Formal Security Reassessment of the 5G-AKA-FS Protocol: Methodological Corrections and Augmented Verification Techniques

. 2024 Dec 13;24(24):7979. doi: 10.3390/s24247979

Algorithm 4 The Challenge–Response Step 2.1 [HN]

Inputs:

k, S Q N_{H N}

Generate an ephemeral private-public key pair (

e p k_{H N}, e p k_{H N}^{- 1}

), where

e p k_{H N} = e p k_{H N}^{- 1} \cdot G

Compute a Diffie-Hellman key

D H K \leftarrow e p k_{H N}^{- 1} \cdot C_{0}

Set

R A N D \leftarrow e p k_{H N}

as a challenge
Compute

M A C \leftarrow f_{1} (k, S Q N_{H N}, A M F, R A N D \oplus D H K)

Compute

A K \leftarrow f_{5} (k, R A N D \oplus D H K)

Compute

C O N C \leftarrow A K \oplus S Q N_{H N}

Set

A U T N \leftarrow (C O N C, A M F, M A C)

Compute

C K \leftarrow f_{3} (k, R A N D \oplus D H K)

and

I K \leftarrow f_{4} (k, R A N D \oplus D H K)

Compute expected response

X R E S \leftarrow f_{2} (k, R A N D \oplus D H K)

Compute

X R E S^{*} \leftarrow K D F (C K ∥ I K, I D_{S N} ∥ R A N D ∥ X R E S)

Compute

H X R E S^{*} \leftarrow L E F T (128, H_{S H A - 256} (R A N D ∥ X R E S^{*}))

Derive

K_{A U S F} \leftarrow K D F (C K ∥ I K, I D_{S N} ∥ C O N C ∥ D H K)

Derive

K_{S E A F} \leftarrow K D F (K_{A U S F}, I D_{S N})

Increase

S Q N_{H N} \leftarrow S Q N_{H N} + 1

Set

HE - AV \leftarrow (R A N D, A U T N, X R E S^{*}, K_{A U S F})

Set

SE - AV \leftarrow (R A N D, A U T N, H X R E S^{*})

Outputs. HN sends

(SE - AV)

to SN.