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1. WO2020115266 - METHODS AND DEVICES FOR SECURED IDENTITY-BASED ENCRYPTION SYSTEMS WITH TWO TRUSTED CENTERS

Note: Text based on automatic Optical Character Recognition processes. Please use the PDF version for legal matters

[ EN ]

CLAIMS

1. A transmitter device (103) for sending an encrypted message to a receiver device (105) in an identity-based cryptosystem (100), said identity-based cryptosystem (100) comprising a transmitter trusted center (101 ) connected to said transmitter device (103) and a receiver trusted center (102) connected to said receiver device (105), wherein the transmitter device (103) is configured to:

- receive, from said transmitter trusted center (101 ), two public authentication keys;

- check if a set of conditions related to a transmitter trusted center public key, to a receiver trusted center public key, and to a transmitter authentication key comprised in said two public authentication keys are satisfied;

- determine a ciphertext set comprising an encrypted message if said set of conditions are satisfied;

- send said ciphertext set to the receiver device (105).

2. The transmitter device (103) of claim 1 , wherein the transmitter trusted center (101 ) is associated with a transmitter trusted center identifier, the transmitter device (103) being configured to receive, from said transmitter trusted center (101 ), transmitter system parameters, a transmitter public key, and a transmitter private key, said transmitter system parameters comprising a prime number, two algebraic groups of order equal to said prime number, an admissible bilinear map, a first cryptographic hash function, a second cryptographic hash function, a third cryptographic hash function, and a transmitter trusted center public key associated with said transmitter trusted center identifier, said transmitter system parameters being dependent on said transmitter trusted center identifier and a transmitter trusted center security parameter held by said transmitter trusted center (101 ), said transmitter private key being dependent on said transmitter system parameters, a transmitter identifier associated with said transmitter device (103), and on a transmitter trusted center master key held by said transmitter trusted center (101 ).

3. The transmitter device (103) of claim 2, wherein the transmitter device (103) is configured to verify a transmitter trusted center public key by comparing a first value to a second value, said first value being determined by applying said bilinear map to the transmitter private key and the transmitter trusted center public key, said second value being determined by applying said bilinear map to the transmitter public key and an intermediate transmitter trusted center public key received from the receiver trusted center (102), the transmitter device (103) being configured to verify the transmitter authentication key by comparing a third value to a fourth value, said third value being determined by applying said bilinear map to the transmitter trusted center public key and the transmitter authentication key, said fourth value being determined by applying said bilinear map to said intermediate transmitter trusted center public key and a receiver trusted center public key received from the receiver trusted center (102).

4. The transmitter device (103) of claims 1 and 2, wherein the ciphertext set further comprises a first component, a second component, and a third component, the transmitter device (103) being configured to:

- determine a random secret key;

- determine a receiver public key by applying the first cryptographic hash function to a receiver identifier associated with the receiver device (105); and

- determine an auxiliary value by applying the third cryptographic hash function to said random secret value and a given message.

5. The transmitter device (103) of claim 4, wherein the transmitter device (103) is further configured to:

- determine said first component by applying an exponentiation function of a basis equal to a receiver trusted center public key received from the receiver trusted center (102) and an exponent equal to said auxiliary value;

- determine said second component by applying an addition operation to said random secret key and the output of the application of the second cryptographic hash function to the output of the application of the bilinear map to a first input and a second input, said first input being given by a receiver public key associated with the receiver device (105) to the power said auxiliary value, said second input being given by the output of the application of the first cryptographic hash function to the recipient trusted center identifier associated with the receiver trusted center (102);

- determine said encrypted message by applying a cipher to said given message, said cipher using said random secret key as encryption key;

- determine said third component by applying the second cryptographic hash function to the output of the product between a first input and a second input to the power said auxiliary value, said first input being given by the output of the application of the bilinear map to the transmitter private key and an intermediate transmitter trusted center public key received from the receiver trusted center (102), said second input being given by the output of the application of the bilinear map to an intermediate receiver trusted center public key received from the receiver trusted center (102) and to a receiver public key associated with the receiver device (105).

6. A receiver device (105) for receiving, from a transmitter device (103), an encrypted message comprised in a ciphertext set, said ciphertext set comprising a first component, a second component, and a third component, said transmitter device (103) being associated with a transmitter identifier, wherein the receiver device (105) is associated with a receiver identifier, the receiver device (105) being configured to receive, from a receiver trusted center (102) a receiver public key and a receiver private key, said receiver trusted center (102) being associated with a receiver trusted center identifier, the receiver device (105) being configured to:

- apply a first cryptographic hash function to the transmitter identifier, which provides a transmitter public key;

- determine a secret key from the first component, the second component and the receiver private key;

wherein the receiver device (105) is configured to decrypt the encoded message using a decipher that uses a secret key as a decryption key.

7. The receiver device (105) of claim 6, wherein the receiver device (105) is further configured to receive, from the receiver trusted center (102), receiver system parameters, said receiver system parameters comprising a prime number, two algebraic groups of order equal to said prime number, an admissible bilinear map, said first cryptographic hash function, a second cryptographic hash function, a third cryptographic hash function, and a receiver trusted center public key associated with said receiver trusted center identifier, said receiver system parameters being

dependent on said receiver trusted center identifier and a receiver trusted center security parameter held by said receiver trusted center (102), said receiver private key being dependent on said receiver system parameters, said receiver identifier associated with said receiver device (105), and on a receiver trusted center master key held by said receiver trusted center (102).

8. The receiver device (105) of claim 7, wherein the receiver device (105) is configured to:

- verify a receiver trusted center public key by comparing the output of the application of the bilinear map to the receiver private key and the receiver trusted center public key to the output of the bilinear map applied to a receiver public key and to an intermediate receiver trusted center public key received from the receiver trusted center (102);

- verify a receiver authentication key received from the transmitter trusted center (101 ) and a transmitter trusted center public key by comparing the output of the bilinear map applied to the receiver trusted center public key and to the receiver authentication key with the output of the of the bilinear map applied to the intermediate receiver trusted center public key and to a transmitter trusted center public key, received from the transmitter trusted center (101 ); and

- verify a transmitter authentication key received from the transmitter trusted center (101 ) by comparing:

• the output of the bilinear map applied to a transmitter trusted center public key and the transmitter authentication key; with

• the output of the bilinear map applied to an intermediate transmitter trusted center public key received from the receiver trusted center (102) and to a receiver trusted center public key.

9. The receiver device (105) of claim 7, wherein, the receiver device (105) is configured to decrypt the encoded message if the receiver trusted center public key, the receiver authentication key, and the transmitter authentication key are verified, and wherein the determination of the secret key comprises applying a subtraction operation between the second component comprised in the ciphertext set and the output of the application of the second cryptographic hash function to the result of the bilinear map applied to the receiver private key and to the first component comprised in the ciphertext set, the receiver device (105) being further configured to:

- determine an auxiliary value by applying the third cryptographic hash function to said secret key and said original message; and

- verify the transmitter identity by comparing the third component comprised in the ciphertext set to the output of the application of the second cryptographic hash function to a value to the power said auxiliary value, said value determined as the product between:

• the output of the bilinear map applied to the transmitter public key and to the intermediate transmitter trusted center public key; and

• the output of the bilinear map applied to the transmitter authentication key and to the receiver private key.

10. An identity-based cryptosystem (100) comprising a transmitter trusted center (101 ) and a receiver trusted center (102), wherein the transmitter trusted center (101 ) is configured to receive, from a transmitter (105), a transmitter identifier, and to determine a transmitter private key from a transmitter trusted center master key, transmitter system parameters and the transmitter identifier, the transmitter trusted center (101 ) being configured to determine a transmitter public key by applying a first hash function to the transmitter identifier and to determine a transmitter private key by applying an exponentiation function defined by a base and an exponent, the base being equal to said transmitter public key, and the exponent being equal to the inverse of the transmitter trusted center master key, transmitter trusted center (101 ) being configured to transmit the transmitter private key to the transmitter device (103) .

1 1. The identity-based cryptosystem (100) of claim 10, wherein the receiver trusted center (102) is configured to receive, from a receiver device (105), a receiver identifier, and to determine a receiver private key from a receiver trusted center master key, receiver system parameters and a receiver identifier, the receiver trusted center (102) being configured to determine a receiver public key by applying the first hash function to the receiver identifier and to determine the receiver private key by applying an exponentiation function defined by a base and an exponent, the base being equal to

said receiver public key, and the exponent being equal to the inverse of the receiver trusted center master key.

12. The identity-based cryptosystem (100) of any preceding claim 10 and 1 1 , wherein the transmitter trusted center (101 ) is associated with a transmitter trusted center identifier and holds a transmitter trusted center security parameter, the transmitter trusted center (101 ) being configured to determine said transmitter system parameters and said transmitter trusted center master key from said transmitter trusted center security parameter and said transmitter trusted center identifier, said transmitter system parameters comprising a prime number, two algebraic groups of order equal to said prime number, an admissible bilinear map, a first cryptographic hash function, a second cryptographic hash function, a third cryptographic hash function, and a transmitter trusted center public key associated with said transmitter trusted center identifier.

13. The identity-based cryptosystem (100) of any preceding claim 1 1 and 12, wherein the receiver trusted center (102) is associated with a receiver trusted center identifier and holds a receiver trusted center security parameter, the receiver trusted center (102) being configured to determine said receiver system parameters and said receiver trusted center master key from said receiver trusted center security parameter and said receiver trusted center identifier, said receiver system parameters comprising a prime number, two algebraic groups of order equal to said prime number, an admissible bilinear map, a first cryptographic hash function, a second cryptographic hash function, a third cryptographic hash function, and a receiver trusted center public key associated with said receiver trusted center identifier.

14. The identity-based cryptosystem (100) of any preceding claim 10 to 13, wherein the receiver trusted center (102) is configured to receive, from the transmitter trusted center (101 ), a transmitter trusted center identifier, and to determine said transmitter trusted center private key from the receiver trusted center master key, the receiver system parameters and the transmitter trusted center identifier, the receiver trusted center (102) being configured to determine an intermediate transmitter trusted center public key by applying the first hash function to the transmitter trusted center identifier and to determine the transmitter trusted center private key by applying an exponentiation function defined by a base and an exponent, the base being equal to

said intermediate transmitter trusted center public key, and the exponent being equal to the inverse of the receiver trusted center master key.

15. The identity-based cryptosystem (100) of any preceding claim 10 to 14, wherein the transmitter trusted center (101 ) is configured to determine two public authentication keys comprising a transmitter authentication key and a receiver authentication key from the transmitter trusted center master key, the transmitter trusted center private key, and the receiver trusted center public key, the transmitter trusted center (101 ) being configured to determine the transmitter authentication key by applying an exponentiation function of a base equal to said transmitter trusted center public key and an exponent equal to the inverse of said transmitter trusted center master key, and to determine the receiver authentication key by applying an exponentiation function of a base equal to said transmitter trusted center private key and an exponent equal to said transmitter trusted center master key.