![nition
Given two dierent f-sequences, we say that they are f-equivalent if one is a
rotation, reverse or both of the other one.
For example:
I Rotation
[1; 2; 1; 3; 1; 2; 1; 3] =f [2; 1; 3; 1; 2; 1; 3; 1]
I Reverse
[1; 2; 1; 3; 1; 2; 1; 3] =f [3; 1; 2; 1; 3; 1; 2; 1]
I Rotation and reverse composition
[1; 2; 1; 3; 1; 2; 1; 3] =f [1; 3; 1; 2; 1; 3; 1; 2]](https://image.slidesharecdn.com/apbozkpbi-141112232017-conversion-gate02/85/Authentication-protocols-based-on-zero-knowledge-proof-Part-2-Brief-talk-29-320.jpg)
Uploaded byIsrael Buitron
Authentication protocols based on zero knowledge proof (Part 2 - Brief talk)
The document discusses authentication protocols based on zero-knowledge proofs, outlining the concepts of interactive proofs and their properties, including completeness and soundness. It proposes a specific authentication protocol that utilizes zero-knowledge proofs and constructs a path graph based on Hamiltonian cycles, while examining related computational challenges like the odd-hole problem. The document also details completed and current tasks in developing this proposed solution within the context of graph theory.
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Authentication protocols based on zero knowledge proof (Part 2 - Brief talk)
- 1. Authentication protocols basedon zero knowledge proof Brief introduction (Part 2) Israel Buitron Damaso1 Guillermo B. Morales Luna1 (Advisor) Feliu Salgols Troncoso2 (Advisor) 1Computer Science Department 2Mathematics Department Center for Research and Advanced Studies of the National Polytechnic Institute November 12, 2014
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- 4. Authentication Idea IAuthentication is the process of verifying an entity's identity, given its credentials. I The entity could be in the form of a person, a computer, a device, a group of network computers, etc.
- 5. Interactive proof Idea I An interactive proof is a protocol between two parties (the prover and the veri
- 6. er). I Thecrucial point is that the veri
- 7. er is restrictedto be a probabilistic polynomial-time algorithm, whereas no such restriction applies to the prover.
- 8. Interactive proof Objetive I By means of an interactive proof, the prover convinces the veri
- 9. er of the validity of a given statement. I A statement is of the form x 2 L, where x is a word and L is a formal language. I The interesting languages are those for which no polynomial-time membership tests (are known to) exist. I It follows that the veri
- 10. er cannot determineon its own whether x 2 L holds.
- 11. Interactive proof Properties Interactive proofs have two basic properties: I Completeness, which means that executions of the protocol between the prover and the veri
- 12. er should resultin the veri
- 13. er accepting theproof, if x 2 L holds. I Soundness, which means that executions of the protocol between the prover and the veri
- 14. er should resultin the veri
- 15. er rejecting theproof, if x62 L holds. This property protects the interest of the veri
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- 17. Zero knowledge proof Idea I Zero-knowledge is a property attributed to interactive proofs. I This property protects the interest of the prover. I By means of a zero-knowledge proof, the prover is able to convince the veri
- 18. er of thevalidity of a given statement, without releasing any knowledge beyond the validity of the statement.
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- 20. Outline Our work Proposed solution Authentication protocol Completed tasks Current tasks
- 21. Proposed solution IGive an authentication protocol, based on: I a zero-knowledge proof I the NP-hardness of the Independence Set Problem in Graph Theory I synthetic problem instances
- 22. Authentication protocol Publicand private keys I Let P be a set of participants. I Each participant p 2 P constructs randomly a Hamiltonian cycle hp and selects as private key a set p of kp non-crossing and disjoint mp-paths. I Then, the participant selects as public key the tuple (kp;mp;Kp), where Kp is the set of pairs of endpoints of the paths in p.
- 23. Authentication protocol Procedure 1. The veri
- 24. er selects asubset Lv Kp and sends it to the prover as a challenge. 2. The prover replies with the list RLp of mp-paths connecting each pair at Lv. 3. The veri
- 25. er accepts accordinglyto whether RLp is a collection of pairwise non-crossing and disjoint mp-paths in the graph.
- 26. Outline Our work Proposed solution Completed tasks f-sequences search Path graphs construction Odd-holes search Encoding problem instances Current tasks
- 27. f-sequences Idea Thef-sequences describe Hamiltonian cycles at the hypercube.
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- 29. nition Given twodierent f-sequences, we say that they are f-equivalent if one is a rotation, reverse or both of the other one. For example: I Rotation [1; 2; 1; 3; 1; 2; 1; 3] =f [2; 1; 3; 1; 2; 1; 3; 1] I Reverse [1; 2; 1; 3; 1; 2; 1; 3] =f [3; 1; 2; 1; 3; 1; 2; 1] I Rotation and reverse composition [1; 2; 1; 3; 1; 2; 1; 3] =f [1; 3; 1; 2; 1; 3; 1; 2]
- 30. f-sequences Search problem I All f-sequences in a hypercube can be found using a breadth-