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. 2026 Jan 26;26(3):825. doi: 10.3390/s26030825
Phase 5: Helper_key_Update—Executed by Helper
Input: User identity IDu, set of public parameter (spp), helper private key hprKu,0 = (ζu, αu), old time t, new time t′
Output: Helper key update hKUpu,t′

  1. It chooses randomly tn and t′n from {1, 2,……, q − 1}

  2. It defines the private key of helper for time t such as
    hprKu,t = (ζu,t, αu,t) and ζu,t = tn + w.Hc(IDu||ζu||αu) (t) and αu.t = αu.tn.D (12)
  3. It defines Helper key update by hKUpu,t′ = (ζu,t′, αu,t′) where
    ζu,t′ = t′n + w.Hd(IDu||ζu,t||αu,t) (t′) and αu.t′ = αu,t.t′n.D (13)

  4. It sent hKUpu,t′ to the user and deletes hprKu,t