Table 1 Symbols and their descriptions
From: An efficient privacy-preserving comparison protocol in smart metering systems
Symbol | Description | Symbol | Description |
|---|---|---|---|
a,b | Secret inputs | h | Uniformly random number |
s k | Secret key | z | The integer 2ℓ+a−b |
p k | Public key | z ℓ | The most significant bit of z |
\(\mathcal {E}\) | Encryption function | d | Masked version of z, d=z+r |
\(\mathcal {D}\) | Decryption function | \(\hat {r}\) | The integer rmod2ℓ |
m | Plaintext | \(\acute {d}\) | The integer dmod2ℓ |
\(\mathbb {Z}_{\eta }\) | Paillier message space | δ | Uniformly random bit |
\(\mathbb {Z}u\) | DGK message space | [.] | Paillier encryption |
∈ R X | A random number in X | s | The integer 1−2·δ |
ℓ | Bit length of secret inputs |
| DGK encryption |
κ | Security parameter | ρ | Number of ciphertext that |
λ η | Carmichael function | can be packed into one | |
r | κ+ℓ-bit random number | Paillier ciphertext | |
ord (α) | The smallest positive integer | \(\hat {d}\) | Packed Paillier ciphertexts |
x such that α x=1modn | λ | Comparison output | |
/ | Integer division | Ψ(x) | ⌊x/2ℓ⌋ |
