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Knowledge proof
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A signature verification, challenger technology, applied in the field of knowledge proof
Pending Publication Date: 2021-12-31
NCHAIN HLDG LTD
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[0010] The problem with traditional hashing puzzles alone is that unscrupulous miners or other nodes can 2 d is observed in the unlocking script, and then the Tx 2 Create and mine (or publish) your own version, in pays itself in the output of Tx instead of paying 2 The intended recipient (eg, Bob) in
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Embodiment 1
[0504] Example 1: Separate line promises
[0505] This section describes key disclosure when the verifier has a separate commitment to each wire in the circuit (i.e. follows the Σ protocol for arithmetic circuit satisfiability, see above).
[0506] 1. Each line i (i=1,...,n) in the circuit has a Pedersen commitment:
[0507] W i =Com(w i ,ρ i )
[0508] in:
[0509] Com(w,r)=w×G+ρ×F
[0510] 2. For the circuit line l that needs the corresponding public key proof (key statement proof), the prover also sends the key public:
[0511] the ko l = ρ l ×F
[0512] 3. If circuit line j needs to be revealed publicly (a fully disclosed line), the prover sends a "fully disclosed" tuple:
[0513] (w j ,ρ j )
[0514] 4. Then, use the above Sigma protocol to prove with zero knowledge that each gate of the circuit satisfies the requirement 4 .
[0515] where, using the above Sigma protocol, it is proved with zero knowledge that each gate of the...
Embodiment 2
[0520] Example 2: Batching vector promises
[0521] In the case of compressed proof systems of circuit satisfiability involving batched vector commitments [Bootle 2016, Groth 2009], the method described below can be used to extract key statement proofs from batched circuit commitments. The full proof protocol will not be described, but only the generation of batch-line commitments and the proof that a specified public key is contained.
[0522] Batch commitments are generated as described below, where line 1 will be provided with a key public. In a vector commit, m lines are batched together.
[0523] 1. The prover generates m-1 random numbers
[0524] 2. The prover calculates the elliptic curve point K i = ξ i ×G (for i=1,...,m-1). These values plus K m =G constitutes the proof key PrK sent to the verifier.
[0525] 3. The prover generates a random value:
[0526] 4. The prover calculates the alignment value w i Commitments (for i=1,...,m) of...
no. 1 example ；
[0572] 1B. A second example of verifying an arithmetic circuit based on E1'-E5';
[0573] 2A. Verify π 1 The preimage requires:
[0574] a) extract ko 1 = ρ 1 F;
[0575] b) calculate
[0576] c) check
[0577] d) Check the equation W m =w m ·G+ρ m F;
[0578] 2B. Verify π 2 The preimage requires:
[0579] a) Extract ko' 1 = ρ' 1 F;
[0580] b) calculate
[0581] c) check
[0582] d) Check the equation W' m =w' m ·G+ρ′ m F;
[0583] 3. Verify the equation of the preimage:
[0584] a)w m =w' m
[0585] It should be noted that, as evident from 3a), although in Figure 16 h in and π in proof transaction 1604 1 and π 2 shown separately, but it doesn't actually need to be a separate element, and can be accessed via w m =w' m implicitly defined.
[0586] Keep the input line w 1 、w 1 ’, and these values are not available from the input line w 1 、w 1 ' public key provided on ko 1 、ko'...
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Abstract
A knowledge proof is performed using a set of transactions for recording in a blockchain maintained in a blockchain network. A challengee receives a competition challenge. The competition challenge has a derivable challenge solution but the challenge solution is not communicated to the challengee directly. The challengee competes with one or more other challengees to derive an independent instance of the challenge solution from the competition challenge. Upon the challengee successfully deriving the independent instance of the challenge solution before any of the other one or more challengees, the challengee uses data thereof as a secret challengee key to sign at least one message, and thereby generate at least one transaction signature, and submits the at least one transaction signature and the at least one message to the blockchain network for verifying at a node of the blockchain network.
Description
technical field [0001] The present disclosure relates to a proof of knowledge implemented via a set of transactions recorded in a blockchain. Background technique [0002] Blockchain refers to a form of distributed data structure in which a copy of the blockchain is maintained at each of multiple nodes in a peer-to-peer (P2P) network. A blockchain consists of a series of data blocks, where each block includes one or more transactions. Each transaction can refer back to previous transactions in the sequence. Transactions can be included in new blocks by committing to the network. The process of creating a new block is called "mining," and it involves each of multiple mining nodes competing to perform "proof-of-work," solving a cryptographic puzzle based on the pool of pending transactions waiting to be included in a block. [0003] Transactions in the blockchain are often used to transfer digital assets, that is, data used as a store of value. But it is also possible to u...
Claims
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