Patent ID: 11909873
Assignee: MITSUBISHI ELECTRIC CORPORATION
Field: Digital communication (Electrical engineering)
Classification: CPC H  G | IPC G  H

Claim 4:
5. The decryption device according to claim 4,
wherein the processing circuitry acquires a ciphertext CT indicated in Formula 1,
acquires a decryption key SK(f) indicated in Formula 2,
computes the operation values Λ′j and Λj by performing a pairing operation as indicated in Formula 3,
computes a value Λ as indicated in Formula 4, and computes an output value depending on a value of the value Λ, CT
        =
        
         (
         
          
           x
           →
          
          ,
          
           
            {
            
             c
             
              ′
              ⁡
              (
              
               ι
               ′
              
              )
             
            
            }
           
           
            
             ι
             ′
            
            ∈
            
             [
             
              n
              ′
             
             ]
            
           
          
          ,
           
          
           
            {
            
             c
             
              (
              ι
              )
             
            
            }
           
           
            ι
            ∈
            
             [
             n
             ]
            
           
          
         
         )
        
       
      
     
     
      
       
        
         ω
         
          ⟵
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          𝔽
          q
         
        
        ,
       
      
     
     
      
       
        
         for
         ⁢
            
         
          ι
          ′
         
        
        ∈
        
         [
         
          n
          '
         
         ]
        
       
      
     
     
      
       
        
         
          ϕ
          
           ι
           ′
          
          ′
         
         
          ⟵
          U
         
         
          𝔽
          q
         
        
        ,
        
         
          c
          
           ′
           ⁡
           (
           
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         =
         
          
           (
           
            
             ω
             ⁡
             (
             
              1
              ,
              
               x
               
                ι
                ′
               
              
             
             )
            
            ,
            
             
              0
              →
             
             4
            
            ,
             
            
             
              0
              →
             
             2
            
            ,
             
            
             ϕ
             
              ι
              ′
             
             ′
            
           
           )
          
          
           𝔹
           
            ι
            ′
           
          
         
        
        ,
       
      
     
     
      
       
        
         for
         ⁢
            
         ι
        
        ∈
        
         [
         n
         ]
        
       
      
     
     
      
       
        
         
          ϕ
          ι
         
         
          ⟵
          U
         
         
          𝔽
          q
         
        
        ,
        
         
          c
          
           (
           ι
           )
          
         
         =
         
          
           (
           
            
             ω
             ⁡
             (
             
              1
              ,
              
               z
               ι
              
             
             )
            
            ,
            
             
              0
              →
             
             4
            
            ,
            
             
              0
              →
             
             2
            
            ,
            
             ϕ
             ι
            
           
           )
          
          
           
            𝔹
            
             
              n
              ′
             
             +
             ι
            
           
           ,
          
         
        
       
      
     
    
   
   
    
     [
     
      Formula
      ⁢
         
      1
     
     ]
    
   
  
 

where
n′,n∈,
({right arrow over (x)},{right arrow over (z)})∈qn′×qn are attribute vectors,, SK
          ⁢
          
           (
           f
           )
          
         
         =
         
          (
          
           f
           ,
           
            
             {
             
              k
              
               ′
               ⁡
               (
               
                j
                ′
               
               )
              
             
             }
            
            
             
              j
              ′
             
             ∈
             
              [
              m
              ]
             
            
           
           ,
           
            
             {
             
              k
              
               (
               j
               )
              
             
             }
            
            
             j
             ∈
             
              [
              n
              ]
             
            
           
          
          )
         
        
        ,
       
      
     
     
      
       
        
         
          (
          
           
            (
            
             
              
               {
               
                σ
                j
               
               }
              
              
               j
               ∈
               
                [
                n
                ]
               
              
             
             ,
             
              
               {
               
                
                 α
                 
                  j
                  ′
                 
                
                ,
                
                 γ
                 
                  j
                  ′
                 
                
               
               }
              
              
               
                j
                ′
               
               ∈
               
                [
                m
                ]
               
              
             
            
            )
           
           ,
           
            
             ρ
             ⁢
             
              :
              [
              m
              ]
             
            
            →
            
             [
             
              n
              ′
             
             ]
            
           
          
          )
         
         
          ⟵
          R
         
         
          PGB
          ⁡
          (
          f
          )
         
        
        ,
       
      
     
     
      
       
        
         ς
         
          ⟵
          U
         
         
          𝔽
          q
         
        
        ,
       
      
     
     
      
       
        
         for
         ⁢
            
         
          j
          ′
         
        
        ∈
        
         [
         m
         ]
        
       
      
     
     
      
       
        
         
          
           κ
           →
          
          
           ′
           ⁡
           (
           
            j
            ′
           
           )
          
         
         
          ⟵
          U
         
         
          𝔽
          q
          2
         
        
        ,
        
         
          
           k
           ′
          
          (
          
           j
           ′
          
          )
         
         =
         
          
           (
           
            
             (
             
              
               γ
               
                j
                ′
               
              
              ,
              
               α
               
                j
                ′
               
              
             
             )
            
            ,
            
             
              0
              →
             
             4
            
            ,
            
             
              
               κ
               →
              
              ′
             
             
              (
              
               j
               ′
              
              )
             
            
            ,
            0
           
           )
          
          
           𝔹
           
            ρ
            ⁡
            (
            
             j
             ′
            
            )
           
           *
          
         
        
        ,
       
      
     
     
      
       
        
         for
         ⁢
            
         j
        
        ∈
        
         [
         n
         ]
        
       
      
     
     
      
       
        
         
          
           κ
           →
          
          
           (
           j
           )
          
         
         
          ⟵
          U
         
         
          𝔽
          q
          2
         
        
        ,
        
         
          k
          ⁡
          (
          j
          )
         
         =
         
          
           (
           
            
             (
             
              
               σ
               j
              
              ,
              ς
             
             )
            
            ,
            
             
              0
              →
             
             4
            
            ,
            
             
              κ
              →
             
             
              (
              j
              )
             
            
            ,
            0
           
           )
          
          
           𝔹
           
            
             n
             ′
            
            +
            1
           
           *
          
         
        
       
      
     
    
   
   
    
     [
     
      Formula
      ⁢
         
      2
     
     ]
    
   
  
 

where
PGB(f) is an algorithm that takes as input a function f, and outputs a set of constants ({σj}j∈[n], {αj′,γj′}j′∈[m])∈Fqn×(Fq2)m, which are elements of a predicate vector, along with a function ρ: [m]→[n′],

Λ′j′=e(c′(ρ(j′)),k′(j′)) for j′∈[m], 

Λj=e(c(j),k(j)) for j∈[n]  [Formula 3], Λ
         =
         
          
           (
           
            
             ∏
             
              
               j
               ′
              
              ∈
              
               [
               m
               ]
              
             
            
            
             Λ
             
              j
              ′
             
             
              ′Ω
              
               j
               ′
              
              ′
             
            
           
           )
          
          ⁢
          
           (
           
            
             ∏
             
              j
              ∈
              
               [
               n
               ]
              
             
            
            
             Λ
             j
             
              Ω
              j
             
            
           
           )
          
         
        
        ,
       
      
     
     
      
       
        
         
          (
          
           
            
             {
             
              Ω
              j
             
             }
            
            
             j
             ∈
             
              [
              n
              ]
             
            
           
           ,
           
            
             {
             
              
               Ω
               ′
              
              
               j
               ′
              
             
             }
            
            
             
              j
              ′
             
             ∈
             
              [
              m
              ]
             
            
           
          
          )
         
         =
         
          R
          ⁢
          E
          ⁢
          
           C
           ⁡
           (
           
            f
            ,
            
             x
             →
            
           
           )
          
         
        
        ,
       
      
     
    
   
   
    
     [
     
      Formula
      ⁢
         
      4
     
     ]
    
   
  
 

where
REC(f,{right arrow over (x)}) is an algorithm that takes as input a function f and x→∈Fqn′, and
outputs a set of coefficients ({Ωj}j∈[n], {Ω′j′}j′∈[m])∈Fqn+m.