Threshold Encryption

Decentralized Key Generation (DKG)

The DKG mechanism in Neo X enables a fully decentralized key generation process among consensus members. Before each epoch change, the upcoming consensus group must successfully complete a DKG round to establish a new threshold public-private key pair. This process ensures that no single participant controls the decryption or signing capabilities.

DKG Process

Each DKG round consists of three key steps:

1. Share – The next consensus group generates $n$ distributed secret shares and a global public key, where $n$ is the number of Neo X consensus nodes.

2. Reshare – The current consensus group (if available) transfers the previous round’s secret to the next group.

3. Recover (Optional) – If up to $f$ secret shares are lost, the remaining $2f+1$ shares reconstruct the secret to complete the transition.

Starting from v0.3.0, the DKG module automates the entire process, except for setting up the initial Anti-MEV keystore with a secret passphrase.

Share Phase

Each participant executes the following steps:

1. Take a random polynomial $f(x) = a_0 + a_1x + a_2x^2 + \dots + a_{t-1}x^{t-1}$ as their local secret, where $t = 2f+1$ (the threshold for consensus).

2. Compute $f_1,f_2,...,f_n$ where $f_i=f(i)$ and share them with corresponding participants, where $i$ is the index of different participants of Share.

3. Accept all $f_i$ from other participants as $f_1(i),f_2(i),...,f_n(i)$, where $i$ is the index of receiver, and compute $s_i=\sum f_i$ to get the final secret key.

Generating the Global Public Key

The global public key is generated using Publicly Verifiable Secret Sharing (PVSS):

1. Each participant uploads $F(x)=f(x)G_1$ within his PVSS to the KeyManagement contract.
2. The contract verifies each PVSS and computes $S=\sum_{i=1}^n F_i(0)$ as the global public key.

A well-constructed PVSS includes:

• $F(x)=f(x)G_1$ as the sender’s local secret commitment.
• $rG_1,rG_2$ as a pair of commitments for a random scalar $r$.
• $F=(F(1),F(2),...,F(n))$ as the commitment share messages.

The KeyManagement contract validates $F(1),F(2),...,F(n)$, and verifies scalar $r$. Recipients validate their received shares using $e(r_1f(i),g_2)=e(F(i),r_2)$.

Future Enhancement: Zero-Knowledge Proofs (ZKPs) will be integrated to enhance encryption verification.

Reshare Phase

Each participant executes the following steps:

1. Regenerate his local secret $f'(x)=a_0+a'_1 x+a'_2 x^2+ \dots +a'_{t-1}x^{t-1}$ while preserving the constant term $a_0$.
2. Follow the step 2 and 3 in the Share phase, but send the shares to the next consensus group.

The KeyManagement contract ensures $F(0)=F'(0)$, preserving the global public key unchanged and preventing leakage of the original secret shares.

Recover Phase (Optional)

If some secret shares are lost, the remaining consensus members help restore them:

1. The current consensus group forwards all received shares $f_i$ from the lost index $i$ to its successor.
2. The recipient reconstructs the original local secrets using Lagrange interpolation.

Security Note: Recover exposes at most $f$ of the original secrets, so it is only allowed when the index $i$ is confirmed absent from Reshare.

Threshold Public Key Encryption (TPKE)

Neo X's DKG enables a Threshold Public Key Encryption (TPKE) scheme, ensuring that encrypted transactions can only be decrypted if at least $2f+1$ consensus nodes cooperate. This mechanism is crucial for preventing premature exposure of transaction details.

Neo X TPKE utilizes the BLS12-381 curve, encoding any secret to $G_1$ for encryption and any message to $G_2$ for signature generation.

Encryption

For a given secret message $msg$, the encryption process follows these steps:

1. A random point $G_1$ point $P$ is chosen as a seed to generate an AES key. The encrypted ciphertext is computed as $C_1=AES(Hash(P), msg)$.
2. To ensure security, a random scalar $r$ is selected to encrypt $P$ as $C_2=P+rS$

   where:

   • $r$ is a random scalar,
   • $S$ is the global public key.
3. The final encrypted message $C$, which is broadcasted across the network, consists of $C=(C_1,C_2)$.

Decryption

To recover the original $msg$, the Neo X consensus network must decrypt $C_1$ to recover $P$. The decryption process follows:

1. Each CN computes and shares $s_iR$, where:

   • $R$ is the commitment of the random scalar $r$,
   • $s_i$ is the local secret key.
2. Since validator indices (DKG indices) are publicly known within Neo X Governance, these shares can be aggregated and solved using a Vandermonde matrix.

3. Once the seed $P$ is recovered, the original message $msg$ can be decrypted using AES.

Signature

For a given message $msg$, Neo X generates a signature through the following process:

1. The message is encoded to $G_2$ as $Q=HashToG2(msg)$
2. A signature share is computed as $s_iH$ where $s_i$ is the local secret key.
3. After collecting enough broadcasted shares, CNs aggregate and get the final signature with Vandermonde matrix in the same way as TPKE decryption.