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1 \documentclass{article} |
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3 |
4 \begin{document} |
4 \begin{document} |
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5 \fnote{\copyright{} Christian Urban, 2014} |
5 |
6 |
6 \section*{Handout 6 (Zero-Knowledge Proofs)} |
7 \section*{Handout 6 (Zero-Knowledge Proofs)} |
7 |
8 |
8 Zero-knowledge proofs (short ZKP) solve a paradoxical puzzle: |
9 Zero-knowledge proofs (short ZKP) solve a paradoxical puzzle: |
9 How to convince somebody else that one knows a secret, without |
10 How to convince somebody else that one knows a secret, without |
377 any NP problem can be used as part of a ZKP protocol. |
378 any NP problem can be used as part of a ZKP protocol. |
378 |
379 |
379 |
380 |
380 \subsubsection*{Using Modular Arithmetic for ZKP Protocols} |
381 \subsubsection*{Using Modular Arithmetic for ZKP Protocols} |
381 |
382 |
382 Another NP-problem is to calculate discrete logarithms. It can |
383 While information can be encoded into graph isomorphisms, it |
383 be used by choosing public numbers $A$, $B$, $p$, and private |
384 is not the most convenient carrier of information. Clearly it |
384 $x$ such that |
385 is much easier to encode information into numbers. Let us look |
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386 at zero-knowledge proofs that use numbers as secrets. For this |
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387 the underlying NP-problem is to calculate discrete logarithms. |
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388 It can be used by choosing public numbers $A$, $B$, $p$, and |
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389 private $x$ such that |
385 |
390 |
386 \begin{center} |
391 \begin{center} |
387 $A^x \equiv B\; mod\; p$ |
392 $A^x \equiv B\; mod\; p$ |
388 \end{center} |
393 \end{center} |
389 |
394 |
403 \end{document} |
408 \end{document} |
404 |
409 |
405 http://btravers.weebly.com/uploads/6/7/2/9/6729909/zero_knowledge_technique.pdf |
410 http://btravers.weebly.com/uploads/6/7/2/9/6729909/zero_knowledge_technique.pdf |
406 http://zk-ssh.cms.ac/docs/Zero_Knowledge_Prinzipien.pdf |
411 http://zk-ssh.cms.ac/docs/Zero_Knowledge_Prinzipien.pdf |
407 http://www.wisdom.weizmann.ac.il/~oded/PS/zk-tut02v4.ps |
412 http://www.wisdom.weizmann.ac.il/~oded/PS/zk-tut02v4.ps |
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413 |
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414 socialist millionares problem |
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415 http://en.wikipedia.org/wiki/Socialist_millionaire |
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416 http://twistedoakstudios.com/blog/Post3724_explain-it-like-im-five-the-socialist-millionaire-problem-and-secure-multi-party-computation |
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417 |
408 |
418 |
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