Phase 6: User_key_Update—run by User

Input: User identity IDu, set of public parameter (spp), Helper key update hKUp. Output: Period private key PrKu,t′ Defining its period private key by combining helper key update and initial private key such as PrKu,t′ = PrKu,0 + hKUpu,t′ = (γu, αu) + (ζu,t′, αu,t′) = (γu + ζu,t′, αu + αu,t′) (14) We pose մu,t = γu + ζu,t′ նu,t = αu+ αu,t′