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Each A u is a binary vector of length.
Each node will then send a binary vector of length u G to all its neighbors over communication channels.
By definition, a TEP, noted by e, is a binary vector of length k and Hamming weight w≤i.
In our scheme, each block is mapped to a binary vector of length, and the length of the password is equal to.
These encode all paths in the molecular graph up to a path length of P into a binary vector of length V, but the default values for V and P are different for each toolkit: 1024 and 7 for OpenBabel, 1024 and 8 for the CDK, and 2048 and 7 for RDKit.
As described in Section 3.1, our packing method can pack a binary vector of length less than n in a single ciphertext, and the computation (6) enables to compute the inner product between two binary vectors of length n over packed ciphertexts.
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In the case of n=2048 and m=10,000, we need ⌈m/n⌉=5 packed ciphertexts and it also takes about 5×5.31=26.55 ms for a secure inner product between two binary vectors of length m=10,000.
According to our implementation, our method enables to compute a secure inner product between two binary vectors of length n=2048 (resp. 4096, 8192, and 16384) in 5.31 ms (resp. 34.34, 71.25, and 159.45 ms).
We consider all sets contain k elements, each of which is binary vectors of length m, then there are a total of 2 m possible elements.
The private keys are binary vectors of length 2 m with k '1's encoding which element exists in an individual's set.
Therefore, the set of compatible haplotypes H i for a given length- L xor-genotype x i consists of all binary vectors of length- L, i.e., H 1 = H 2 = ⋯ = H N = { 0, 1 } L × 2 L ≜ Z.
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