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. 2026 Jan 26;26(3):825. doi: 10.3390/s26030825
Phase 9: Certificateless_de-encapsulated run by receiver
Input: Encapsulated tuple Ψ = (C, S, Ω), the set of public parameter (D, Ha, Hb, Hc, Hd, |Fq|, F1, F2, C, g), sender and receiver Identity (IDs, IDr), sender public key PuKs = (βs, δs), receiver periode private key PrKr,t′ = (մr,t, նr,t), receiver public key PuKr = (βr, δr)
Output: Acknowledgement of secure received message
  1. Defining
    ϯ = նr,t . Ω (22)
  2. Recovering the secret key
    M′ = C ⊕ Hb(Ω||ℛ′||ϯ||IDr) where ℛ′ = Ω(մr,t + նr,t) (23)
  3. Verifying equation
    S . D = (βS + Ha(IDs||βs||δs).U + δs.Hc(Ω||ℛ′||M′||IDs||δs) + Ω.Hc(Ω||ℛ′||M′||IDs||βS) (24)