![Page 1: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/1.jpg)
iO from FE for Simple Functions
Prabhanjan Ananth Abhishek Jain Amit Sahai
![Page 2: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/2.jpg)
Our result
FE supporting decryption keys for this functionalityimplies iO for circuits
![Page 3: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/3.jpg)
(Non-compact FE) implies compact FE
![Page 4: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/4.jpg)
(Non-compact FE) implies compact FE
Supports multi-keys
![Page 5: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/5.jpg)
(Non-compact FE) implies compact FE
• This work + [AJ15,BV15]: Non-compact FE implies iO
• Implication: iO based on GGHZ14 mmap assumptions
![Page 6: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/6.jpg)
(Non-compact FE) implies compact FE
Also observed by Bitansky-Vaikuntanathan’15
• This work + [AJ15,BV15]: Non-compact FE implies iO
• Implication: iO based on GGHZ14 mmap assumptions
![Page 7: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/7.jpg)
Main Idea
![Page 8: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/8.jpg)
Non Compact FE
Enc( m ) f
![Page 9: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/9.jpg)
Non Compact FE
Enc( m ) f
depends on the size of f
![Page 10: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/10.jpg)
Non Compact FE
Enc( m ) f
Break the functional key into many parts
![Page 11: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/11.jpg)
Non Compact FE
Enc( m )
1st part of f
nth part of f
.
..
![Page 12: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/12.jpg)
Non Compact FE
Enc( m )
1st part of f
nth part of f
.
..
ciphertext shrinks
![Page 13: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/13.jpg)
Resulting scheme: Compact FE !!
Enc( m )
1st part of f
nth part of f
.
..
![Page 14: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/14.jpg)
• Showed: FE for fsimple implies iO for all functions
![Page 15: iO from FEcrypto.2015.rump.cr.yp.to/2a8d73a9a9b067ae3c886a72d05b... · 2015-08-19 · Prabhanjan Ananth Abhishek Jain Amit Sahai. Our result FE supporting decryption keys for this](https://reader034.vdocument.in/reader034/viewer/2022050106/5f44438ff1c0ac185c65fdc5/html5/thumbnails/15.jpg)
• link: http://eprint.iacr.org/2015/730.pdf