Patent ID: 11968304
Assignee: NCHAIN LICENSING AG
Field: Digital communication (Electrical engineering)
Classification: CPC H | IPC H

Claim 6:
7. The method of claim 5, wherein, in order to provide the set of signature components, each participant i of the signing subset π provides an inverse computation component:

Ci=bi,πkici mod n, in which ci is a share of a signing secret and bi,π is an interpolation factor given by:

bi,π=bi,π(0), b
        
         i
         ,
         π
        
       
       (
       x
       )
      
      =
      
       
        ∏
        
         
          j
          ∈
          π
         
         ,
         
          j
          ≠
          i
         
        
       
       
        
         x
         -
         
          x
          j
         
        
        
         
          x
          i
         
         -
         
          x
          j
         
        
       
      
     
     ;
    
   
   
     
   
  
 

wherein the inverse computation components are combined to compute a multiplicative inverse as:, k
     
      -
      1
     
    
    ⁢
    
     c
     
      -
      1
     
    
    ⁢
    mod
    ⁢
    n
   
   =
   
    
     
      (
      
       kc
       ⁢
       mod
       ⁢
       n
      
      )
     
     
      -
      1
     
    
    ⁢
    mod
    ⁢
    n
   
  
  ,
  
  
   
    
     kc
     ⁢
     mod
     ⁢
     n
    
    =
    
     
      (
      
       
        ∑
        
         i
         ∈
         π
        
       
       
        C
        i
       
      
      )
     
     ⁢
     mod
     ⁢
     n
    
   
   ;
  
 

wherein each participant i of the signing subset π uses the multiplicative inverse, k−1c−1 mod n, to provide the signature component for that participant i as:

si=(bi,π)(k−1c−1ci(ms+Vir)mod n,, in which Vi is a private keyshare of that participant i and ms is signed message data of the at least one proof transaction, and r is a common r-part used for each signature component si;
wherein the s-part is computed from a released signature components as:, s
  =
  
   
    (
    
     
      ∑
      
       i
       ∈
       π
      
     
     
      s
      i
     
    
    )
   
   ⁢
   mod
   ⁢
   
    n
    .