Table 1 Notations and explanations

ID _A

Identity of entity A

TS

Current time stamp

A → B {M}

Entity A sends message M to entity B

SIGN_ALG(M)

Use ALG to sign M

MSK _i

Master key of group i

PK _A /SK _A

Entity A’s public/private key pair

ENCR_ALG_PK(M)

Use ALG to encrypt M with public key PK

A\({_{ALG\_.PK/SK}}\)

Entity A’s public/private key pair in ALG

CERT_A_WMN _i

A’s certificate at WMN group i

M ₁∥ M₂

Concatention of M₁ and M₂

Auth _A

Entity A’s warrant for proxy signature

K _A−B

Shared key between A and B

SE _K (M)

Encrypt M with shared key K