A transmitter device for sending an encrypted message to a receiver device in an identity-based cryptosystem, the transmitter device being associated with a transmitter identifier. The transmitter device is configured to receive a transmitter partial private key from a trusted center, the transmitter device being configured to: send a request for two public session keys to the receiver device; receive from the receiver device a first ciphertext set, the first ciphertext set being derived from an encryption and authentication of two public session keys; decrypt and authenticate the two public session keys from the first ciphertext set using a receiver identifier and the transmitter partial private key; determine a second ciphertext set from the transmitter partial private key, from the receiver identifier, and from the two public session keys, the second ciphertext comprising an encrypted message; send the second ciphertext set to the receiver device.
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