Format preserving encryption has the characteristics of unchanged data format and data length after encryption, and does not destroy the data format constraints, thereby reducing the cost of modifying the data format. The existing format preserving encryption schemes for sensitive information are based on the symmetric encryption system, which has problems such as low key transmission security and high key management cost. This paper proposes a format preserving encryption scheme for sensitive information in identity cryptosystems. Compared with the existing format preserving encryption schemes, the two parties do not need to transmit a key, and the key derivation function is used to generate an encryption key and a decryption key. The use of hybrid encryption improves the security of sensitive information transmission. It is proved that the scheme satisfies the security of identity-based pseudo-random permutation. At the same time, the scheme has cipher text indistinguishability under adaptive selective plaintext attack.