A bisectional multivariate quadratic equation system for RFID anti-counterfeiting

This paper proposes a novel scheme for RFID anti-counterfeiting by applying bisectional multivariate quadratic equations (BMQE) system into an RF tag data encryption. In the key generation process, arbitrarily choose two matrix sets (denoted as A and B) and a base Rab such that [AB] = λR
_AB
^T
, and generate 2n BMQ polynomials (denoted as p) over finite field F
_q
. Therefore, (F
_q
, p) is taken as a public key and (A, B, λ) as a private key. In the encryption process, the EPC code is hashed into a message digest d
_m
. Then d
_m
is padded to d'
_m
which is a non-zero 2n×2n matrix over F
_q
. With (A, B, λ) and d'
_m
, S
_m
is formed as an n-vector over F
₂
. Unlike the existing anti-counterfeit scheme, the one we proposed is based on quantum cryptography, thus it is robust enough to resist the existing attacks and has high security.