https://github.com/Georeactor/encrypted-geofence

testing out homomorphic encryption
https://github.com/Georeactor/encrypted-geofence

encryption geofences homomorphic-encryption paillier

Last synced: about 2 months ago
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testing out homomorphic encryption

• Host: GitHub
• URL: https://github.com/Georeactor/encrypted-geofence
• Owner: Georeactor
• Created: 2016-07-17T00:56:47.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2019-04-10T18:37:23.000Z (over 5 years ago)
• Last Synced: 2024-08-04T00:04:04.053Z (5 months ago)
• Topics: encryption, geofences, homomorphic-encryption, paillier
• Language: JavaScript
• Size: 42 KB
• Stars: 36
• Watchers: 9
• Forks: 6
• Open Issues: 3
• Metadata Files:
  • Readme: README.md

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• awesome-he - crypto-geofence - Geo-fencing demo application based on Paillier scheme. (Applications)

README

        
# crypto-geofence

Is it possible for me to check if I'm inside a geofence, without revealing my location to

the server, and without the server giving me the true geofence?

Video at DEF-CON Crypto & Privacy Village 2018: https://www.youtube.com/watch?v=ySl2ywGiFkw

## What is homomorphic encryption?

Homomorphic encryption is a new technique where you can perform arithmetic operations on

encrypted numbers.  It's possible with a few different algorithms, including the factoring-based one

used here (Paillier).  In the future it might be better to use a quantum-resistent algorithm

based on lattice cryptography.

If you send the encrypted numbers and a public key, another computer can perform arithmetic on

the number and scalar values without seeing the actual values.

## Applying it to Geofences

Encrypted coordinates and the public key are POSTed to the server

Originally I was hoping to find if you were in the box by testing this:

```python

latitude_offset = (north - latitude) * (south-latitude)

```

The number would be negative for ```south < latitude < north```, and positive in any other

condition.  It would also be difficult to find north and south by factoring the result.

Unfortunately, multiplying encrypting numbers is not possible in the Paillier

cryptosystem.  I got this funny error:



Anyway, you can obfuscate offsets by multiplying by a random scalar instead:

```python

north_offset = (north - latitude) * random()

south_offset = (south - latitude) * random()

```

One of the offsets should be positive and the other negative, but the random factor makes

it difficult to figure out the true offset to the geofence. Combined with rate-limiting,

this could make your fence exta-secret.

### Going forward

I would like to:

- calculate geofences for more complex shapes, by breaking them into rectangles or triangles

- calculate distance, using a different cryptosystem which allows multiplication

## Libraries used

Using Brian Thorne's homomorphicjs on the client,

and Australia NICTA's Python-Paillier

on the server

## License

MIT license