handouts/ho06.tex
changeset 366 34a8f73b2c94
parent 357 5b91f5ad2772
child 370 ddac52c0014c
equal deleted inserted replaced
365:942205605c30 366:34a8f73b2c94
     1 \documentclass{article}
     1 \documentclass{article}
     2 \usepackage{../style}
     2 \usepackage{../style}
     3 
     3 
     4 \begin{document}
     4 \begin{document}
       
     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
       
   386 at zero-knowledge proofs that use numbers as secrets. For this
       
   387 the underlying NP-problem is to calculate discrete logarithms.
       
   388 It can be used by choosing public numbers $A$, $B$, $p$, and
       
   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
       
   413 
       
   414 socialist millionares problem
       
   415 http://en.wikipedia.org/wiki/Socialist_millionaire
       
   416 http://twistedoakstudios.com/blog/Post3724_explain-it-like-im-five-the-socialist-millionaire-problem-and-secure-multi-party-computation
       
   417 
   408 
   418 
   409 %%% Local Variables: 
   419 %%% Local Variables: 
   410 %%% mode: latex
   420 %%% mode: latex
   411 %%% TeX-master: t
   421 %%% TeX-master: t
   412 %%% End: 
   422 %%% End: