# DecryptNode for non-leaf Node in CP-ABE

I've looked at paper Ciphertext-Policy Attribute-Based Encryption by Bethencourt, Sahai, Waters and see this an answer here for the explanation of DecrypNode for a leaf node.

I could understand the derivation of this $$f_n$$ for a leaf node but not for a non-leaf node in the $$s$$.

I could not understand the move from step 4 to 5 ( the last move).

I will be very grateful Can somebody help in understanding the last move here?

How qx(0) = qx(1) /\1(0) . qx(2) /\2(0) . qx(3) /_\3(0) . ... ? I dont think legarange interpolation says this. I think i am missing something heere. Please help me in understanding this.

Thanks and Regards

• Welcome to Cryptography. Your question is not clear. Could you post a link? Jan 12 '19 at 20:17
• It is 11 months ago. Maybe you can delete this and ask again in a better way... Jan 6 '20 at 12:47

The last two steps is from Lagrange interpolation such that $$\sum_{i\in S_x'} q_x(i)\triangle_{i,S_x'}(0)=q_x(0)$$. The concept is the same as that of leaf node, but now we are at the parent node. Doing this recursively up to the root node would give the secret exponent.