Multi-Party Diffie-Hellman (mpdh)

mpdh is a Go application that demonstrates a 2-party Diffie-Hellman key exchange protocol involving a Sender, a Recipient, and a Cloud provider. It uses the NIST P-256 elliptic curve.

Protocol Overview

The protocol splits the recipient's private key between the recipient (Alice) and the cloud (Chuck).

1. Key Generation: Alice and Chuck generate random scalars $a_1$ and $a_2$. The effective public key is $P = (a_1 + a_2)G$.
2. Encryption (Sender): The sender uses the public key $P$ to perform a standard ECDH, generating an ephemeral key pair $(b, bG)$ and a shared secret $S = bP$.
3. Decryption (Recipient): The recipient receives $bG$. To recover $S$, they compute $a_1(bG)$ and obtain $a_2(bG)$ from the cloud. The sum is $(a_1 + a_2)bG = b(a_1+a_2)G = bP = S$.

Usage

Build the application:

go build -o mpdh mpdh.go

1. Generate Keys

Generates the split private shares and the combined public key.

./mpdh generate <pubkey_file> <chuck_share_file> <alice_share_file>

Example:

./mpdh generate pk.pem chuck.key alice.key

2. Send (Sender)

Simulates a sender performing the Diffie-Hellman exchange.

./mpdh send <pubkey_input_file> <ephemeral_pubkey_output_file>

Example:

./mpdh send pk.pem ephemeral.pem

This outputs the sender's computed shared secret to stdout.

3. Recover (Recipient)

Simulates the recipient recovering the shared secret using their share and the cloud's share.

./mpdh recover <ephemeral_pubkey_input_file> <chuck_share_file> <alice_share_file> <output_secret_file>

Example:

./mpdh recover ephemeral.pem chuck.key alice.key secret.bin

Helper Scripts

For convenience, the following shell scripts are provided to automate the flow:

• ./keygen.sh: Runs the generate command.
• ./send.sh: Runs the send command and logs the secret.
• ./recover.sh: Runs the recover command.
• ./verify.sh: Compares the sender's secret with the recovered secret to verify correctness.

License

This project is licensed under the MIT License - see the LICENSE file for details.