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. 2026 Jan 26;26(3):825. doi: 10.3390/s26030825
Phase 8: Certificateless_encapsulated. Run by Sender
Input: Sender and receiver identity (IDs, IDr), the set of public parameter (D, Ha, Hb, Hc,|Fq|, F1, F2, C, g), receiver public key PuKr = (βr, δr), update nonce Non, a sender period private key, the variable Ω, ℛ, Ƒ
Output: Encapsulated tuple Ψ consists of the ciphertext C, signature S and variable ℛ for receiver

  1. Choosing Shared Secret Key (SSK) from Advanced Encryption Standard

  2. Constituting the message M so that
    M = (SSK||M||Non||IDs) (18)
  3. Encrypting his message thanks to the equation
    C = Hb(Ω||ℛ||Ƒ||IDr) ⊕ M (19)
  4. Defining signature S of the message such as
    S = մs,t + նs,t. Hc(Ω||ℛ||M||IDs||δs) + μ . Hc(Ω||ℛ||M||IDs||βr) (20)
  5. Producing the encapsulated tuple
    Ψ = (C, S, Ω), and send it to the receiver (21)