Blockchain Transaction Authorization with Low-Entropy Passwords
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Solution Overview
Problem
The recovery of cryptographic assets when a private key is lost is a significant challenge in blockchain systems, particularly for cryptocurrencies like Bitcoin, due to the lack of a decentralized mechanism, leading to locked and unusable wallets, with existing solutions like brainwallets being insecure against brute-force attacks.
Innovation Solution
A method and system that utilize a consensus mechanism involving a group of nodes to authorize transactions with a password, using a cryptographic key generated based on a user-chosen password and private key shares, employing a bilinear mapping on an elliptic curve digital signature scheme, ensuring secure password usage without exposing it directly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If brainwallets are used to store cryptographic assets, then ease of operation is improved, but security deteriorates due to vulnerability against brute-force attacks
Solution Approach 1:
The private key is segmented into multiple shares distributed among different nodes in a decentralized network. Instead of storing a single private key that can be brute-forced, the system divides it into parts that require collaboration to reconstruct, making brute-force attacks computationally infeasible while maintaining ease of operation through simple password-based access.
Solution Approach 2:
A decentralized network of nodes acts as an intermediary between the user and the cryptographic assets. The nodes collectively hold and protect the private key shares, mediating access control through consensus mechanisms. This intermediary layer prevents direct exposure of the private key to potential attackers while allowing legitimate users to access their assets through password verification.
2Reliability
If high-entropy passwords are used, then security is improved, but ease of operation deteriorates due to reduced memorability
Solution Approach 1:
The system replaces the mechanical requirement of remembering complex high-entropy passwords with a cryptographic verification mechanism. Users can employ low-entropy, easily memorable passwords because the security doesn't rely on password complexity but on the cryptographic proof-of-work mechanism and distributed key sharing, substituting human memory capacity with computational verification.
Solution Approach 2:
The security model changes the critical parameter from password entropy to computational difficulty. Instead of requiring passwords with high entropy (which are hard to remember), the system uses low-entropy passwords combined with computationally intensive verification processes and distributed key shares, transforming the security bottleneck from human cognition to computational resources.
3Reliability
If traditional private key storage is used, then security is improved, but ease of operation deteriorates due to loss of access when private key is lost
Solution Approach 1:
The private key is divided into multiple shares distributed across different nodes in the decentralized network. This segmentation ensures that no single point of failure exists - if one node or share is lost, the user can still recover access by combining shares from other nodes. This eliminates the catastrophic loss scenario of traditional private key storage while maintaining security through the requirement of multiple shares for reconstruction.
Solution Approach 2:
The decentralized network of nodes serves as an intermediary that holds and protects portions of the private key. This intermediary structure provides redundancy and fault tolerance - if the user loses their local copy or access method, the network intermediaries preserve the key shares and enable recovery through consensus-based reconstruction, eliminating the all-or-nothing access problem of traditional storage.
Data Source
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AI summary
There may be provided a blockchain-implemented security method involving a requestor and a group of nodes, which includes generating a cryptographic key of the requestor based on a password chosen by the requestor and first quantities sent by the group of nodes (which are derived from private key shares of the group of nodes and a generator function of a digital signature scheme employing a bilinear mapping on an elliptic curve). A cryptographic signature for a requestor blockchain transaction can be generated where the signature corresponds to the requestor's cryptographic key. The signature can be based on the password and second quantities sent by the group of nodes (which are also derived from the group private key shares). The method can further include verifying the cryptographic signature of the blockchain transaction using the requestor's cryptographic key. Additionally or alternatively, the method can employ a consensus mechanism involving the group of nodes to allow the requestor to authorise a transaction with a password. The method can be logically partitioned into a sequence of phases, including an initialisation phase, a funding phase, and a payment authorization phase (which involves a pre-spending transaction and a spending transaction).