG+20peWRTh2cm2X/wEL1Yx1lWbtS5ZpVn+e5uonggT3LNgJ7wbYQWDUuRpXKsRZVvlCL9igiQV0KSFJIGrFPDiV4dsgiphjYLqXAFCKv2JeU0Ti4XWRJZDhAD/HtYLVToiHWuWZSsAVO8fEqME2a5s/8is/5lF/zV/45VCstNHIvfczugCvj9uTx3Y0f/2UFmDUd/GFd6FnTPtULrx68xwWSVyEG/N6Tp+cbi43pdIZP+Bv8v+Az/ogKwt538XJdNp5f4CeBVlDcYB/v3kAR5+X3YaIuVeZL5A1XEcUdKPjroCpNecN/d9UcHmzaNQu/w/pcdelR2foxmqJ7dB/9XaAlWqE1akL9Gb2nU/pkHBtvjLfGu0GqMVJy7tBfw/jwC572t7o=</latexit>
C � Raist � Rcrypto ) M<latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit><latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit><latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit><latexit sha1_base64="AjXYTvYyzU3IAZI/NZ6pruxkyEU=">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</latexit>
Not secure if users collude ☹
😈
😈 mix&match}
Rcrypto(s)<latexit sha1_base64="CWnV7Wrjbtg3wF8+jwYnfArVJ9s=">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</latexit><latexit sha1_base64="CWnV7Wrjbtg3wF8+jwYnfArVJ9s=">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</latexit><latexit sha1_base64="CWnV7Wrjbtg3wF8+jwYnfArVJ9s=">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</latexit><latexit sha1_base64="CWnV7Wrjbtg3wF8+jwYnfArVJ9s=">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</latexit>
12
aist, crypto
aist, AI
phd, cryptomix&match
Key Idea [SW05]
string function
7!
7!
Attribute Based Encryption: Key Idea
Raist(s)<latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit><latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit><latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">AAAC53ichVJNaxRBEH0Zv2L8yBovgpfFJRIvS80Yyeop6MVjsnGTQBKWmUlnbTJfzPQuWYf9A168qSAIEUTFn+HFP+AhJ8/iMYIXD76ZHREPG3vo6erqeq9fVbWXBDozIkdT1qnTZ86emz4/c+HipcuztStz61ncT33V8eMgTjc9N1OBjlTHaBOozSRVbugFasPbf1CcbwxUmuk4emSGidoJ3V6k97TvGrq6tbl2N9826sDkLi8bjRayW91aQ5p2644stuo07jq3xaHhLDk2Dbsp5WigGitx7Su2sYsYPvoIoRDB0A7gIuO3BRuChL4d5PSltHR5rjDCDLF9RilGuPTu89/jbqvyRtwXnFmJ9nlLwJkSWce8fJEPciyf5aN8k18TufKSo9Ay5OqNsSrpzj69tvbzv6iQq8Hjv6gTNRvsoVVq1dSelJ4iC3+MHzx5cbx2rz2f35Q38p36D+VIPjGDaPDDf7uq2q9O0JORKywrOOTcHTPyvqIedeaVVvGKcZNZ/LIGKfX1mJXBiA3/09X6ZGPdadp8DquLjeX7VeuncR03sMD+LmEZD7GCDtkP8Brv8N7S1jPrufVyHGpNVZir+GdYh78BR8upZg==</latexit><latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit>
Raist<latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit><latexit sha1_base64="RWonJrPMWdRW+jD5KhoQuzuyCnE=">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</latexit>
Raist(s)<latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit><latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit><latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit><latexit sha1_base64="hwc8qbOlL4jaDY0f2UZJBow4v/4=">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</latexit>
👿
👿
RAI(t)<latexit sha1_base64="iiaXOObhrPy57LgLFib6y3XsBqg=">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</latexit><latexit sha1_base64="iiaXOObhrPy57LgLFib6y3XsBqg=">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</latexit><latexit sha1_base64="iiaXOObhrPy57LgLFib6y3XsBqg=">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</latexit><latexit sha1_base64="iiaXOObhrPy57LgLFib6y3XsBqg=">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</latexit>
Raist(t)<latexit sha1_base64="bXWX0GQ1+iLiakWZGjfR9mRaVXs=">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</latexit><latexit sha1_base64="bXWX0GQ1+iLiakWZGjfR9mRaVXs=">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</latexit><latexit sha1_base64="bXWX0GQ1+iLiakWZGjfR9mRaVXs=">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</latexit><latexit sha1_base64="bXWX0GQ1+iLiakWZGjfR9mRaVXs=">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</latexit>
Rcrypto(u)<latexit sha1_base64="dsEBGHqCiatEUq7qDmYfnvInI8c=">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</latexit><latexit sha1_base64="dsEBGHqCiatEUq7qDmYfnvInI8c=">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</latexit><latexit sha1_base64="dsEBGHqCiatEUq7qDmYfnvInI8c=">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</latexit><latexit sha1_base64="dsEBGHqCiatEUq7qDmYfnvInI8c=">AAAC6XichVK/TxRBFH4s8kNEONCCxObiBYPN5e0K4aAi2FjC4QEJkMvuMJyb21+ZnbtwbO4fsKOCaKMYC/TPoOEfsKCyNpaY2Fjw7d4SY3E4m9l58+Z933zvvXEiz40189WAMXhvaHhk9P7Yg/GHE5OFqenNOGwpIWsi9EK17dix9NxA1rSrPbkdKWn7jie3nObL9HyrLVXshsFr3Ynknm83AvfAFbaGq154XK0nu1oe6kSoTqTDbneu9bxeKHHZrCzwfKUIY8l6wRYMa9EyYZhlzkaJ8rEWFr7TLu1TSIJa5JOkgDRsj2yK8e2QSUwRfHuUwKdgudm5pC6NAdtClESEDW8T/wZ2O7k3wD7ljDO0wC0epgKySLP8jc/5mi/5K//gP325kowj1dLB6vSwMqpPvp3Z+P1flI9V05u/qDs1azqgSqbVhfYo86RZiB6+fXRyvbFcnU2e8Rn/hP6PfMUXyCBo/xKf12X1/R16YnD5WQU7mPs9RtyX1qOIvFQeLxHXn0VkNVDQ10BWmrpo+G1Xi/2NTats4jmsz5dWVvPWj9ITekpz6O8irdArWqMa2I/oA53TF6NpHBunxrteqDGQYx7RP8P4dAPyPaps</latexit>
Rphd(u)<latexit sha1_base64="umRtbASwpGC4rzWPuQD1ImgAAjU=">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</latexit><latexit sha1_base64="umRtbASwpGC4rzWPuQD1ImgAAjU=">AAAC5nichVI9bxNBEH05vkL4iAMNEo2FFRQaa+4SFEMVQUOZODiJlETW3Xljn3Jfuls7MSf/AQo6lAIhARIgxM+g4Q9QpKJGlEGioeDd+RCicNjT3s7Oznv7Zmad2PdSLXI8ZZw5e+78hemLM5cuX7k6W5m7tpFG/cRVLTfyo2TLsVPle6FqaU/7aitOlB04vtp09h/m55sDlaReFD7Ww1jtBnY39PY819Z0tStzzXa2o9WhzuJeZzRa6N9pV2pSNxt3ZalRpXHPWhSLhrVsmTTMuhSjhnKsRpWv2EEHEVz0EUAhhKbtw0bKbxsmBDF9u8joS2h5xbnCCDPE9hmlGGHTu89/l7vt0htyn3OmBdrlLT5nQmQV8/JFPsiJfJaP8k1+TeTKCo5cy5CrM8aquD379Mb6z/+iAq4avb+oUzVr7KFRaPWoPS48eRbuGD94cnSyfr85n92WN/Kd+l/LsXxiBuHgh/t2TTVfnKInJVdQVHDI2Rkz8r68HlXmlZTxinGTWdyiBgn1dZmVxogN/9PV6mRjw6qbfA5rS7WVB2Xrp3ETt7DA/i5jBY+wihbZD/AS7/De6BnPjOfG0TjUmCox1/HPMF79BgIuqOk=</latexit><latexit sha1_base64="umRtbASwpGC4rzWPuQD1ImgAAjU=">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</latexit><latexit sha1_base64="umRtbASwpGC4rzWPuQD1ImgAAjU=">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</latexit>
failed!
💧
💧 }
13
aist, crypto
aist, AI
phd, crypto
M<latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">AAAC1HichVI9TxRRFD2MX4goqzQkNhM3EKvNHVx3WSsCDY0JC+5CgoTMDI91wnxl5u0m60pFaDSxglBYaWJh/Bk2/gELKmtjiYmNhWdmxxiLxTd58+67757zzr33ObHvpVrkbMy4dPnK1Wvj1yduTN68NVW6faedRt3EVS038qNk07FT5XuhamlP+2ozTpQdOL7acPaXs/ONnkpSLwqf6H6stgO7E3p7nmtrupqPd0plqVj1Wq3aMKVSe7hgPZinUW1Y9UbDtCqSjzKKsRqVvuIpdhHBRRcBFEJo2j5spPy2YEEQ07eNAX0JLS8/VzjABLFdRilG2PTu89/hbqvwhtxnnGmOdnmLz5kQaWJWvsgHOZfP8lG+ya+RXIOcI9PS5+oMsSremXo5s/7zv6iAq8azv6gLNWvsYSHX6lF7nHuyLNwhvvf89Hz90drsYE7eyXfqfytn8okZhL0f7vumWntzgZ6UXEFewT7n7pCR92X1MJlXUsQrxo1mcfMaJNTXYVYaB2z4n66ao432fMXiu2hWy4tLRevHcRf3cJ/9rWMRK1hFi+wKr3CME6NtvDAOjaNhqDFWYKbxzzBe/wZyc6HJ</latexit>
(aist crypto)^
Attribute Based Encryption: Toy Scheme
A� s + Baist s + Bcrypto
A� t + Baist t + BAI
A� u + Bphd u + Bcrypto
M + A
BcryptoBaistC =
still one-time, private-key scheme ☹
{
Attribute Based Encryption
14
The Toy scheme ABE
one-time enc
private-key enc
multiple-time enc
public-key enc
Key idea
A 7! A(r)
B 7! gB mod N
• Public-key scheme: Anyone can encrypt.gB mod N B
(crypto basic: discrete log is hard.)
• hides , and hence can be public.
15
2-input AND
Bounded boolean formulae
Unbounded boolean formulae
Inner product Subspace membership
Boolean circuits
Arithmetic circuits
Turing machines
ABE for any policies?
XY
General Design Framework for ABE
16
M<latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit><latexit sha1_base64="u2fF7alAosVaRxNK/vR3FQA1JoA=">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</latexit>
if R(Y, X)=1
if R(Y, X)=0
Main results: - [Attrapadung EUROCRYPT14] - [Attrapadung ASIACRYPT16] - [Attrapadung PKC17] - Independently by [Wee TCC14], [Chen et. al. EUROCRYPT15]
Introduce “Pair encoding” functions f(Y) and g(X)
+ ?
17
Big Data
Utility Privacy
Attribute Based Encryption
Q.
Cryptography Platform
attribute-based encryption
attribute-based signature
homomorphic signaturehomomorphic encryption
secure multi-party computationpseudo-random functions
+ Privacy/Security/AuthenticityUtility
functional encryption
secure boot in trusted execution environment
+ ?
19
Big Data
Utility Privacy
Attribute Based Encryption
Q.
when accessing
+ ?
20
Big Data
Utility Privacy
Computing over encrypted data
Q.
when computing
Homomorphic Encryption
21
2 5⇥ + 3 7⇥
= 31
• Application: Secure outsourcing • Fully homomorphic: can do any , • Leveled homomorphic: limited number of
• Ours: fastest 2-level scheme [Attrapadung et al. AsiaCCS18]
+ ⇥⇥
Encrypt 0.96 msec
Multiply 24.3 msec
Decrypt 12.6 msec
@Safari iPhone 7
Our WebAssembly implementation
Secure Outsourced Computation
22
xx
f(x)f(x)
f “in the box”
• Hot topic: f for machine learning (training/classification) • example: Microsoft Cryptonet [Dowlin et al. ICML16], …
23
f: cancer probability calculation
y%y%
Example: Private Personal Genome Test
• Not practical yet when f is heavy ☹
Your chance of getting cancer:
where f(x)=y
x
+ ?
24
Big Data
Utility Privacy
Secure Multi-Party Computation Protocol
Q.
in joint computing..
Secure Multi-Party Computation (MPC)
25
…
x2<latexit sha1_base64="jcDCoxmhwZIIuBDmGcVJcLMsMlM=">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</latexit><latexit sha1_base64="jcDCoxmhwZIIuBDmGcVJcLMsMlM=">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</latexit><latexit sha1_base64="jcDCoxmhwZIIuBDmGcVJcLMsMlM=">AAAC1nichVK/TxRBFP5YFREFTm1MaC5cMFSXtyuGw4poYwkcB5cguewuw7Fhf2V37sJ5wc6QkJhYSWGFiYXxz7DhH6CgsjaWmNhY+O3eGkNxMJvZefPmfd98771xYt9Ltcj5iHHj5q3R22N3xu/em5icKt1/sJ5GncRVDTfyo6Tp2KnyvVA1tKd91YwTZQeOrzacvRfZ+UZXJakXhWu6F6utwG6H3o7n2pqu+n7LapUqUjVrT2W+VqaxaD0Ri4a1YJk0zKrko4JiLEel73iFbURw0UEAhRCatg8bKb9NmBDE9G2hT19Cy8vPFQ4wTmyHUYoRNr17/Le52yy8IfcZZ5qjXd7icyZEljErZ/JFLuRUvsoP+TOUq59zZFp6XJ0BVsWtqaNH9d/XogKuGrv/UVdq1thBLdfqUXuce7Is3AG++/r4ov5sdbb/WD7JT+o/kXP5xgzC7i/384pa/XiFnpRcQV7BHuf2gJH3ZfUoM6+kiFeMG87i5jVIqK/NrDQO2PB/XS0PN9atqsnnsDJfWXpetH4M05jBHPu7gCW8xDIaZG/jHT7g2Ggab4y3xuEg1BgpMA9xaRjv/wIru6Jx</latexit><latexit sha1_base64="jcDCoxmhwZIIuBDmGcVJcLMsMlM=">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</latexit>
x1<latexit sha1_base64="koJC9Q9XwjMHcOdwYm79mnh5TsQ=">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</latexit><latexit sha1_base64="koJC9Q9XwjMHcOdwYm79mnh5TsQ=">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</latexit><latexit sha1_base64="koJC9Q9XwjMHcOdwYm79mnh5TsQ=">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</latexit><latexit sha1_base64="koJC9Q9XwjMHcOdwYm79mnh5TsQ=">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</latexit>
xn<latexit sha1_base64="vQSt99oXUnYv4NQagPzRxQ1oi4U=">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</latexit><latexit sha1_base64="vQSt99oXUnYv4NQagPzRxQ1oi4U=">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</latexit><latexit sha1_base64="vQSt99oXUnYv4NQagPzRxQ1oi4U=">AAAC1nichVK/TxRBFP5YFREFTm1MaC5cMFSXtyuGw4poYwkcB5cguewuw7Fhf2V37sJ5wc6QkJhYSWGFiYXxz7DhH6CgsjaWmNhY+O3eGkNxMJvZefPmfd98771xYt9Ltcj5iHHj5q3R22N3xu/em5icKt1/sJ5GncRVDTfyo6Tp2KnyvVA1tKd91YwTZQeOrzacvRfZ+UZXJakXhWu6F6utwG6H3o7n2pqu+n4rbJUqUjVrT2W+VqaxaD0Ri4a1YJk0zKrko4JiLEel73iFbURw0UEAhRCatg8bKb9NmBDE9G2hT19Cy8vPFQ4wTmyHUYoRNr17/Le52yy8IfcZZ5qjXd7icyZEljErZ/JFLuRUvsoP+TOUq59zZFp6XJ0BVsWtqaNH9d/XogKuGrv/UVdq1thBLdfqUXuce7Is3AG++/r4ov5sdbb/WD7JT+o/kXP5xgzC7i/384pa/XiFnpRcQV7BHuf2gJH3ZfUoM6+kiFeMG87i5jVIqK/NrDQO2PB/XS0PN9atqsnnsDJfWXpetH4M05jBHPu7gCW8xDIaZG/jHT7g2Ggab4y3xuEg1BgpMA9xaRjv/wK9+6Kt</latexit><latexit sha1_base64="vQSt99oXUnYv4NQagPzRxQ1oi4U=">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</latexit>
y = f (x1, . . . , xn)<latexit sha1_base64="/3f2MpBVj2W7GyBsLsN/DPpMwJQ=">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</latexit><latexit sha1_base64="/3f2MpBVj2W7GyBsLsN/DPpMwJQ=">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</latexit><latexit sha1_base64="/3f2MpBVj2W7GyBsLsN/DPpMwJQ=">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</latexit><latexit sha1_base64="/3f2MpBVj2W7GyBsLsN/DPpMwJQ=">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</latexit>
Each holds private input At the end
knows only xi , y<latexit sha1_base64="+z9L178j89z5KqvGCItcQk5Robg=">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</latexit><latexit sha1_base64="+z9L178j89z5KqvGCItcQk5Robg=">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</latexit><latexit sha1_base64="+z9L178j89z5KqvGCItcQk5Robg=">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</latexit><latexit sha1_base64="+z9L178j89z5KqvGCItcQk5Robg=">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</latexit>
(i)<latexit sha1_base64="oA07zW7DNizmQ5PwGJSlgCYueWk=">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</latexit><latexit sha1_base64="oA07zW7DNizmQ5PwGJSlgCYueWk=">AAAC1nichVI9TxRRFD2MX4gfLNqY0GzcYLDZ3BkxrFZEG0pgXdgECZkZHusL85WZt5ssG+yMiYmJlRRUmFgQfoaNf8CCytpYQkJj4ZnZMcZi8U3evPvuu+e8c+99XhLozIicjFmXLl+5em38+sSNm7duT1am7qxmcTf1VcuPgzhte26mAh2pltEmUO0kVW7oBWrN23men6/1VJrpOHph+onaCN1OpLe17xq6mrP64WalJnW78VjmGlUaT5xH4tBw5h2bhl2XYtRQjqW48h0vsYUYProIoRDB0A7gIuO3DhuChL4NDOhLaeniXGEPE8R2GaUY4dK7w3+Hu/XSG3Gfc2YF2uctAWdKZBUz8k2O5FS+yrH8kF8juQYFR66lz9UbYlWyOfnuXvP8v6iQq8Grv6gLNRtso1Fo1dSeFJ48C3+I7+3unzafrswMHsgn+Un9h3IiX5hB1DvzPy+rlYML9GTkCosK9jm3hoy8L69HlXmlZbxi3GgWv6hBSn0dZmWwx4b/6Wp1tLHq1G0+h+W52sKzsvXjmMZ9zLK/81jAIpbQInsH7/ER+1bbem29sd4OQ62xEnMX/wzrw29qhqIi</latexit><latexit sha1_base64="oA07zW7DNizmQ5PwGJSlgCYueWk=">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</latexit><latexit sha1_base64="oA07zW7DNizmQ5PwGJSlgCYueWk=">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</latexit>
..
• Hot topic: f for machine learning
• SecureML [CCS17], MiniONN [CCS17], Gazelle [USENIX18], Tapas [ICML18], …, Mobius [Our paper, arXiv18]
interactive protocol
26
App: Outsource to Non-colluding servers
x
f(x)
x1 x2x1 x2
..
y1 y2y1 y2
secret sharing f on shares
• Our result: Practical protocols via client-aid techniques [Morita, Attrapadung, Teruya, Ohata, Nuida, Hanaoka ESORICS18]
aid randomness
MPC
+ ?
27
Big Data
Utility Privacy
Attribute Based Signature
Q.
while authenticating
Attribute Based Signature
28
X Ycan sign if R(X, Y)=1
X: aist, crypto Y: (aist phd) (crypto AI)^_ _
Privacy: X is private
• Applications: anonymous credentials • Our result: Schemes for any circuits/ Turing machines
• [Sakai, Attrapadung, Hanaoka PKC16] • [Sakai, Katsumata, Attrapadung, Hanaoka Asiacrypt18]
+ ?Authenticity
29
Big Data
Util.
Homomorphic Signature
Q.
Homomorphic Signature
30
+⇥
=
• Application: Verifiable computation • Fully homomorphic: can do any , • Linear homomorphic: can do
• Ours: efficient schemes [Attrapadung et al. PKC11, PKC13 ASIACRYPT12]
+ ⇥
a=2Bob
+
b=5Bob
⇥c=3Bob
d=7Bob
ab+cd=31Bob
Cryptography Platformattribute-based encryption
attribute-based signature
homomorphic signaturehomomorphic encryption
secure multi-party computationpseudo-random functions
+ Privacy/Security/AuthenticityUtility
functional encryption
secure boot in trusted execution environment
What We Do from Now
Cryptography Platformattribute-based encryption
attribute-based signature
homomorphic signaturehomomorphic encryption
secure multi-party computationpseudo-random functions
+ Privacy/Security/AuthenticityUtility
functional encryption
secure boot in trusted execution environment
What We Do from Now
• New applications Society 5.0
• New primitives/improved schemes• “Cryptographic Agility”
ability to switch/combine tools
Summary: I introduced
33
• attribute based / homomorphic encryption • attribute based / homomorphic signature • secure multi-party computation protocols
• Ongoing work • Cryptographic Agility • Secure and fast implementations
..
• Cryptography Platform Research Team @
Thank you !