International Association
for Cryptologic Research

We remark that the structure of bilinear groups of a large composite order(at least 1024 bits) could make group operation inefficient and lose the advantages of elliptic curve cryptography which gained mainly from smaller parameter size. As of 2013, the longest parameter recommended by NIST for elliptic curves has 571 bits.

From the practical point of view, such an algebraic structure is unlikely applicable to cryptographic schemes.