( 26th August 2019 )
Here is a list of known proof-of-work functions:
1. Integer square root modulo a large prime
2. Weaken Fiat Shamir signatures
3. Ong Schnorr Shamir signature broken by Pollard
Partial hash inversion this paper formalizes the idea of a proof of work (POW) and introduces "the dependent idea of a bread pudding protocol", a "re-usable Proof of Work" (RPOW) system as Hashcash
Hash sequences
i. Puzzles
ii. Diffie Hellman-based puzzle
iii. Moderate
iv. Mbound
v. Hokkaido
vi. Cuckoo Cycle
vii. Merkle tree based
viii. Guided tour puzzle protocol
Reusable proof-of-work as e-money
Computer scientist Hal Finney built on the proof-of-work idea, yielding a system that exploited reusable proof of work ("RPOW"). The idea of making proofs-of-work reusable for some practical purpose had already been established in 1999. Finney's purpose for RPoW was as token money. Just as a gold coin's value is thought to be underpinned by the value of the raw gold needed to make it, the value of an RPoW token is guaranteed by the value of the real-world resources required to 'mint' a PoW token. In Finney's version of RPoW, the PoW token is a piece of Hashcash.
A website can demand a PoW token in exchange for service. Requiring a PoW token from users would inhibit frivolous or excessive use of the service, sparing the service's underlying resources, such as bandwidth to the Internet, computation, disk space, electricity and administrative overhead.
Finney's RPoW system differed from a PoW system in permitting the random exchange of tokens without repeating the work required to generate them. After someone had "spent" a PoW token at a website, the website's operator could exchange that "spent" PoW token for a new, unspent RPoW token, which could then be spent at some third-party website similarly equipped to accept RPoW tokens. This would save the resources otherwise needed to 'mint' a PoW token. The anti-counterfeit property of the RPoW token was guaranteed by remote attestation. The RPoW server that exchanges a used PoW or RPoW token for a new one of equal value uses remote attestation to allow any interested party to verify what software is running on the RPoW server. Since the source code for Finney's RPoW software was published (under a BSD-like license), any sufficiently knowledgeable programmer could, by inspecting the code, verify that the software (and, by extension, the RPoW server) never issued a new token except in exchange for a spent token of equal value.
Until 2009, Finney's system was the only RPoW system to have been implemented; it never saw economically significant use. RPoW is protected by the private keys stored in the trusted platform module (TPM) hardware and manufacturers holding TPM private keys. Stealing a TPM manufacturer's key or obtaining the key by examining the TPM chip itself would subvert that assurance.
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