1 Answers
A cryptographic n {\displaystyle n} -multilinear map is a kind of multilinear map, that is, a function e : G 1 × ⋯ × G n → G T {\displaystyle e:G_{1}\times \cdots \times G_{n}\rightarrow G_{T}} such that for any integers a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} and elements g i ∈ G i {\displaystyle g_{i}\in G_{i}} , e = e ∏ i = 1 n a i {\displaystyle e=e^{\prod _{i=1}^{n}a_{i}}} , and which in addition is efficiently computable and satisfy some security properties. It has several applications on cryptography, as key exchange protocols, identity-based encryption, and broadcast encryption. There exist constructions of cryptographic 2-multilinear maps, known as bilinear maps, however, the problem of constructing such multilinear maps for n > 2 {\displaystyle n>2} seems much more difficult and the security of the proposed candidates is still unclear.