Advances in Multimedia

Research Article

A Novel Anonymous Proxy Signature Scheme

Table 1

The definitions of used notations
NotationsDefinitions
𝐺 1 A cyclic additive group on an Elliptic Curve with order π‘ž generated and a base point 𝑃
𝐺 2 A cyclic multiplicative group with order π‘ž
𝑒 A bilinear map which is defined as 𝑒 ∢ 𝐺 1 Γ— 𝐺 1 β†’ 𝐺 2
{ 𝒫 1 , 𝒫 2 , … , 𝒫 𝑛 } A proxy signer group
π‘š A message to be signed
π‘š 𝑀 A warrant which contains the original signer’s and proxy signer’s identities, delegation, authorization period, valid period, and so forth
𝒫 𝑖 A proxy signer in the proxy signer group { 𝒫 1 , 𝒫 2 , … , 𝒫 𝑛 }
𝒫 𝑠 The real signer in the proxy signer group { 𝒫 1 , 𝒫 2 , … , 𝒫 𝑛 }
( π‘₯ 0 , π‘Œ 0 ) The private/public key pair of the original signer
( π‘₯ 𝑖 , π‘Œ 𝑖 ) The private/public key pair of 𝒫 𝑖
p s k 𝑠 The proxy secrect key computed by 𝒫 𝑠
π‘Ÿ 𝑖 A random integer in 𝑍 π‘ž βˆ—
β€– A concatenation of two strings
𝐻 0 ( β‹… ) A hash function mapping from { 0 , 1 } βˆ— Γ— 𝐺 1 to 𝑍 π‘ž βˆ—
𝐻 1 ( β‹… ) A hash function mapping from { 0 , 1 } βˆ— to 𝑍 π‘ž βˆ—
𝐻 2 ( β‹… ) A hash function mapping from { 0 , 1 } βˆ— Γ— 𝐺 1 Γ— 𝐺 1 to 𝑍 π‘ž βˆ—
𝜎 𝑖 The random point ( = π‘Ÿ 𝑖 𝑉 ) constructed by 𝒫 𝑠 to stand for the signatures as if they were really made by 𝒫 𝑖 , where 𝑠 β‰  𝑖 , correspondingly
𝜎 𝑠 The signature generated by 𝒫 𝑠 , where 𝑠 β‰  𝑖
𝑝 𝜎 s u m βˆ‘ = ( 𝑛 𝑖 ( β‰  𝑠 ) = 1 𝜎 𝑖 ) + 𝜎 𝑠 (the summation of partial proxy signatures)
𝐴 , 𝐡 , 𝐢 , 𝐷 , 𝐿 , π‘ˆ , 𝑉 , 𝑅 The points in 𝐺 1