I could not understand one step in correctness proof of paper titled "A tree-based CP-ABE scheme with hidden policy supporting secure data sharing in cloud computing" authored by Runhua Xu, Yang Wang, Bo Lang.

Link to paper: https://www.researchgate.net/publication/271482056_A_Tree-Based_CP-ABE_Scheme_with_Hidden_Policy_Supporting_Secure_Data_Sharing_in_Cloud_Computing

Please refer the screenshot attached. Specifically, I could not understand the move from step 3 to step 4 in which they replaced one of the denominator (highlighted in screenshot).

I will be very grateful if someone can help me understand this move. Many thanks in advance.enter image description hereenter image description hereenter image description hereenter image description here

  • $\begingroup$ What is the definition of R_j? $\endgroup$ – Mahdi Sedaghat Jan 26 at 9:52
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    $\begingroup$ Sir, these are random elements in group G. I missed adding link to the paper. It is available at researchgate.net/publication/…. $\endgroup$ – user60588 Jan 27 at 17:37
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    $\begingroup$ Sir, I saw two very good reference papers from you on same area. But I could not find their soft copies. If possible, request you to kindly share them (bakshi.puneet@gmail.com). (1) An efficient and secure data sharing in Smart Grid: Ciphertext-policy attribute-based signcryption. (2) An Efficient and Secure Attribute-Based Signcryption Scheme for Smart Grid Applications $\endgroup$ – user60588 Jan 27 at 17:44

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