Systems and methods for identity-based encryption and related cryptographic techniques

A method for generating a decryption key based on a public identifier ID, the method comprising:

• (a) obtaining a master key and a set of system parameters associated with an identity-based encryption system;
• (b) obtaining an element QID of an algebraic group, wherein the element QID is derived from the public identifier ID;
• and
• (c) computing the decryption key dID from the master key and QID using an action of the master key on QID, wherein the decryption key dID is a member of the algebraic group.

A method for encrypting a message in an identity-based cryptosystem to produce corresponding ciphertext, the method comprising:

• (a) obtaining a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 0×1→2, where 0, 1 and 2 are (not necessarily distinct) algebraic groups;
• (b) selecting a public identifier ID comprising information identifying an intended receiver of the message;
• (c) computing an element QIDε0 from the public identifier ID;
• (d) computing a secret message key gε2 using ê and QID;
• and
• (e) computing the ciphertext from the message using the message key g.

A method for decrypting ciphertext in an identity-based cryptosystem to produce an original message, the method comprising:

• (a) obtaining a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 0×1→2, where 0, 1 and 2 are (not necessarily distinct) algebraic groups;
• (b) selecting a public identifier ID comprising information identifying an intended receiver of the message;
• (c) obtaining a private key dIDε0 corresponding to the public identifier ID;
• (d) computing a secret message key gε2 using ê and the private key dID;
• and
• (e) computing the original message from the ciphertext using the message key g.

A method for encrypting a message to produce ciphertext, the method comprising:

• (a) obtaining a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 1×1→2, where 1 and 2 are algebraic groups, and elements P, sPε1, where sε is a secret master key;
• (b) obtaining a public key xPε1 corresponding to an intended receiver, where xε is a secret of the intended receiver;
• (c) computing a message key gε2 using ê, sP, the public key xP, and a randomly selected rε;
• and
• (d) computing the ciphertext from the message using the message key g.

A method for decrypting a ciphertext to produce message, the method comprising:

• (a) obtaining a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 1×1→2, where 1 and 2 are algebraic groups, and elements P, sPε1, where sε is a secret master key;
• (b) computing a message key gε2 using ê, sP, a private key x and an element rPε1 received from a sender, where rε is a secret of the sender;
• and
• (c) computing the message from the ciphertext using the message key g.

A method for decrypting a ciphertext to produce a message, the method comprising:

• (a) obtaining a secret master key sε and a set of parameters associated with a cryptographic system, wherein the parameters comprise an admissible map ê:
• 1×1→2, where 1 and 2 are algebraic groups;
• (b) obtaining a public key xPε1 corresponding to an intended receiver of the message, where xε is a secret of the intended receiver;
• (c) computing a message key gε2 using ê, the public key xP, the secret master key s, and an element rPε1 received from a sender, where rε is a secret of the sender;
• and
• (d) computing the message from the ciphertext using the message key g.

A method for encrypting an e-mail message addressed to a receiver, the method comprising:

• (a) obtaining a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 0×1→2, where 0, 1 and 2 are algebraic groups;
• (b) selecting a public identifier ID comprising an e-mail address of the receiver;
• (c) computing an element QIDε0 corresponding to the public identifier ID;
• (d) computing a message key gε2 using ê, QID and a randomly selected secret rε;
• and
• (e) computing an encrypted message from the message using the message key g.

A method of generating a decryption key corresponding to an encryption key, wherein the encryption key is based on a first piece of information, the method comprising:

• providing an algebraic group having a group action;
• providing a master key;
• generating the encryption key based on the first piece of information;
• and generating the decryption key based on the group action applied to the master key and the encryption key.

A method for communicating between a sender and a receiver, the method comprising:

• encrypting a message to be sent from the sender to the receiver using an encryption key derived in part from a message identifier;
• sending the encrypted message from the sender to the receiver;
• receiving a request from the receiver for a decryption key, wherein the request includes the message identifier;
• after receiving the request for the decryption key, generating receipt information indicating that the receiver has received the message, and providing the decryption key to the receiver.

A method for communicating between a sender and a receiver, the method comprising:

• obtaining identifying information of the receiver;
• specifying a credential required for the receiver to gain a decryption key;
• deriving an encryption key from the identifying information of the receiver and the credential;
• encrypting a message using the encryption key and a bilinear map;
• sending the encrypted message from a sender to the receiver;
• receiving a request from the receiver of the message for a decryption key;
• determining whether the receiver has the credential;
• if the receiver has the credential, providing the decryption key to the receiver;
• decrypting the encrypted message using the decryption key and the bilinear map.

A system for encrypting a message in an identity-based cryptosystem to produce corresponding ciphertext, the system comprising:

• (a) a resource that obtains a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 0×1→2, where 0, 1 and 2 are (not necessarily distinct) algebraic groups;
• (b) a resource that selects a public identifier ID comprising information identifying an intended receiver of the message;
• (c) a resource that computes an element QIDε0 from the public identifier ID;
• (d) a resource that computes a secret message key gε2 using ê and QID;
• and
• (e) a resource that computes the ciphertext from the message using the message key g.

An electronic message comprising ciphertext computed from a message and a message key g, wherein g is generated by:

• (a) obtaining a set of parameters associated with a cryptographic system, wherein the parameters comprise a bilinear map ê:
• 0×1→2, where 0, 1 and 2 are (not necessarily distinct) algebraic groups;
• (b) selecting a public identifier ID comprising information identifying an intended receiver of the message;
• (c) computing an element QIDε0 from the public identifier ID;
• and (d) computing the message key gε2 using ê and QID.