<img src="https://github.com/KaoruTeranishi/EncryptedControl/blob/master/logo.png?raw=true" align="center" width="400" alt="header pic"/>
# ECLib
This is a Python library for numerical simulation of encrypted control.
# Encrypted control
Cybersecurity is a critical issue of networked control systems in a modern society.
Encrypted control is a novel concept of control using cryptographic tools for secure computation, such as homomorphic encryption and secret sharing.
ECLib helps researchers and students to implement their new idea of encrypted control using homomorphic encryption.
# Supported encryption schemes
- ElGamal<sup> [1]</sup>
- Dynamic-key ElGamal<sup> [2]</sup>
- Paillier<sup> [3]</sup>
- Regev (LWE)<sup> [4]</sup>
- GSW<sup> [5]</sup>
- GSW-LWE<sup> [6]</sup>
# Installation
Run pip command on your terminal.
`pip install eclib`
# Usage
See [tutorial_slide_1.pdf](https://github.com/KaoruTeranishi/EncryptedControl/blob/master/doc/tutorial_slide_1.pdf), [tutorial_slide_2.pdf](https://github.com/KaoruTeranishi/EncryptedControl/blob/master/doc/tutorial_slide_2.pdf), and [example codes](https://github.com/KaoruTeranishi/EncryptedControl/tree/master/examples).
# License
BSD License 2.0
# Author
Kaoru Teranishi
- E-mail: teranishi (at) uec.ac.jp
- Homepage: [https://kaoruteranishi.xyz](https://kaoruteranishi.xyz)
# References
[1] T. Elgamal, "A public key cryptosystem and a signature scheme based on discrete logarithms," IEEE Transactions on Information Theory, vol. 31, no. 4, pp. 469–472, 1985.
[2] K. Teranishi, T. Sadamoto, A. Chakrabortty, and K. Kogiso, "Designing optimal key lengths and control laws for encrypted control systems based on sample identifying complexity and deciphering time," IEEE Transactions on Automatic Control (Early access)
[3] P. Paillier, "Public-key cryptosystems based on composite degree residuosity classes," in International Conference on Theory and Application of Cryptographic Techniques, 1999, pp. 223–238.
[4] O. Regev, "On lattices, learning with errors, random linear codes, and cryptography," Journal of the ACM, vol. 56, no. 6, pp. 1-40, 2009.
[5] C. Gentry, A. Sahai, and B. Waters, "Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based," Cryptology ePrint Archive, Paper 2013/340, 2013.
[6] J. Kim, H. Shim, and K. Han, "Dynamic controller that operates over homomorphically encrypted data for infinite time horizon," IEEE Transactions on Automatic Control, vol. 68, no. 2, pp. 660–672, 2023.
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