Implement Interpolation and Decryption Algorithm

[ymarcus93]

From the paper on p.11:

Since the code for generating the (U, s) values occurs on the client side, a malicious adversary could alter the (U,s) values of their share, producing combinations that cannot be used to derive a valid key, k. To mitigate this threat, the decryption algorithm is provided a vector of matched shares containing (U,s) values as well as ciphertexts to be decrypted. The algorithm first tries to interpolate the first two (U, s) values. If a valid key, k, is found, it is used to decrypt as many remaining c_e or c_a values as possible. Otherwise, it tries to interpolate and find a valid k with all remaining shares. If no valid key is found, an error message is produced for the current share and the algorithm moves onto repeat this process for the next share. This process is described below.

See the attached algorithm (from the paper): inter-decrypt-alg.pdf