SUMMARYIn our previous work, we introduced new concepts of secure scan design; shift register equivalent circuits (SR-equivalents, for short) and strongly secure circuits, and also introduced generalized shift registers (GSRs, for short) to apply them to secure scan design. In this paper, we combine both concepts of SR-equivalents and strongly secure circuits and apply them to GSRs, and consider the synthesis problem of strongly secure SR-equivalents using GSRs. We also consider the enumeration problem of GSRs that are strongly secure and SR-equivalent, i.e., the cardinality of the class of strongly secure SR-equivalent GSRs to clarify the security level of the secure scan architecture. key words: design-for-testability, scan design, generalized feedback/feedforward shift registers, security, scan-based side-channel attack