1-To-n Oblivious Transfer protocol based on ElGamal Cryptosystem

What is an Oblivious Transfer

An Oblivious Transfer (OT) is a protocol between a sender S and a receiver R that allows R to obtain a message m_i from a set of messages M = {m₀,...,m_n} held by S without S learning which message R obtained and with R only learning m_i and no other messages in M.
OT protocols have applications in areas such as secure multiparty computation and private set intersection.
It this project, a pure Rust Implementation of a 1-to-n OT protocol based on ElGamal Cryptosystem is implemented.

Preliminaries

ElGamal Cryptosystem

Given a cyclic group G of prime order n and one of its generator g, ElGamal Cryptosystem is a triple of polynomial time algorithms (Gen, Enc, Dec) with the following properties:

• The key generation algorithm Gen samples at random a value x belonging to the set Z^*_n(set of integers using modular n arithmetic, i.e., modulo n is applied on all operations) and computes y=g^x mod n. The value x is the secret key and the value y is the public key.
• The encryption algorithm Enc takes as input a public key y and a message m belonging to the group G. Then, it samples at random a secret value r belonging to Z^*_n. After, it computes c₁ = g^r mod n and c₂ = m.y^r mod n = m.g^x.r mod n. Finally, it outpus (c₁, c₂).
• The decryption algorithm Dec takes as inputs a secret key x and a tuple of ciphertexts (c₁, c₂). Then, it computes k = c₁^xmod n = g^x.r mod n. Using k, it computes m = c₂.k^-1mod n = m.g^x.r.g^-(x.r) mod n

The protocol

Following is a diagram that depicts the execution of the protocol:

How to run (Linux)

Have the following components installed:

1. Rust >= version 1.45
2. OpenSSL >= version 1.1.1

Once the different environment dependencies have been installed, create an RSA private key and a signed certificate for the server (both in PEM format) using OpenSSL and place those files in src/keyfile folder.

Next, With the terminal working directory set to the project director, run the command cargo build --release

• To launch the Server/Sender program, executes the command ./target/release/server
• To launch the Client/Receiver program, executes the command ./target/release/client

Output example

Following is an example between a client and a server: As we can see, The client selected message at index 3, and after, it is only able to obtain a plaintext version of message at index 3.

Thus, 1-n OT protocol is respected.

Reference

1. D. Boneh and V. Shoup, "A Graduate Course in Applied Cryptography", Chapter 11