Proof of Knowledge Sample Clauses

Proof of Knowledge. ‌ Proof of knowledge [11] is an interactive cryptographic mechanism providing compu- tational proof of “knowledge”. This mechanism works between two parties, namely the prover, that wants to prove his knowledge of some secret to a second party, and the verifier, that accepts or rejects the veracity of the published statement. This scheme can also work without the necessity to unravel the secret to the verifier, as in the case of so-called zero-knowledge proof. The two-party proof of knowledge, without the knowledge-error, is built upon two properties: • Completeness that states that if the send statement to the verifier is true, the verifier will always accept the proof, and • Validity that requires that the success probability of knowledge must be at least as high as the success probability of the prover in convincing the verifier, as this property guarantees, that some prover without the knowledge can succeed in convincing the verifier. With the knowledge-error is the validity property replaced with the property soundness, that states, that there is only a small probability of accepting a wrong statement by the verifier [4]. To prove various statements, such as those built on the discrete logarithm prob- lem (also in a specific form), can be verified by using so-called sigma protocols (sometimes marked as the Σ-protocols). These protocols use a three-way challenge- response structure with the first step called the commitment. The prover, to verify some knowledge interact with the verifier as follows: 1. The prover generates parameter 𝑟 from Z*𝑞 at random, counts parameter 𝑐 = 𝑔𝑟, where 𝑞 and 𝑔 are a published parameters, and sends the parameter 𝑐 to the verifier. 2. The verifier generates parameter 𝑒 from Z*𝑞 at random and sends it to the 3. After receiving parameter 𝑒, the prover counts and sends to the verifier pa- rameter 𝑧 = 𝑟 + 𝑒𝑤 mod 𝑞, where 𝑤 ∈ Z*�� is the statement to verify. The verifier than accepts if the 𝑔𝑧 ≡ ℎ𝑒𝑐 mod 𝑞, where ℎ = 𝑔𝑤, is true [38]. One of the most used and simplest sigma protocol is the ▇▇▇▇▇▇▇ protocol, which per- mits the proof of knowledge of statements regarding the discrete logarithm problem. ▇▇▇▇▇▇▇ protocol is depicted on Figure 2.1. Fig. 2.1 ▇▇▇▇▇▇▇ protocol scheme with the discrete logarithm based statement ▇. ▇▇▇▇▇▇▇ protocol has a set of properties: • Completeness property, that states, as mentioned above, that if the send statement to the verifier is true, the verifier will always accept the proof,
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Proof of Knowledge. For every polynomial-size prover P∗, there exists a polynomial-size extractor 𝖲P∗ such that for every security parameter n ∈ N, every auxiliary input aux ∈ {0, 1}poly(n), and every time bound B ∈ N,  SNARK Verify( ) = 1 (σ, τ ) ← SNARK.Gen(1n, B)  Pr  (y, w) ∈/ R𝐶 (y, π) ← P∗(aux, σ) w ← 𝖲P∗ (aux, σ)  ≤ negl(n).
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Related to Proof of Knowledge

  • No Knowledge The Company has no knowledge of any event which would be more likely than not to have the effect of causing such Registration Statement to be suspended or otherwise ineffective.

  • Schedules; Knowledge Each party is presumed to have full knowledge of all information set forth in the other party's schedules delivered pursuant to this Agreement.

  • Seller’s Knowledge For purposes of this Agreement, the term “Seller’s knowledge” or words of similar import shall mean and refer solely to the actual knowledge of the following representatives of Seller without duty of investigation or inquiry on the part of any of them: K▇▇ ▇▇▇▇▇▇▇, C▇▇▇▇ ▇▇▇▇▇, C▇▇▇ ▇▇▇▇▇▇▇, T▇▇ ▇▇▇▇ and B▇▇▇▇ ▇▇▇▇▇.

  • Knowledge Whenever a representation or warranty or other statement in this Agreement (including, without limitation, Schedule I hereto) is made with respect to a Person's "knowledge," such statement refers to such Person's employees or agents who were or are responsible for or involved with the indicated matter and have actual knowledge of the matter in question.

  • Knowledge of Trustee Notwithstanding the provision of this Article or any other provisions of this Indenture, the Trustee shall not be charged with knowledge of the existence of any Senior Debt, of any default in payment of principal of, premium, if any, or interest on, rent or other payment obligation in respect of any Senior Debt, or of any facts which would prohibit the making of any payment of moneys to or by the Trustee, or the taking of any other action by the Trustee, unless a Responsible Officer of the Trustee having responsibility for the administration of the trust established by this Indenture shall have received written notice thereof from the Company, any Holder of Securities, any Paying or Conversion Agent of the Company or the holder or representative of any class of Senior Debt, and, prior to the receipt of any such written notice, the Trustee shall be entitled in all respects to assume that no such default or facts exist; provided, however, that unless on the third Business Day prior to the date upon which by the terms hereof any such moneys may become payable for any purpose the Trustee shall have received the notice provided for in this Section 13.7, then, anything herein contained to the contrary notwithstanding, the Trustee shall have full power and authority to receive such moneys and apply the same to the purpose for which they were received, and shall not be affected by any notice to the contrary which may be received by it on or after such date.