Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.

Abstract: A method and apparatus for the distributed, privacy preserving and integrity preserving technical implementation of an order book where a group of computing devices belonging to agents (traders, brokers, or groups thereof) wishing to engage in distributed double auctions and markets can (1) keep private the information about the solvency of the individual agent owing the trader's computer; (2) publicly register the values of buy and sell orders while (a) maintaining confidential the information about the owner of the buy (resp. sell) order and (b) still having the possibility to accrue matched buy/sell transactions to the accounts of the computing devices of the individual agents owing those orders; (3) maintain the financial integrity of the market as implemented by a distributed systems of computing devices; and (4) keep private the possible exit from the market by computing devices operated by agents who could no longer meet their contractual obligations.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.

Abstract: A method and apparatus for the distributed, privacy preserving and integrity preserving technical implementation of an order book where a group of computing devices belonging to agents (traders, brokers, or groups thereof) wishing to engage in distributed double auctions and markets can (1) keep private the information about the solvency of the individual agent owing the trader's computer; (2) publicly register the values of buy and sell orders while (a) maintaining confidential the information about the owner of the buy (resp. sell) order and (b) still having the possibility to accrue matched buy/sell transactions to the accounts of the computing devices of the individual agents owing those orders; (3) maintain the financial integrity of the market as implemented by a distributed systems of computing devices; and (4) keep private the possible exit from the market by computing devices operated by agents who could no longer meet their contractual obligations.

Abstract: A system includes circuitry for wrapping up blockchains into blockchain loops. A blockchain may include a series of blocks extending from an initial block to a terminal block. The circuitry may wrap-up the blockchain by storing an integrity output coding-consistent with the terminal block within the initial block. In some cases, when the terminal block and initial block include end blocks for the blockchain, wrapping-up the series may form a closed-loop.

Abstract: A system includes circuitry for rewriting blockchains in a validity-preserving operation. In some cases, using a key secret held by a trusted party. In some cases, the blockchains may include a series of blocks secured integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret. In some cases, the key may allow valid but tamper-evident rewrites of the blockchain by trusted entities. In some cases, integrity outputs may be generated from the integrity codes based on the content of the previous blocks in the series such that attempts by untrusted parties to replace a block may be detected through coding-inconsistencies with other blocks.

Abstract: A system includes circuitry for performing hybrid blockchain rewrites by trusted parties. The hybrid blockchain may include blocks with multiple parts. In some cases, the blocks may include a core part and a tertiary part. The system may include conditions for validity preserving and/or non-tamper-evident rewrites to the parts of the block. The conditions to support rewrites to the core part may be more stringent than the corresponding conditions to support rewrites to the tertiary part. In some cases, the core part may be write-locked.

Abstract: A system includes circuitry for performing hybrid blockchain rewrites by trusted parties. The hybrid blockchain may include blocks with multiple parts. In some cases, the blocks may include a core part and a tertiary part. The system may include conditions for validity preserving and/or non-tamper-evident rewrites to the parts of the block. The conditions to support rewrites to the core part may be more stringent than the corresponding conditions to support rewrites to the tertiary part. In some cases, the core part may be write-locked.

Abstract: A system includes circuitry for rewriting blockchains in a validity-preserving operation. In some cases, using a key secret held by a trusted party. In some cases, the blockchains may include a series of blocks secured integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret. In some cases, the key may allow valid but tamper-evident rewrites of the blockchain by trusted entities. In some cases, integrity outputs may be generated from the integrity codes based on the content of the previous blocks in the series such that attempts by untrusted parties to replace a block may be detected through coding-inconsistencies with other blocks.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.

Abstract: A system includes circuitry for rewriting blockchains in a validity-preserving operation. In some cases, using a key secret held by a trusted party. In some cases, the blockchains may include a series of blocks secured integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret. In some cases, the key may allow valid but tamper-evident rewrites of the blockchain by trusted entities. In some cases, integrity outputs may be generated from the integrity codes based on the content of the previous blocks in the series such that attempts by untrusted parties to replace a block may be detected through coding-inconsistencies with other blocks.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held by a trusted party. The blockchains may include a series of blocks secured integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret. In some cases, the key may allow valid but tamper-evident rewrites of the blockchain by trusted entities. Integrity outputs may be generated from the integrity codes based on the content of the previous blocks in the series such that attempts by untrusted parties to replace a block may be detected through coding-inconsistencies with other blocks.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held by a trusted party. The blockchains may include a series of blocks secured by a chameleon hash that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret. Rewrite circuitry of the system may determine randomness data from the chameleon hash and altered data from a rewrite. The randomness data may be written to the randomness field of a block overwritten with the altered data such that the block remains coding-consistent with the chameleon hash and other blocks in the blockchain.

Abstract: A system includes circuitry for performing hybrid blockchain rewrites by trusted parties. The hybrid blockchain may include blocks with multiple parts. In some cases, the blocks may include a core part and a tertiary part. The system may include conditions for validity preserving and/or non-tamper-evident rewrites to the parts of the block. The conditions to support rewrites to the core part may be more stringent than the corresponding conditions to support rewrites to the tertiary part. In some cases, the core part may be write-locked.

Abstract: A system includes circuitry for wrapping up blockchains into blockchain loops. A blockchain may include a series of blocks extending from an initial block to a terminal block. The circuitry may wrap-up the blockchain by storing an integrity output coding-consistent with the terminal block within the initial block. In some cases, when the terminal block and initial block include end blocks for the blockchain, wrapping-up the series may form a closed-loop.

Abstract: A system includes circuitry for performing hybrid blockchain rewrites by trusted parties. The hybrid blockchain may include blocks with multiple parts. In some cases, the blocks may include a core part and a tertiary part. The system may include conditions for validity preserving and/or non-tamper-evident rewrites to the parts of the block. The conditions to support rewrites to the core part may be more stringent than the corresponding conditions to support rewrites to the tertiary part. In some cases, the core part may be write-locked.

Abstract: A system includes circuitry for rewriting blockchains in a non-tamper-evident or tamper-evident operation using a key secret held in portions by multiple individually untrusted parties. The blockchains may include a series of blocks secured by integrity codes that may prevent non-tamper-evident rewrites by non-trusted parties that are not in possession of the key secret or individually-untrusted parties in possession of only a portion of the key secret. In some cases, multiple individually-untrusted parties may combine their portions into the key secret. As a group, the multiple individually-untrusted parties may perform non-tamper-evident operation with respect to at least one integrity code within the blockchain.