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Testing business processes is crucial to assess the compliance of business process models with requirements. Automating this task optimizes testing efforts and reduces human error while also providing improvement insights for the business process modeling activity. The primary purposes of this paper are to conduct a literature review of Business Process Model and Notation (BPMN) testing and formal verification and to propose the Business Process Evaluation and Research Framework for Enhancement and Continuous Testing (bPERFECT) framework, which aims to guide business process testing (BPT) research and implementation. Secondary objectives include (1) eliciting the existing types of testing, (2) evaluating their impact on efficiency and (3) assessing the formal verification techniques that complement testing.

The methodology used is based on Kitchenham's (2004) original procedures for conducting systematic literature reviews.

Results of this study indicate that three distinct business process model testing types can be found in the literature: black/gray-box, regression and integration. Testing and verification approaches differ in aspects such as awareness of test data, coverage criteria and auxiliary representations used. However, most solutions pose notable hindrances, such as BPMN element limitations, that lead to limited practicality.

The databases selected in the review protocol may have excluded relevant studies on this topic. More databases and gray literature could also be considered for inclusion in this review.

Three main originality aspects are identified in this study as follows: (1) the classification of process model testing types, (2) the future trends foreseen for BPMN model testing and verification and (3) the bPERFECT framework for testing business processes.

The practical purpose of this research is to propose a candidate for post-quantum signature standard that is free of significant drawback of the finalists of the NIST world competition, which consists in the large size of the signature and the public key. The practical purpose is to propose a fundamentally new method for development of algebraic digital signature algorithms.

The proposed method is distinguished by the use of two different finite commutative associative algebras as a single algebraic support of the digital signature scheme and setting two different verification equation for a single signature. A single public key is computed as the first and the second public keys, elements of which are computed exponentiating two different generators of cyclic groups in each of the algebras.

Additionally, a scalar multiplication by a private integer is performed as final step of calculation of every element of the public key. The same powers and the same scalar values are used to compute the first and the second public keys by the same mathematic formulas. Due to such design, the said generators are kept in secret, providing resistance to quantum attacks. Two new finite commutative associative algebras, multiplicative group of which possesses four-dimensional cyclicity, have been proposed as a suitable algebraic support.

The introduced method is novel and includes new techniques for designing algebraic signature schemes that resist quantum attacks. On its base, a new practical post-quantum signature scheme with relatively small size of signature and public key is developed.