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| Abbreviations/notations | Meaning |
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| Secure parameter |
| Big prime |
| Additive group on an elliptic curve of the order |
| Multiplicative group on an elliptic curve of the order |
| Bilinear function |
| Generator of the group |
| The private key, the public key, and the shared public key of the KGC |
| The private key, the public key, and the shared public key of the CPC |
| The shared public key of the CPCn that equals to |
| A secure hash function that takes a string of any length as input and gives an element on |
| A secure hash function that takes an element on and gives a string of length |
| A secure hash function that takes a string of length and gives a string of length |
| A secure hash function that takes a string of any length and gives an element on |
| A secure hash function that takes a string of any length and an element on and gives an element on |
| A secure hash function that takes two strings of length and gives a string of length |
| Secure key derivation function that takes an element on and a string of length and gives a string of length |
| Number of users |
| Initially empty revocation list |
| A binary tree with at least leaf nodes representing states |
| Minimum time interval |
| The private key of key authority |
| Part of the system parameter of key authority and |
| System parameter of the KGC |
| System parameter of the CPCs |
| System parameter of key authority |
| The final public parameter in the setup step |
| Identity of the receiver |
| Identity of the sender |
| Mapping of on |
| Mapping of on |
| The private key of the receiver |
| The private key of the sender |
| Mapping of on |
| The time when the encryption occurs |
| Mapping of on |
| The input of the root chain in the double ratchet algorithm |
| Revocation key |
| The input of the root chain in the CONNECTION part of the IBE-signal scheme |
| Message key for the encryption of the first message |
| Blinding factor in the private key issuance process |
| Timestamp used to prevent replay attacks |
| Receiver’s local time |
| The message that needs to be signed |
| Signature |
| Private keys for revocation |
| Key updates for revocation |
| Revocation key selected from and |
| Bob’s public and private keys in Diffie–Hellman key exchange in CONNECTION part |
| Alice’s public and private keys in Diffie–Hellman key exchange in CONNECTION part |
| The message key of the sender in the session |
| The message key of the receiver in the session |
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