title: Deficiencies of the cryptography based on multiple-parameter fractional Fourier transform.
abstract: Methods of image encryption based on fractional Fourier transform have an incipient flaw in security. We show that the schemes have the deficiency that one group of encryption keys has many groups of keys to decrypt the encrypted image correctly for several reasons. In some schemes, many factors result in the deficiencies, such as the encryption scheme based on multiple-parameter fractional Fourier transform [Opt. Lett.33, 581 (2008)]. A modified method is proposed to avoid all the deficiencies. Security and reliability are greatly improved without increasing the complexity of the encryption process.
authors.affiliation: State Key Laboratory of Tunable Laser Technology Research, Institute of Optic-Electronics, Harbin Institute of Technology, Harbin 150001, China. qiwenran@hit.edu.cn
authors.forename: Qiwen
authors.initials: Q
authors.lastname: Ran
authors.forename: Haiying
authors.initials: H
authors.lastname: Zhang
authors.forename: Jin
authors.initials: J
authors.lastname: Zhang
authors.forename: Liying
authors.initials: L
authors.lastname: Tan
authors.forename: Jing
authors.initials: J
authors.lastname: Ma