SCIENCE CHINA Information Sciences, Volume 62 , Issue 3 : 032113(2019) https://doi.org/10.1007/s11432-018-9738-2

Universally composable secure geographic area verification without pre-shared secret

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  • ReceivedAug 31, 2018
  • AcceptedJan 11, 2019
  • PublishedJan 29, 2019



This work was supported by National Natural Science Foundation of China (Grant Nos. 61472310, U1536202, 61672413, 61672415, 61601107, U1708262) and China 111 Project (Grant No. B16037).


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  • Figure 2

    Protocol CAV.

  • Figure 5

    (Color online) FAR under different $O$ in protocol ${\rm~CAV}_{\delta=1}$.

  • Figure 6

    (Color online) FAR and FRR under different $\delta$.

  • Table 1   Notations
    Notation Description
    $V_i$ The $i$th verifier located at $v_i$
    $P_j$ The $j$th prover located at $p_j$
    $A_k$ The $k$th adversary located at $a_k$
    Area$(O,R)$ The circular area with center $O$ and radius $R$
    $X_i$ The $i$th BRM message
    $n_i$ The $i$th random number
    $C$ The traveling speed of messages
    $d(p,q)$ The distance between position $p$ and position $q$
    $F(\cdot)$ A secure BSM pseudorandom generator
    $g(\cdot)$ A secure MAC function
  • Table 2   Comparison with related studies
    ProtocolRB DB SP SPreg Ours
    Area verification $\checkmark$$\times$$\times$$\times$$\checkmark$
    Batch verification $\checkmark$$\checkmark$$\times$$\times$$\checkmark$
    Resist colluding attacks $\times$$\checkmark$$\checkmark$$\checkmark$$\checkmark$
    Without pre-shared key $\checkmark$$\times$$\checkmark$$\times$$\checkmark$
    Composition security $-$$-$$-$$\checkmark$$\checkmark$
  • Table 3   Communication and computation overhead
    Verifier Prover VerifierProverVerifierProver
    Communication overhead $|X|+|n|$ $|n|$ $|X|+2|n|$ $2|n|$ $2|X|+|n|$ $|n|$
    Computation overhead $3F$ $3F$ $3F+g$$6F+3g$$6F+g$$6F+g$