Multi-party fair exchange protocol

<h2 id="definition">Definition</h2>
<p><a href="/facts/Matthew_K._Franklin/Vw7jruGp">Matthew K. Franklin</a> and <a href="/facts/Gene_Tsudik/oFpj0mEp">Gene Tsudik</a> suggested in 1998<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> the following classification:
</p>
<ul><li>An 
  
    
      
        n
      
    
    {\displaystyle n}
  
-party single-unit general exchange is a <a href="/facts/Permutation/JSw9ukmv">permutation</a> 
  
    
      
        σ
      
    
    {\displaystyle \sigma }
  
 on 
  
    
      
        {
        1...
        n
        }
      
    
    {\displaystyle \{1...n\}}
  
, where each party 
  
    
      
        
          P
          
            i
          
        
      
    
    {\displaystyle P_{i}}
  
 offers a single unit of commodity 
  
    
      
        
          K
          
            i
          
        
      
    
    {\displaystyle K_{i}}
  
 to 
  
    
      
        
          P
          
            σ
            (
            i
            )
          
        
      
    
    {\displaystyle P_{\sigma (i)}}
  
, and receives a single unit of commodity 
  
    
      
        
          K
          
            
              σ
              
                −
                1
              
            
            (
            i
            )
          
        
      
    
    {\displaystyle K_{\sigma ^{-1}(i)}}
  
 from 
  
    
      
        
          P
          
            
              σ
              
                −
                1
              
            
            (
            i
            )
          
        
      
    
    {\displaystyle P_{\sigma ^{-1}(i)}}
  
.</li>
<li>An 
  
    
      
        n
      
    
    {\displaystyle n}
  
-party multi-unit general exchange is a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> of baskets, where the entry 
  
    
      
        
          B
          
            i
            j
          
        
      
    
    {\displaystyle B_{ij}}
  
 in row 
  
    
      
        i
      
    
    {\displaystyle i}
  
 and column 
  
    
      
        j
      
    
    {\displaystyle j}
  
 is the basket of goods given by 
  
    
      
        
          P
          
            i
          
        
      
    
    {\displaystyle P_{i}}
  
 to 
  
    
      
        
          P
          
            j
          
        
      
    
    {\displaystyle P_{j}}
  
.</li></ul>
<h2 id="see-also">See also</h2>
<p><a href="/facts/Secure_multi-party_computation/7xJbbvIo">Secure multi-party computation</a>
</p>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Mukhamedov, Aybek; Kremer, Steve; Ritter, Eike. "Analysis of a Multi-Party Fair Exchange Protocol and Formal Proof of Correctness in the Strand Space model". Financial Crypto. 2005. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Franklin, Matthew K.; Tsudik, Gene (1998). "Secure group barter: Multi-party fair exchange with semi-trusted neutral parties". Financial Cryptography. Lecture Notes in Computer Science. Vol. 1465. pp. 90–102. doi:10.1007/BFb0055475. ISBN 978-3-540-64951-9. <a href="978-3-540-64951-9" target="_blank">978-3-540-64951-9</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Multi-party fair exchange protocol open-in-new

Multi-party fair exchange protocol