Abstract. A purely peer-to-peer electronic credit system would allow individuals to extend credit directly to one another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending and over-leveraging. We propose a solution to these problems using a distributed network where credit capacity is determined by trust relationships, debt obligations are recorded on a transparent ledger, and the system maintains a zero-sum constraint to prevent inflation. The network is robust in its unstructured simplicity. Nodes work with little coordination. They do not need to be identified, since credit flows through paths of trust relationships, and participants are incentivized to maintain honest behavior through reputation mechanisms.

Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust-based model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions.

More fundamentally, the current system excludes billions of people who lack access to traditional banking. Two billion people worldwide have no bank account. Four billion cannot access credit at reasonable rates. This exclusion is not due to lack of trustworthiness, but lack of collateral, documentation, or geographic proximity to financial institutions.

What is needed is an electronic credit system based on trust relationships rather than physical collateral, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Credit that is computationally impractical to over-leverage would protect lenders, and routine escrow mechanisms could easily be implemented to protect borrowers.

In this paper, we propose a solution to the credit access problem using a peer-to-peer distributed network. The network timestamps transactions by hashing them into an ongoing chain of trust relationships, forming a record that cannot be changed without redoing the proof-of-trust. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of trust relationships.

We define a credit unit as a chain of digital signatures representing debt obligations. Each creditor extends credit by digitally signing a hash of the previous transaction and the public key of the next debtor and adding these to the credit unit. A payee can verify the signatures to verify the chain of ownership.

The problem of course is the payee can't verify that one of the debtors didn't over-leverage themselves by borrowing from multiple creditors simultaneously. A common solution is to introduce a trusted central authority, or credit bureau, that checks every transaction for over-leveraging. After each transaction, the credit unit must be returned to the bureau to issue a new credit unit, and only credit units issued directly from the bureau are trusted not to be over-leveraged.

The problem with this solution is that the fate of the entire credit system depends on the credit bureau, with every transaction having to go through them, just like a bank.

We need a way for the payee to know that the previous creditors did not extend credit to an over-leveraged borrower. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to over-leverage. The only way to confirm the absence of over-leveraging is to be aware of all transactions. In the bureau-based model, the bureau was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced, and we need a system for participants to agree on a single history of the order in which they were received.

The network is structured as a graph of trust relationships. Each edge in the graph represents a bilateral credit line between two participants. The edge has properties:

• Credit Limit: Maximum debt the creditor is willing to extend

• Used Capacity: Current debt outstanding on this edge

• Trust Score: Assessment of the debtor's reliability

The aggregate of all incoming edges to a node determines that node's total borrowing capacity. The aggregate of all outgoing edges determines that node's total lending exposure.

Credit flows through the network along paths of trust relationships. When Alice wants to send credit to David but has no direct relationship, the system finds a path through intermediaries: Alice → Bob → Charlie → David. Each hop along the path records a debt obligation.

This structure has several key properties:

Distributed: No central authority controls the network. Each participant maintains their own trust relationships.

Transparent: All debt obligations are recorded on a public ledger, visible to all participants.

Self-Regulating: The system automatically limits borrowing based on aggregate trust, preventing over-leveraging.

Resilient: The failure of any single node does not threaten the network. Debt is localized to trust relationships.

The system maintains a fundamental mathematical invariant:

Σ(credit balances) = Σ(debt obligations)

Every unit of credit in circulation corresponds to a debt obligation recorded on a trust edge. Money cannot be created without someone owing it. This zero-sum constraint prevents inflation by design.

When Alice transfers 100 units to Bob:

• If Alice has balance: Her balance decreases by 100, Bob's increases by 100 (net zero)

• If Alice uses capacity: A debt of 100 is recorded on the Alice-Bob edge, Bob's balance increases by 100 (net zero)

The total money supply equals the total debt. This is not a policy choice. This is a mathematical constraint enforced by the protocol.

When debt obligations form cycles, they can be automatically eliminated without transferring value. If Alice owes Bob 100, Bob owes Charlie 100, and Charlie owes Alice 100, these obligations cancel out.

Before each transaction, the system:

1. Detects cycles involving the sender and receiver

2. Calculates the minimum debt in each cycle

3. Reduces all obligations in the cycle by that amount

4. Executes the remaining transfer

This continuous optimization reduces network debt, frees capacity, and improves efficiency without requiring any participant action.

When credit flows to a participant with existing debt, the system creates a warrant—locked backing that shortens debt chains while maintaining the zero-sum property.

If Bob owes Charlie 200 units and Alice sends Bob 100 units:

• Bob's debt to Charlie reduces to 100 units

• A warrant of 100 units is created (locked, earns 5% interest)

• The debt chain is shortened

Warrants improve network stability by:

• Reducing cascade risk (shorter chains)

• Distributing backing across multiple parties

• Providing interest income on locked capital

• Enabling automatic optimization

Credit capacity between any two nodes is not limited to direct relationships but aggregates across all network paths.

If Alice wants to send to David:

• Path 1: Alice → Bob → David (capacity: 100)

• Path 2: Alice → Charlie → David (capacity: 150)

• Path 3: Alice → Eve → Frank → David (capacity: 50)

Total capacity: 300 units (sum of all paths)

This creates powerful network effects:

• More participants → More paths → More capacity

• Weak ties contribute to aggregate capacity

• Network becomes more liquid as it grows

• Redundancy provides resilience

When transactions form closed loops (A → B → C → A), the system rewards all participants by strengthening their trust relationships.

Loop detection algorithm:

1. After each transaction, scan for closed loops

2. Calculate loop bonus based on size, value, and frequency

3. Strengthen all edges in the loop (increase capacity and credit)

This incentivizes:

• Sustained trust relationships

• Productive circular exchange

• Community cohesion

• Reciprocity

Social interactions are automatically converted to economic capacity through daily point distribution.

Process:

1. System tracks interactions between participants (messages, endorsements, collaborations)

2. Each participant receives daily point allocation (e.g., 50 points)

3. Points distributed proportionally based on interaction frequency

4. Points strengthen trust edges (increase capacity and credit)

This bridges social and economic capital:

• Interaction frequency → Stronger relationships

• No credit applications required

• Organic capacity growth

• Decay for inactive relationships (after 7 days)

Every participant's total debt is publicly visible to the entire network, preventing hidden leverage and enabling democratic accountability.

Aggregate calculation:

User Total Debt = Σ(all outbound edge obligations)

Benefits:

• Prevents over-leveraging (all debt visible)

• Enables independent verification (anyone can audit)

• Provides early warning (rising debt signals risk)

• Eliminates information asymmetry

• Enables collective risk assessment

Privacy is maintained through:

• Pseudonymous identifiers (not real-world identity)

• Aggregate totals public, bilateral details can be private

• Cryptographic proofs (verify without revealing)

System parameters are governed through distributed consensus:

Voting Mechanism:

• One person, one vote (democratic)

• Reputation weighting (proven track records have more influence)

• Transparent processes (all proposals visible)

• Reversible decisions (bad choices can be undone)

Governed Parameters:

• Interest rates (warrant: 5%, direct debt: 8%)

• Capacity limits (max per edge: 2000 units)

• Decay rates (inactive edges: -1 point/day after 7 days)

• System rules and algorithms

This ensures:

• Democratic control (not corporate boards)

• Adaptive system (can evolve with needs)

• Transparent governance (all decisions visible)

• Community ownership (participants control the system)

The steps to run the network are as follows:

1. New transactions are broadcast to all nodes

2. Each node collects new transactions into a block

3. Each node works on finding a proof-of-trust for its block

4. When a node finds a proof-of-trust, it broadcasts the block to all nodes

5. Nodes accept the block only if all transactions in it are valid and not over-leveraged

6. Nodes express their acceptance by working on creating the next block in the chain, using the hash of the accepted block as the previous hash

Nodes always consider the longest chain to be the correct one and will keep working on extending it. If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer. The tie will be broken when the next proof-of-trust is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one.

New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach many nodes, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a node does not receive a block, it will request it when it receives the next block and realizes it missed one.

The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous.

The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the "tape", is made public, but without telling who the parties were.

As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner.

We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them.

An attacker can only try to change one of his own transactions to take back money he recently spent. The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the honest chain being extended by one block, increasing its lead by +1, and the failure event is the attacker's chain being extended by one block, reducing the gap by -1.

The probability of an attacker catching up from a given deficit is analogous to a Gambler's Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows:

Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.

Bitcoin demonstrated that decentralized digital currency is possible. BitCredit extends this concept from currency to credit:

Bitcoin:

• Fixed supply (21 million coins)

• Proof-of-work mining

• Store of value (digital gold)

• Energy intensive

• Not suitable for everyday transactions

BitCredit:

• Elastic supply (constrained by trust)

• Proof-of-trust (reputation-based)

• Medium of exchange (everyday credit)

• Energy efficient

• Designed for transactions

Bitcoin solved the double-spending problem for digital currency. BitCredit solves the over-leveraging problem for digital credit.

The system has several advantages over traditional credit systems:

Universal Access: Anyone can participate, regardless of assets, documentation, or location.

No Collateral Required: Trust replaces physical collateral as the basis for credit.

Inflation-Proof: Zero-sum constraint prevents money creation without backing.

Transparent: All debt obligations visible, enabling collective risk assessment.

Democratic: Governance through consensus, not corporate control.

Efficient: Automatic optimization through circular netting and warrant mechanisms.

Resilient: Distributed structure prevents single points of failure.

Inclusive: Two billion unbanked people can access credit through trust networks.

The system has some limitations that should be acknowledged:

Network Effects Required: The system becomes more valuable with more participants. Early networks may have limited liquidity.

Trust Building Takes Time: New participants must build trust relationships before accessing significant capacity.

Default Risk: While localized, defaults can still occur. Lenders must assess risk carefully.

Regulatory Uncertainty: Decentralized credit systems may face regulatory challenges in some jurisdictions.

Technical Complexity: While the user experience can be simple, the underlying system is complex.

Cultural Adaptation: Some cultures may be more receptive to trust-based credit than others.

These limitations are not fundamental flaws but challenges to be addressed through careful implementation and gradual adoption.

Several areas warrant further research and development:

Scalability: Optimizing the system for millions or billions of participants.

Privacy Enhancements: Implementing zero-knowledge proofs and other cryptographic techniques to enhance privacy while maintaining transparency.

Interoperability: Enabling BitCredit networks to interact with traditional financial systems and other cryptocurrency networks.

Governance Mechanisms: Refining consensus governance to balance efficiency with democratic participation.

Risk Models: Developing sophisticated models for assessing and pricing credit risk in trust networks.

Legal Frameworks: Working with regulators to establish appropriate legal frameworks for decentralized credit.

User Experience: Simplifying the interface to make the system accessible to non-technical users.

We have proposed a system for electronic credit without relying on trust in financial institutions. We started with the usual framework of credit units made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent over-leveraging. To solve this, we proposed a peer-to-peer network using proof-of-trust to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of trust relationships.

The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-trust chain as proof of what happened while they were gone.

They vote with their trust relationships, expressing their acceptance of valid transactions by working to extend them and rejecting invalid transactions by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.

The result is a credit system that is:

• Accessible to everyone

• Based on trust, not assets

• Inflation-proof by design

• Transparent and auditable

• Democratically governed

• Efficient and self-optimizing

• Resilient and antifragile

This is not just an improvement on traditional finance. This is a new foundation for economic organization—one that enables universal participation, rewards cooperation, and aligns individual incentives with collective welfare.

The technology exists. The mathematics is sound. The need is urgent.

What remains is adoption—the gradual recognition that credit based on trust is not just possible, but superior to credit based on collateral. That decentralized systems are not just viable, but more robust than centralized ones. That the future of finance is not institutional gatekeeping, but peer-to-peer cooperation.

BitCredit is not the end of this journey. It is the beginning.

[1] Satoshi Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System" (2008)

[2] W. Dai, "b-money" (1998)

[3] H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal trust requirements" (1999)

[4] S. Haber, W.S. Stornetta, "How to time-stamp a digital document" (1991)

[5] D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping" (1992)

[6] R.C. Merkle, "Protocols for public key cryptosystems" (1980)

[7] M. Granovetter, "The Strength of Weak Ties" (1973)

[8] R. Putnam, "Bowling Alone: The Collapse and Revival of American Community" (2000)

[9] E. Ostrom, "Governing the Commons: The Evolution of Institutions for Collective Action" (1990)

[10] F.A. Hayek, "The Use of Knowledge in Society" (1945)

Version: 1.0
Date: November 25, 2025
License: Open Source (MIT)

Abstract. A purely peer-to-peer electronic credit system would allow individuals to extend credit directly to one another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending and over-leveraging. We propose a solution to these problems using a distributed network where credit capacity is determined by trust relationships, debt obligations are recorded on a transparent ledger, and the system maintains a zero-sum constraint to prevent inflation. The network is robust in its unstructured simplicity. Nodes work with little coordination. They do not need to be identified, since credit flows through paths of trust relationships, and participants are incentivized to maintain honest behavior through reputation mechanisms.

Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust-based model. Completely non-reversible transactions are not really possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for small casual transactions.

More fundamentally, the current system excludes billions of people who lack access to traditional banking. Two billion people worldwide have no bank account. Four billion cannot access credit at reasonable rates. This exclusion is not due to lack of trustworthiness, but lack of collateral, documentation, or geographic proximity to financial institutions.

What is needed is an electronic credit system based on trust relationships rather than physical collateral, allowing any two willing parties to transact directly with each other without the need for a trusted third party. Credit that is computationally impractical to over-leverage would protect lenders, and routine escrow mechanisms could easily be implemented to protect borrowers.

In this paper, we propose a solution to the credit access problem using a peer-to-peer distributed network. The network timestamps transactions by hashing them into an ongoing chain of trust relationships, forming a record that cannot be changed without redoing the proof-of-trust. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of trust relationships.

We define a credit unit as a chain of digital signatures representing debt obligations. Each creditor extends credit by digitally signing a hash of the previous transaction and the public key of the next debtor and adding these to the credit unit. A payee can verify the signatures to verify the chain of ownership.

The problem of course is the payee can't verify that one of the debtors didn't over-leverage themselves by borrowing from multiple creditors simultaneously. A common solution is to introduce a trusted central authority, or credit bureau, that checks every transaction for over-leveraging. After each transaction, the credit unit must be returned to the bureau to issue a new credit unit, and only credit units issued directly from the bureau are trusted not to be over-leveraged.

The problem with this solution is that the fate of the entire credit system depends on the credit bureau, with every transaction having to go through them, just like a bank.

We need a way for the payee to know that the previous creditors did not extend credit to an over-leveraged borrower. For our purposes, the earliest transaction is the one that counts, so we don't care about later attempts to over-leverage. The only way to confirm the absence of over-leveraging is to be aware of all transactions. In the bureau-based model, the bureau was aware of all transactions and decided which arrived first. To accomplish this without a trusted party, transactions must be publicly announced, and we need a system for participants to agree on a single history of the order in which they were received.

The network is structured as a graph of trust relationships. Each edge in the graph represents a bilateral credit line between two participants. The edge has properties:

• Credit Limit: Maximum debt the creditor is willing to extend

• Used Capacity: Current debt outstanding on this edge

• Trust Score: Assessment of the debtor's reliability

The aggregate of all incoming edges to a node determines that node's total borrowing capacity. The aggregate of all outgoing edges determines that node's total lending exposure.

Credit flows through the network along paths of trust relationships. When Alice wants to send credit to David but has no direct relationship, the system finds a path through intermediaries: Alice → Bob → Charlie → David. Each hop along the path records a debt obligation.

This structure has several key properties:

Distributed: No central authority controls the network. Each participant maintains their own trust relationships.

Transparent: All debt obligations are recorded on a public ledger, visible to all participants.

Self-Regulating: The system automatically limits borrowing based on aggregate trust, preventing over-leveraging.

Resilient: The failure of any single node does not threaten the network. Debt is localized to trust relationships.

The system maintains a fundamental mathematical invariant:

Σ(credit balances) = Σ(debt obligations)

Every unit of credit in circulation corresponds to a debt obligation recorded on a trust edge. Money cannot be created without someone owing it. This zero-sum constraint prevents inflation by design.

When Alice transfers 100 units to Bob:

• If Alice has balance: Her balance decreases by 100, Bob's increases by 100 (net zero)

• If Alice uses capacity: A debt of 100 is recorded on the Alice-Bob edge, Bob's balance increases by 100 (net zero)

The total money supply equals the total debt. This is not a policy choice. This is a mathematical constraint enforced by the protocol.

When debt obligations form cycles, they can be automatically eliminated without transferring value. If Alice owes Bob 100, Bob owes Charlie 100, and Charlie owes Alice 100, these obligations cancel out.

Before each transaction, the system:

1. Detects cycles involving the sender and receiver

2. Calculates the minimum debt in each cycle

3. Reduces all obligations in the cycle by that amount

4. Executes the remaining transfer

This continuous optimization reduces network debt, frees capacity, and improves efficiency without requiring any participant action.

When credit flows to a participant with existing debt, the system creates a warrant—locked backing that shortens debt chains while maintaining the zero-sum property.

If Bob owes Charlie 200 units and Alice sends Bob 100 units:

• Bob's debt to Charlie reduces to 100 units

• A warrant of 100 units is created (locked, earns 5% interest)

• The debt chain is shortened

Warrants improve network stability by:

• Reducing cascade risk (shorter chains)

• Distributing backing across multiple parties

• Providing interest income on locked capital

• Enabling automatic optimization

Credit capacity between any two nodes is not limited to direct relationships but aggregates across all network paths.

If Alice wants to send to David:

• Path 1: Alice → Bob → David (capacity: 100)

• Path 2: Alice → Charlie → David (capacity: 150)

• Path 3: Alice → Eve → Frank → David (capacity: 50)

Total capacity: 300 units (sum of all paths)

This creates powerful network effects:

• More participants → More paths → More capacity

• Weak ties contribute to aggregate capacity

• Network becomes more liquid as it grows

• Redundancy provides resilience

When transactions form closed loops (A → B → C → A), the system rewards all participants by strengthening their trust relationships.

Loop detection algorithm:

1. After each transaction, scan for closed loops

2. Calculate loop bonus based on size, value, and frequency

3. Strengthen all edges in the loop (increase capacity and credit)

This incentivizes:

• Sustained trust relationships

• Productive circular exchange

• Community cohesion

• Reciprocity

Social interactions are automatically converted to economic capacity through daily point distribution.

Process:

1. System tracks interactions between participants (messages, endorsements, collaborations)

2. Each participant receives daily point allocation (e.g., 50 points)

3. Points distributed proportionally based on interaction frequency

4. Points strengthen trust edges (increase capacity and credit)

This bridges social and economic capital:

• Interaction frequency → Stronger relationships

• No credit applications required

• Organic capacity growth

• Decay for inactive relationships (after 7 days)

Every participant's total debt is publicly visible to the entire network, preventing hidden leverage and enabling democratic accountability.

Aggregate calculation:

User Total Debt = Σ(all outbound edge obligations)

Benefits:

• Prevents over-leveraging (all debt visible)

• Enables independent verification (anyone can audit)

• Provides early warning (rising debt signals risk)

• Eliminates information asymmetry

• Enables collective risk assessment

Privacy is maintained through:

• Pseudonymous identifiers (not real-world identity)

• Aggregate totals public, bilateral details can be private

• Cryptographic proofs (verify without revealing)

System parameters are governed through distributed consensus:

Voting Mechanism:

• One person, one vote (democratic)

• Reputation weighting (proven track records have more influence)

• Transparent processes (all proposals visible)

• Reversible decisions (bad choices can be undone)

Governed Parameters:

• Interest rates (warrant: 5%, direct debt: 8%)

• Capacity limits (max per edge: 2000 units)

• Decay rates (inactive edges: -1 point/day after 7 days)

• System rules and algorithms

This ensures:

• Democratic control (not corporate boards)

• Adaptive system (can evolve with needs)

• Transparent governance (all decisions visible)

• Community ownership (participants control the system)

The steps to run the network are as follows:

1. New transactions are broadcast to all nodes

2. Each node collects new transactions into a block

3. Each node works on finding a proof-of-trust for its block

4. When a node finds a proof-of-trust, it broadcasts the block to all nodes

5. Nodes accept the block only if all transactions in it are valid and not over-leveraged

6. Nodes express their acceptance by working on creating the next block in the chain, using the hash of the accepted block as the previous hash

Nodes always consider the longest chain to be the correct one and will keep working on extending it. If two nodes broadcast different versions of the next block simultaneously, some nodes may receive one or the other first. In that case, they work on the first one they received, but save the other branch in case it becomes longer. The tie will be broken when the next proof-of-trust is found and one branch becomes longer; the nodes that were working on the other branch will then switch to the longer one.

New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach many nodes, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a node does not receive a block, it will request it when it receives the next block and realizes it missed one.

The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by breaking the flow of information in another place: by keeping public keys anonymous.

The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the "tape", is made public, but without telling who the parties were.

As an additional firewall, a new key pair should be used for each transaction to keep them from being linked to a common owner. Some linking is still unavoidable with multi-input transactions, which necessarily reveal that their inputs were owned by the same owner. The risk is that if the owner of a key is revealed, linking could reveal other transactions that belonged to the same owner.

We consider the scenario of an attacker trying to generate an alternate chain faster than the honest chain. Even if this is accomplished, it does not throw the system open to arbitrary changes, such as creating value out of thin air or taking money that never belonged to the attacker. Nodes are not going to accept an invalid transaction as payment, and honest nodes will never accept a block containing them.

An attacker can only try to change one of his own transactions to take back money he recently spent. The race between the honest chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the honest chain being extended by one block, increasing its lead by +1, and the failure event is the attacker's chain being extended by one block, reducing the gap by -1.

The probability of an attacker catching up from a given deficit is analogous to a Gambler's Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to try to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the honest chain, as follows:

Given our assumption that p > q, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn't make a lucky lunge forward early on, his chances become vanishingly small as he falls further behind.

Bitcoin demonstrated that decentralized digital currency is possible. BitCredit extends this concept from currency to credit:

Bitcoin:

• Fixed supply (21 million coins)

• Proof-of-work mining

• Store of value (digital gold)

• Energy intensive

• Not suitable for everyday transactions

BitCredit:

• Elastic supply (constrained by trust)

• Proof-of-trust (reputation-based)

• Medium of exchange (everyday credit)

• Energy efficient

• Designed for transactions

Bitcoin solved the double-spending problem for digital currency. BitCredit solves the over-leveraging problem for digital credit.

The system has several advantages over traditional credit systems:

Universal Access: Anyone can participate, regardless of assets, documentation, or location.

No Collateral Required: Trust replaces physical collateral as the basis for credit.

Inflation-Proof: Zero-sum constraint prevents money creation without backing.

Transparent: All debt obligations visible, enabling collective risk assessment.

Democratic: Governance through consensus, not corporate control.

Efficient: Automatic optimization through circular netting and warrant mechanisms.

Resilient: Distributed structure prevents single points of failure.

Inclusive: Two billion unbanked people can access credit through trust networks.

The system has some limitations that should be acknowledged:

Network Effects Required: The system becomes more valuable with more participants. Early networks may have limited liquidity.

Trust Building Takes Time: New participants must build trust relationships before accessing significant capacity.

Default Risk: While localized, defaults can still occur. Lenders must assess risk carefully.

Regulatory Uncertainty: Decentralized credit systems may face regulatory challenges in some jurisdictions.

Technical Complexity: While the user experience can be simple, the underlying system is complex.

Cultural Adaptation: Some cultures may be more receptive to trust-based credit than others.

These limitations are not fundamental flaws but challenges to be addressed through careful implementation and gradual adoption.

Several areas warrant further research and development:

Scalability: Optimizing the system for millions or billions of participants.

Privacy Enhancements: Implementing zero-knowledge proofs and other cryptographic techniques to enhance privacy while maintaining transparency.

Interoperability: Enabling BitCredit networks to interact with traditional financial systems and other cryptocurrency networks.

Governance Mechanisms: Refining consensus governance to balance efficiency with democratic participation.

Risk Models: Developing sophisticated models for assessing and pricing credit risk in trust networks.

Legal Frameworks: Working with regulators to establish appropriate legal frameworks for decentralized credit.

User Experience: Simplifying the interface to make the system accessible to non-technical users.

We have proposed a system for electronic credit without relying on trust in financial institutions. We started with the usual framework of credit units made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent over-leveraging. To solve this, we proposed a peer-to-peer network using proof-of-trust to record a public history of transactions that quickly becomes computationally impractical for an attacker to change if honest nodes control a majority of trust relationships.

The network is robust in its unstructured simplicity. Nodes work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Nodes can leave and rejoin the network at will, accepting the proof-of-trust chain as proof of what happened while they were gone.

They vote with their trust relationships, expressing their acceptance of valid transactions by working to extend them and rejecting invalid transactions by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.

The result is a credit system that is:

• Accessible to everyone

• Based on trust, not assets

• Inflation-proof by design

• Transparent and auditable

• Democratically governed

• Efficient and self-optimizing

• Resilient and antifragile

This is not just an improvement on traditional finance. This is a new foundation for economic organization—one that enables universal participation, rewards cooperation, and aligns individual incentives with collective welfare.

The technology exists. The mathematics is sound. The need is urgent.

What remains is adoption—the gradual recognition that credit based on trust is not just possible, but superior to credit based on collateral. That decentralized systems are not just viable, but more robust than centralized ones. That the future of finance is not institutional gatekeeping, but peer-to-peer cooperation.

BitCredit is not the end of this journey. It is the beginning.

[1] Satoshi Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System" (2008)

[2] W. Dai, "b-money" (1998)

[3] H. Massias, X.S. Avila, and J.-J. Quisquater, "Design of a secure timestamping service with minimal trust requirements" (1999)

[4] S. Haber, W.S. Stornetta, "How to time-stamp a digital document" (1991)

[5] D. Bayer, S. Haber, W.S. Stornetta, "Improving the efficiency and reliability of digital time-stamping" (1992)

[6] R.C. Merkle, "Protocols for public key cryptosystems" (1980)

[7] M. Granovetter, "The Strength of Weak Ties" (1973)

[8] R. Putnam, "Bowling Alone: The Collapse and Revival of American Community" (2000)

[9] E. Ostrom, "Governing the Commons: The Evolution of Institutions for Collective Action" (1990)

[10] F.A. Hayek, "The Use of Knowledge in Society" (1945)

Version: 1.0
Date: November 25, 2025
License: Open Source (MIT)