Homomorphic Encryption
Aniket Sharma
@aniket965
Ujjwal Upadhyay
@ujjwal-9
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What is Homomorphic Encryption?
<Cryptocomputing>
The first fully homomorphic encryption system, built by Craig Gentry, was incredibly slow, taking 100 trillion times as long to perform calculations of encrypted data than plaintext analysis.
Why it's important?
While traditional encryption schemes can be used to privately outsource data storage to the cloud, the data cannot be used for computations without first decrypting it, resulting in a huge loss of utility.
People tend to remove useful documents from safe storage at the first chance they get. This exposes them to all the usual threats and explains why so few cases of document theft involve safecracking. Typically the same principle holds for encryption. People decrypt their data so they can use it
This may seem like an exotic property
Trust me, it’s not
In fact, cryptographers have put a lot of effort into removing the homomorphic properties from common public-key schemes like RSA. Without those protections, both schemes are homomorphic with respect to (modular) multiplication.
Can Homomorphic Encryption be Practical?
We exhibit a number of real-world applications, in the medical, financial, and the advertising domains, which require only that the encryption scheme is “somewhat” homomorphic.
But that scheme has been slowly improving. fully homomorphic encryption would multiply the computing time necessary for a function by roughly a million times
Homomorphic encryption has some immediate practical applications
- Banking
- Voting System
- Statistical Analysis
- Secure Computing
and many more ...
Application in Banking
Application in voting
Maths & Encryption
Or is it magic ?
Encryption & Decryption Algorithm
** (Key Point) Decryption is faster than Encryption !!!
elaboration
Additive Homomorphism
Multiplicative Homomorphism
SWHE vs PHE vs FHE
We're here (SWHE & PHE)
FHE
Many Add & Many Product
RSA & Friends
Many Product & Zero Add
PHE (Partially Homomorphic Encryption) schemes are in general more efficient than SHE and FHE, mainly because they are homomorphic w.r.t to only one type of operation: addition or multiplication. SWHE (SomeWhat Homomorphic Encryption) is more general than PHE in the sense that it supports homomorphic operations with additions and multiplications. The drawback is that you can perform only a limited number hom. operations.
PHE Examples
PHE is most used type of Homomorphic Encryption
Demo is on this cryptosystem
Let's have a look at the Demo...
Demo Code
Proof-of-concept
Homomorphic Encryption
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References
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https://www.microsoft.com/en-us/research/project/homomorphic-encryption/ - https://simons.berkeley.edu/talks/wichs-brakerski-2015-07-06
- https://www.networkworld.com/article/3196121/security/how-to-make-fully-homomorphic-encryption-practical-and-usable.html
- https://crypto.stanford.edu/craig/craig-thesis.pdf
- https://arxiv.org/pdf/1409.0829.pdf
- https://en.wikipedia.org/wiki/Paillier_cryptosystem