2019 Volume E102.A Issue 1 Pages 270-277
A compression-function-based MAC function called FMAC was presented as well as a vector-input PRF called vFMAC in 2016. They were proven to be secure PRFs on the assumption that their compression function is a secure PRF against related-key attacks with respect to their non-cryptographic permutations in the single user setting. In this paper, it is shown that both FMAC and vFMAC are also secure PRFs in the multi-user setting on the same assumption as in the single user setting. These results imply that their security in the multi-user setting does not degrade with the number of the users and is as good as in the single user setting.