Efficient Verifiable Random Functions with Compact Proofs and Keys
        
        
        
        
          
        
        
      
        
    
        
        A novel VRF construction achieves short proofs and keys by directly utilizing bilinear maps, enhancing cryptographic randomness efficiency.
        
        Group Verifiable Random Functions Advance Anonymous Token Scalability
        
        
        
        
          
        
        
      
        
    
        
        A new cryptographic primitive, Group Verifiable Random Functions, enables anonymous, scalable token issuance by decentralizing randomness generation.
