So far, the security of the most of the cryptographic primitives depends on the high-quality and unpredictable randomness. In cryptography, the pseudorandom number generator (PRNG) is used to generate randomness. Thus, the security of the PRNG will directly impact the security of cryptographic algorithms. However, there have been some reports showing that many human factors can lead to the failure randomness generated by the PRNG which is referred to as the backdoored pseudorandom number generator (BPRNG). A good example of this BPRNG is the dual elliptic curves PRNG (Dual EC PRNG) which has been exposed to generate bad randomness. With the emerging of BPRNG, new challenges will be confronted with the study of cryptographic algorithms. Therefore, it is important to investigate the cryptographic primitives against the BPRNG. This study first reviews the research background of the cryptographic primitives against the BPRNG, and then summarizes the existing schemes in this field.