To achieve multiple color images encryption, a secure double-color-image encryption algorithm is designed based on the quaternion multiple parameter discrete fractional angular transform (QMPDFrAT), a nonlinear operation and a plaintext-related joint permutation-diffusion mechanism. QMPDFrAT is first defined and then applied to encrypt multiple color images. In the designed algorithm, the low-frequency and high-frequency sub-bands of the three color components of each plaintext image are obtained by two-dimensional discrete wavelet transform. Then, the high-frequency sub-bands are further made sparse and the main features of these sub-bands are extracted by a Zigzag scan. Subsequently, all the low-frequency sub-bands and high-frequency fusion images are represented as three quaternion signals, which are modulated by the proposed QMPDFrAT with three quaternion random phase masks, respectively. The spherical transform, as a nonlinear operation, is followed to nonlinearly make the three transform results interact. For better security, a joint permutation-diffusion mechanism based on plaintext-related random pixel insertion is performed on the three intermediate outputs to yield the final encryption image. Compared with many similar color image compression-encryption schemes, the proposed algorithm can encrypt double-color-image with higher quality of image reconstruction. Numerical simulation results demonstrate that the proposed double-color-image encryption algorithm is feasibility and achieves high security.

Since security protocols form the cornerstones of modern secure networked systems, it is important to develop informative, accurate, and deployable approach for finding errors and proving that protocols meet their security requirements. We propose a novel approach to check security properties of cryptographic protocols using authentication event logic. Compared with logic of algorithm knowledge, authentication event logic guarantees that any well-typed protocol is robustly safe under attack while reasoning only about the actions of honest principals in the protocol. It puts no bound on the size of the principal and requires no state space enumeration and it is decidable. The types for protocol data provide some intuitive explanation of how the protocol works. Our approach has led us to the independent rediscovery of flaws in existing protocols and to the design of improved protocols.

Protocol security in a composition protocol environment has always been an open problem in the field of formal analysis and verification of security protocols. As a well-known tool to analyze and verify the logical consistency of concurrent systems, SPIN (Simple Promela Interpreter) has been widely used in the analysis and verification of the security of a single protocol. There is no special research on the verification of protocol security in a composition protocol environment. To solve this problem, firstly, a formal analysis method for composition protocol based on SPIN is proposed, and a formal description of protocol operation semantics is given. Then the attacker model is formalized, and a message specification method based on field detection and component recognition is presented to alleviate the state explosion problem. Finally, the NSB protocol and the NSL protocol are used as examples for compositional analysis. It is demonstrated that the proposed method can effectively verify the security of the protocol in a composition protocol environment and enhance the efficiency of composition protocol verification.

Ultralightweight mutual authentication protocols (UMAP) of Radio frequency identification (RFID) systems have attracted much attention from researchers. Many studies reveal that most of UMAP suffer malicious attack. To improve security of UMAP, formal analysis is performed with Simple promela interpreter (SPIN). Two typical UMAPs, which are RCIA and RAPP, are selected as our case study. A protocol abstract modeling method is presented to make UMAP can be formalized simply. Using SPIN, verification results show that RCIA and RAPP are both vulnerable against desynchronization attack. A Generalized model of UMAP (G-UMAP) and a general patching scheme are presented for resisting the attack. To validate the patching scheme, formal verification is then performed for the improved protocol. SPIN verification shows that the improved RCIA and RAPP both gain higher security. The above proposed modeling method has great significance for similar UMAP analyzing, and the proposed patching scheme is proved to be practical and reliable.

The verification of security protocols is an important basis for network security. Now, some security protocols add timestamps to messages to defend against replay attacks by network intruders. Therefore, verifying the security properties of protocols with timestamps is of great significance to ensure network security. However, previous formal analysis method of such protocols often extracted timestamps into random numbers in order to simplify the model before modeling and verification, which probably cause time-dependent security properties that are ignored. To solve this problem, a method for verifying security protocols with timestamps using model checking technique is proposed in this paper. To preserve the time-dependent properties of the protocol, Promela (process meta language) is utilized to define global clock representing the protocol system time, timer representing message transmission time, and the clock function representing the passage of time; in addition, a mechanism for checking timestamps in messages is built using Promela. To mitigate state space explosion in model checking, we propose a vulnerable channel priority method of using Promela to build intruder model. We take the famous WMF protocol as an example by modeling it with Promela and verifying it with model checker SPIN (Simple Promela Interpreter), and we have successfully found two attacks in the protocol. The results of our work can make some security schemes based on WMF protocol used in the Internet of things or other fields get security alerts. The results also show that our method is effective, and it can provide a direction for the analysis of other security protocols with timestamp in many fields.

The Signal is an end-to-end encrypted communication protocol composed of a double ratchet (DR) protocol and an extended triple Diffie-Hellman (X3DH) protocol. Its complex ratchet structure and the characteristics of protocol composition make it challenging to realize formal analysis. A formal analysis method based on logic of events theory (LoET) is proposed to conduct a security analysis of the Signal protocol. The method includes inference rules with key relation and key chain as the core to realize the formal analysis of ratchet structure, and the inference relation between sub-protocols is established by putting forward the composition theorem. The proposed method achieves a formal analysis of Signal, revealing that it does not satisfy a strong authentication property during the X3DH phase. The results show that the LoET-based method can be effectively applied in the formal analysis of Signal protocols, thus promoting the application and development of these protocols with ratchet structure and composition properties.