Digital Notary Solutions

Multi-Signature Wallets

1. Definitions and Preliminaries

Sets

• $N$: Set of all Notary wallets

• $U$: Set of all User wallets

• $E$: Set of all Escrow contracts

• $A$: Set of all Assets (Real Estate properties)

• $S$: State of the Notary wallet, $S∈{online,offline,soon_available}$

• $F$: Fee to the Notary, $3≤F≤15$

2. Notary Wallet Structure and Construction

2.1 Definition

A Notary Wallet $Ni$ is represented as a 4-tuple:

$Ni={IDi,Stakei,Si,Ksi}$

where $Ksi$ is the signing key used for authorizing transactions.

3. Escrow Contract Description

3.1 Definition

$Ej={Aj,Ubj,Usj,Nij,VCLj,ζj}$

where $VCL$ is the Video Chat Link and $ζ$ is the transaction status.

3.2 State Transition Function

Given the state transition function $τ:S×E→S×E$, the goal is to optimize the assignment of notary wallets to escrow contracts while minimizing waiting times for all parties involved:

$τ(Si,Ej)↦(Si′,Ej′)$

4. Notary Selection and Interaction Algorithm

4.1 Notary Selection Algorithm

The system must provide a mechanism $ϕ$ for identifying an appropriate notary, satisfying:

$ϕ:E×N×S→N$

s.t.

$∀Ej∃Ni:Si=online$

4.2 Interaction and Verification

Given an escrow contract $Ej$ and a selected notary $Ni$, two options for verification are available:

Option 1: Direct verification via secured Video Chat.

Option 2: Verification through Zero-Knowledge Proof (ZKP).

5. Mathematical Formulation of Verification Options

5.1 Video Chat Verification

$Γ:E×VCL→{0,1}$

5.2 ZKP Verification

$Ψ:E×ZKP→{0,1}$

where $ZKP$ consists of ID checks, live video verification, etc.

6. Transaction Completion and Asset Transfer

6.1 Dual-Signature Confirmation

Given a transaction $T$, two signatures are required: one from the user $Ub$ (buyer) and one from the notary $Ni$ after verification:

$Ξ:Ubj×Ni→{0,1}$

6.2 Asset Transfer Function

$Θ:A×Usj×Ubj→Ub$

7. Fee Distribution and Notary Compensation

7.1 Fee Distribution Function

$Ω:F×N→N$

Where $Ω$ ensures that the fee $F$ is transferred to the notary wallet upon successful verification and completion of a transaction.

8. Security Considerations and Future Directions

• Security and Anonymity: Strategies to maintain the privacy and security of the involved parties should be implemented.

• Regulatory Compliance: The structure must adhere to real estate laws and blockchain regulations, and adjust according to varying legal frameworks globally.

• Scalability: Mechanisms for scaling the approach to handle increasing transaction loads and notary numbers need to be devised.

• Automation and AI Integration: Future developments may consider incorporating AI to automate aspects of the verification process, creating a hybrid system.