Blinding Factor

A blinding factor is a cryptographically secure random number used to blind or mask a piece of data before it is processed. This prevents an observer from learning the original value, even if they see the blinded output. It is a foundational component for privacy-enhancing technologies on blockchain.

• Purpose: To break the direct link between input and output data.
• Generation: Created using a cryptographically secure pseudo-random number generator (CSPRNG).
• Example: In a confidential transaction, the blinding factor hides the amount being transferred.

In privacy-focused cryptocurrencies like Monero and Mimblewimble-based chains, blinding factors are essential for hiding transaction amounts. The sender commits to an amount using a Pedersen Commitment, which combines the amount with a secret blinding factor. This creates a cryptographic commitment that can be verified for correctness (e.g., no new coins are created) without revealing the actual amount or the blinding factor to the network.

Blinding factors are critical in zero-knowledge proof (ZKP) systems like zk-SNARKs and zk-STARKs. They are used to randomize proof generation, ensuring that each proof is unique and does not leak information about the private inputs (witnesses) used to create it. This prevents linkage between different transactions or proofs, enhancing user anonymity and privacy.

The blinding factor r is typically used in commitment schemes. A common form is the Pedersen Commitment: C = r*G + v*H, where:

• C is the resulting commitment.
• G and H are independent generator points on an elliptic curve.
• v is the value (e.g., transaction amount) to be hidden.
• r is the secret blinding factor. Knowledge of r is required to open or prove knowledge of the committed value v.

The security of the entire privacy mechanism depends on the secrecy and randomness of the blinding factor. If the blinding factor is leaked, guessed, or reused improperly, it can compromise transaction privacy.

• Must be unique: Reusing a blinding factor can link transactions.
• Must be secret: Known only to the prover/creator of the commitment.
• Must be destroyed: After use, it should be securely erased to prevent future compromise.

Blinding factors interact with several other cryptographic primitives:

• Commitment Scheme: The broader cryptographic construct that uses a blinding factor.
• Range Proof: A proof that a committed value lies within a certain range (e.g., is non-negative), which also relies on blinding factors.
• One-Time Pad: Analogous in its use of randomness for perfect secrecy, though applied in a different cryptographic context.
• Private Key: Similar in its requirement for absolute secrecy, but used for digital signatures rather than data blinding.

A blinding factor is a cryptographically secure random number applied to data before it is signed in a commitment scheme. This process, called blinding, allows a prover to demonstrate knowledge of or commitment to a value (e.g., a transaction amount) without revealing the value itself. The signature remains valid for the unblinded data, enabling later verification.

In privacy-focused blockchains like Monero or Zcash, blinding factors are essential for breaking the link between transaction inputs and outputs. By using unique blinding factors for each output, observers cannot determine which spent input corresponds to which newly created output, providing transaction graph anonymity. This prevents chain analysis from tracing the flow of funds.

Blinding factors are often used with Pedersen Commitments, a homomorphic encryption scheme. Here, a commitment C = v*G + b*H is created, where v is the confidential value, b is the blinding factor, and G and H are generator points. The blinding factor b ensures the commitment is hiding (doesn't reveal v) and binding (cannot be changed later), proving funds are not created from thin air.

The security of a blinding factor depends entirely on it being unpredictable and used only once. Reusing a blinding factor or using a weak random number generator can lead to catastrophic privacy failures:

• Reuse can allow attackers to link transactions.
• Predictability can enable the secret value to be solved for, breaking the commitment. Secure systems use cryptographically secure pseudo-random number generators (CSPRNGs).

In Confidential Transactions (CT), blinding factors enable the encryption of transaction amounts. The protocol uses additive homomorphism, where the sum of input commitments minus output commitments equals a commitment to zero (the transaction fee). The blinding factors cancel out in this equation, allowing the network to verify that no new money was created without knowing any actual amounts.

While blinding factors provide privacy, they can be selectively disclosed for audit purposes. Protocols may allow a user to reveal their blinding factor to a trusted third party (e.g., an auditor or regulator) alongside the transaction data. This selective disclosure proves the transaction's validity and compliance with rules without exposing the information to the public network, balancing privacy with accountability.

A cryptographic protocol where a party commits to a chosen value while keeping it hidden, with the ability to later reveal it. The blinding factor is a key input used to create the initial, opaque commitment. This ensures the original data cannot be deduced until the factor is provided, enabling properties like binding (cannot change the value) and hiding (value is concealed).

An additive homomorphic commitment scheme commonly used in confidential transactions. It uses a blinding factor (a secret random number) and cryptographic generators to create a commitment to a value. Key properties include:

• Information-theoretic hiding: The commitment reveals nothing about the value.
• Computational binding: It's infeasible to find two different values that open the same commitment.
• Additivity: Commitments to values can be added to create a commitment to their sum.

A method by which one party (the prover) can prove to another (the verifier) that a statement is true, without revealing any information beyond the validity of the statement. Blinding factors are often used within ZKP constructions to mask the prover's secret inputs, ensuring the proof is zero-knowledge. This is fundamental to privacy-preserving protocols like zk-SNARKs and zk-STARKs.

A type of blockchain transaction that hides the amount being transferred while still allowing the network to verify its validity. This is achieved using Pedersen Commitments, where the transaction amount is combined with a blinding factor. The network validates the transaction by checking that the sum of input commitments equals the sum of output commitments, proving no money was created without revealing the actual amounts.

An ideal theoretical model of a cryptographic hash function that responds to every unique query with a truly random response, consistent for identical queries. In practice, blinding factors are often generated using cryptographically secure random number generators and processed through hash functions modeled as random oracles. This ensures the blinding is unpredictable and does not leak information about the underlying secret data.

A form of encryption that allows computations to be performed on ciphertexts, generating an encrypted result which, when decrypted, matches the result of operations performed on the plaintexts. While distinct from a simple blinding factor, the concept is related through homomorphic commitments (like Pedersen). The blinding factor enables additive homomorphism, allowing commitments to be combined while preserving the hidden value's mathematical relationships.