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Otherwise, hop r uses a key derivation function (KDF) initialized with s r to derive k M A C,r and verify the integrity of the query.
Since the derivation function of s n ( x ) is a polynomial, all of the derivatives must exist for all real numbers.
Suppose that is a secure key derivation function, and is a secure hash function.
A better DOWMAP is the "Password-Based Key Derivation Function 2" (PBKDF2) [ 32], as it adds entropy (called salt) and a computing effort (called iteration count) to a one-way function like the HMAC.
(Step-①②) The personalized programmer first computes the session key K j using the key derivation function kdf: (1) K j = k d f (K pID, SN j, dID, pID ), where SN j is the jth patient session number, dID is IMD's device identification number, and pID is physician's identification number.
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The derivation functions hc 1 = dHC/dk = ∇ k {HC} and ch 1 = dHC/dn = ∇ n {HC} also belong to the family of HCs.
These are used to encrypt the connections between the MT and the authenticators F1, F2, F3 Irreversible key derivation functions InitAuth flag A flag set only in the initial authentication.
For each pair ((L,S inn {mathcal N}{mathcal F}{mathcal C}{mathcal S},(s_{0},s_{1},c_{0},c_{1} )), the rules (r L^{prime }rightarrow R^{prime }) in ({mathcal A}{mathcal R}(L,SS)) are non-repeatedly listed using the two derivation functions ({mathcal F}{mathcal S}(L)), ({mathcal F}{mathcal S}(Sbackslash L^{prime })_{L^{prime }}) proposed by [9].
Key freshness: Since the keying materials are transferred from the old AS, this property could be verified by considering the key derivation functions (KDFs) for the MS = PRF (UUK, R 1|R 2), AK = PRF (MS, R 1|R 2) and SK = PRF 2(MS, R 1|R 2) in the initial AKA protocol.
Also, on the basis of the known criteria, for each function in the family of derivations functions, we define the maximum value of the HC function by equating its derivative with zero.
where ( {f}_Q^{hbox ) indicates the derivation of function f with respect to Q.
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