Patent ID: 11888968
Assignee: MITSUBISHI ELECTRIC CORPORATION
Field: Digital communication (Electrical engineering)
Classification: CPC G  H | IPC G  H

Claim 4:
5. The signature device according to claim 4,
wherein the signature is sig indicated in Formula 3, sig
       =
       
        (
        
         
          s
          
           *
           
            (
            0
            )
           
          
         
         ,
         …
           
         ,
         
          s
          
           *
           
            (
            
             m
             +
             1
            
            )
           
          
         
        
        )
       
      
      ⁢
      

      	
      where
      ⁢
      

      	
      
       
        
         s
         
          *
          
           (
           0
           )
          
         
        
        =
        
         
          ξ
          ⁢
          
           k
           
            *
            
             (
             0
             )
            
           
          
         
         +
         
          r
          
           *
           
            (
            0
            )
           
          
         
        
       
       ,
       

       
        
         s
         
          *
          
           (
           j
           )
          
         
        
        =
        
         
          
           
            ξΩ
            j
           
           ⁢
           
            k
            
             *
             
              (
              
               ρ
               ⁡
               (
               j
               )
              
              )
             
            
           
          
          +
          
           
            σ
            j
            ′
           
           (
           
            
             b
             
              *
              
               (
               
                1
                ,
                1
               
               )
              
             
            
            +
            
             
              ρ
              ⁡
              (
              j
              )
             
             ⁢
             
              b
              
               *
               
                (
                
                 1
                 ,
                 2
                
                )
               
              
             
            
           
           )
          
          +
          
           
            Ω
            j
            ″
           
           ⁢
           
            b
            
             *
             
              (
              
               1
               ,
               3
              
              )
             
            
           
          
          +
          
           
            Ω
            j
            ′
           
           ⁢
           
            b
            
             *
             
              (
              
               1
               ,
               4
              
              )
             
            
           
          
          +
          
           
            r
            
             *
             
              (
              j
              )
             
            
           
           ⁢
              
           for
           ⁢
              
           j
          
         
         ∈
         
          [
          m
          ]
         
        
       
       ,
       

       	
       
        
         s
         
          *
          
           (
           
            m
            +
            1
           
           )
          
         
        
        =
        
         
          ξ
          ⁡
          (
          
           
            k
            
             *
             
              (
              
               
                n
                +
                1
               
               ,
               1
              
              )
             
            
           
           +
           
            
             H
             ⁡
             (
             
              MSG
              ⁢
              
               
                ❘
                "\[LeftBracketingBar]"
               
               
                ❘
                "\[RightBracketingBar]"
               
              
              ⁢
              𝕊
             
             )
            
            ⁢
            
             k
             
              *
              
               (
               
                
                 n
                 +
                 1
                
                ,
                2
               
               )
              
             
            
           
          
          )
         
         +
         
          r
          
           *
           
            (
            
             m
             +
             1
            
            )
           
          
         
        
       
       ,
       

       	
       ξ
       ,
       
        
         σ
         j
         ′
        
        
         ⟵
         U
        
        
         𝔽
         q
        
       
       ,
       

       	
       
        
         
          r
          
           *
           
            (
            0
            )
           
          
         
         
          ⟵
          U
         
         SPAN
        
        ⁢
        
         〈
         
          b
          
           *
           
            (
            
             0
             ,
             3
            
            )
           
          
         
         〉
        
       
       ,
       
        
         
          r
          
           *
           
            (
            j
            )
           
          
         
         
          ⟵
          U
         
         SPAN
        
        ⁢
        
         〈
         
          
           b
           
            *
            
             (
             
              1
              ,
              11
             
             )
            
           
          
          ,
          
           b
           
            *
            
             (
             
              1
              ,
              12
             
             )
            
           
          
         
         〉
        
       
       ,
       

       	
       
        
         
          r
          
           *
           
            (
            
             m
             +
             1
            
            )
           
          
         
         
          ⟵
          U
         
         SPAN
        
        ⁢
        
         〈
         
          
           b
           
            *
            
             (
             
              2
              ,
              5
             
             )
            
           
          
          ,
          
           b
           
            *
            
             (
             
              2
              ,
              6
             
             )
            
           
          
         
         〉
        
       
       ,
       

       
        k
        
         *
         
          (
          0
          )
         
        
       
       ,
       …
         
       ,
       
        k
        
         *
         
          (
          n
          )
         
        
       
       ,
       
        k
        
         *
         
          (
          
           
            n
            +
            1
           
           ,
           1
          
          )
         
        
       
       ,
       
        
         k
         
          *
          
           (
           
            
             n
             +
             1
            
            ,
            2
           
           )
          
         
        
        ⁢
        are
        ⁢
           
        elements
        ⁢
           
        of
        ⁢
           
        a
        ⁢
           
        signature
        ⁢
           
        key
       
       ,
       

       	
       
        
         k
         
          *
          
           (
           0
           )
          
         
        
        =
        
         
          (
          
           ω
           ,
           0
           ,
           
            ϕ
            0
           
           ,
           0
          
          )
         
         
          𝔹
          0
          *
         
        
       
       ,
       

       	
       
        
         k
         
          *
          
           (
           ι
           )
          
         
        
        =
        
         
          (
          
           
            
             σ
             ι
            
            (
            
             1
             ,
             t
            
            )
           
           ,
           
            ω
            ⁡
            (
            
             1
             ,
             
              x
              ι
             
            
            )
           
           ,
           
            
             0
             →
            
            6
           
           ,
           
            
             ϕ
             →
            
            
             (
             ι
             )
            
           
           ,
           
            
             0
             →
            
            2
           
          
          )
         
         
          𝔹
          1
          *
         
        
       
       ,
       

       	
       
        
         k
         
          *
          
           (
           
            
             n
             +
             1
            
            ,
            1
           
           )
          
         
        
        =
        
         
          
           
            (
            
             
              ω
              ⁡
              (
              
               1
               ,
               0
              
              )
             
             ,
             
              
               0
               →
              
              2
             
             ,
             
              
               ϕ
               →
              
              
               (
               
                
                 n
                 +
                 1
                
                ,
                1
               
               )
              
             
             ,
             
              
               0
               →
              
              2
             
            
            )
           
           
            𝔹
            2
            *
           
          
          ⁢
             
          for
          ⁢
             
          ι
         
         ∈
         
          [
          n
          ]
         
        
       
       ,
       

       	
       
        
         k
         
          *
          
           (
           
            
             n
             +
             1
            
            ,
            2
           
           )
          
         
        
        =
        
         
          (
          
           
            ω
            ⁡
            (
            
             1
             ,
             0
            
            )
           
           ,
           
            
             0
             →
            
            2
           
           ,
           
            
             ϕ
             →
            
            
             (
             
              
               n
               +
               1
              
              ,
              2
             
             )
            
           
           ,
           
            
             0
             →
            
            2
           
          
          )
         
         
          𝔹
          2
          *
         
        
       
       ,
       

       	
       
        
         ω
         
          ⟵
          U
         
         
          𝔽
          q
         
        
        ⁢
        \
        ⁢
        
         {
         0
         }
        
       
       ,
       
        
         ϕ
         0
        
        
         ⟵
         U
        
        
         𝔽
         q
        
       
       ,
       

       	
       
        
         for
         ⁢
            
         ι
        
        ∈
        
         
          [
          n
          ]
         
         ⁢
         
          
           
            σ
            ι
           
           
            ⟵
            U
           
           
            𝔽
            q
           
          
          ⁢
          \
          ⁢
          
           {
           0
           }
          
         
        
       
       ,
       
        
         ϕ
         →
        
        
         (
         ι
         )
        
       
       ,
       
        
         ϕ
         →
        
        
         (
         
          
           n
           +
           1
          
          ,
          1
         
         )
        
       
       ,
       
        
         
          ϕ
          →
         
         
          (
          
           
            n
            +
            1
           
           ,
           2
          
          )
         
        
        
         ⟵
         U
        
        
         𝔽
         q
         2
        
       
       ,
      
     
    
   
   
    
     [
     
      Formula
      ⁢
         
      3
     
     ]
    
   
  
 

H is a hash function, MSG is a message, and b* is a basis vector of a basis B*.