Individual Transaction Key (ITK) Creation

Protocol Description

For each transaction, a unique Individual Transaction Key (ITK) is derived from the relevant MVK and a high-resolution timestamp $(Y, M, D, h, m, s)$.

Deposit ITK

$$k_{\text{ITK}, D} \triangleq \text{Poseidon}( k_{\text{MVK}, \text{SOL}}, Y, M, D, h, m, s )$$

Claim ITK

$$k_{\text{ITK}, C} \triangleq \text{Poseidon}( k_{\text{MVK}, U_i}, Y, M, D, h, m, s )$$

Key Derivation Process

For Deposits

1. Input: Solana MVK $k_{\text{MVK}, \text{SOL}}$ (field element)
2. Timestamp Components: Year, Month, Day, Hour, Minute, Second
3. Hash Function: Poseidon hash function
4. Output: Deposit ITK $k_{\text{ITK}, D}$

For Claims

1. Input: Umbra address MVK $k_{\text{MVK}, U_i}$ (field element)
2. Timestamp Components: Year, Month, Day, Hour, Minute, Second
3. Hash Function: Poseidon hash function
4. Output: Claim ITK $k_{\text{ITK}, C}$

Timestamp Resolution

The high-resolution timestamp ensures:

• Uniqueness: Each transaction gets a unique ITK
• Time-Bound: ITKs are tied to specific moments in time
• Public Input: Timestamp is publicly observable on-chain
• Granularity: Second-level precision prevents collisions

Transaction Types

Deposit Transactions

• Use the Solana MVK $k_{\text{MVK}, \text{SOL}}$
• Generate deposit ITK $k_{\text{ITK}, D}$
• Enable linking deposits to the user's primary Solana address

Claim Transactions

• Use the Umbra address MVK $k_{\text{MVK}, U_i}$
• Generate claim ITK $k_{\text{ITK}, C}$
• Enable linking claims to the specific Umbra address

Security Analysis

Security Proof: Security of ITKs

Goal: An ITK must only be derivable by the holder of the corresponding MVK.

Assumption: Poseidon-as-a-PRF.

Argument: The MVK serves as the secret key for the PRF, and the public timestamp is the input. An on-chain observer cannot compute the ITK without the MVK.

Properties

• MVK-Dependent: Only derivable by holders of the corresponding MVK
• Time-Bound: Tied to specific transaction timestamps
• Unique: Each transaction produces a unique ITK
• Unlinkable: Without the MVK, ITKs appear random
• Transaction-Specific: Different for deposits vs claims