Table 1 Meaning of scheme notations
From: An authorizable and preprocessable data transmission scheme based on elliptic curves
Category | Notation | Description |
|---|---|---|
Scheme construction | \(\leftarrow\) | Assignment operation |
\(\lambda\) | Security parameter | |
p, q, n | Prime numbers | |
\(F_q\) | Finite field with characteristic q | |
\(Z_n\) | Integers modulo n | |
\(Z_n^*\) | Multiplicative group modulo n | |
a, b | Elements in \(F_q\) | |
\((\mathbb {G},G,p)\) | Cyclic group of order p, with generator G | |
\((0,1)^*\) | Set of all binary strings | |
\(\alpha _1,\alpha _2\) | Random integers in \(\mathbb {Z}_n\), used as private keys | |
r, k | Random elements from \(\mathbb {Z}_n^*\) | |
i, j | Index values | |
msg | Plaintext message | |
\(\sigma =\left( R,s \right)\) | Signature of msg | |
\(C=\left( C_1,C_2,C_3 \right)\) | Ciphertext, composed of three components | |
(PK, sk) | Public/private key pair. Among them, PK represents the public key and sk represents the private key. | |
\((PK^{OneTime},sk^{OneTime})\) | One-time public/private key pair for encryption/decryption | |
Complexity assumptions | G, H | Elements of group |
a, b, c | Integers from the set of integers | |
Security proof | \(\mathcal {A}\) | Adversary in the security model |
\(\mathcal {B}\) | Simulator in the security model | |
\(\mathcal {H}\) | Random oracle | |
\(\varepsilon\) | Advantage of the adversary | |
t | Time complexity of the adversary | |
\(q_s\) | Number of signing queries | |
\(\iota ,z,w\) | Secret random values selected from \(\mathbb {Z}_p^*\) |
