Fair blind signature process

A computer-readable medium encoded with a computer program executed on a computing system including a user computing device, a signer computing device and a trusted authority computing device, for causing the computing system to provide a digital signature for a message, comprising:

• program code for generating, by the signer computing device, first parameters comprising elements of a public key of the signer;
• program code for generating second parameters which are chosen uniformly at random by the signer computing device;
• program code for generating third parameters which are chosen uniformly at random by the user computing device;
• program code for calculating, by the user computing device, a code to identify said user computing device;
• program code for calculating, by the user computing device, an intermediate value based on a parameter chosen uniformly at random by the user computing device and on a parameter chosen uniformly at random by the signer computing device;
• program code for calculating, by the user computing device, an additional parameter in accordance with the relationship:
• C2=a1xa2ma4t (mod n);
• and
• program code for issuing the digital signature by:
• obtaining, by the user computing device, data from the signer computing device to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are said first parameters,
• m is said message to be signed,
• e and s are said second parameters,
• t and xu are said third parameters,
• x is said intermediate value,
• IdU is said code which identifies the user computing device,
• C2 is said additional parameter, and
• A is another parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n);
• and
• generating, by the user computing device, the digital signature based on said data obtained by the user computing device from the signer computing device.

A digital signature generating system configured to implement a fair blind digital signature scheme in which a user interacts with a signer in a signature-issuing phase to obtain the fair blind digital signature of a message, wherein the signer has a public key and anonymity of the digital signature is revocable by a trusted authority, the signature system comprising:

• a user apparatus;
• signer apparatus;
• and
• trusted authority apparatus;
• wherein the user apparatus is configured to cooperate with said signer apparatus to perform a signature-issuing protocol;
• wherein the trusted authority apparatus and the signer apparatus are configured to cooperate to perform a tracing protocol;
• wherein the user apparatus and the signer apparatus are configured to perform the signature-issuing protocol to provide the user apparatus with data from the signer apparatus to enable said user apparatus to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of the public key of the signer and are generated at the signer apparatus,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random at the signer apparatus,
• t and xu are parameters chosen uniformly at random at the user apparatus,
• x is an intermediate value calculated at the user apparatus based on a parameter chosen uniformly at random at the user apparatus and on a parameter chosen uniformly at random at the signer apparatus, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n),
• where C2 is a parameter calculated at the user apparatus in accordance with the relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed at the user apparatus to identify said user apparatus;
• and
• wherein the user apparatus is configured to generate said digital signature based on said data obtained by said user apparatus from the signer apparatus during performance of the signature-issuing protocol.

User apparatus configured to participate in a fair blind digital signature scheme in which a user interacts with a signer in a signature-issuing phase to obtain a fair blind digital signature for a message, wherein the signer has a public key and anonymity of the digital signature is revocable by a trusted authority, the user apparatus comprising:

• message providing means for providing the message;
• and
• signature request means for emitting to the apparatus of the signer a request for the digital signature of said message according to a predetermined signature-issuing protocol;
• wherein the user apparatus is configured to cooperate with the apparatus of the signer to perform said signature-issuing protocol;
• wherein performance of said signature-issuing protocol provides the user apparatus with data from the apparatus of the signer to enable said user apparatus to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of the public key of the signer and are generated at the apparatus of the signer,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random at the apparatus of the signer,
• t and xu are parameters chosen uniformly at random at the user apparatus,
• x is an intermediate value calculated at the user apparatus based on a parameter chosen uniformly at random at the user apparatus and on a parameter chosen uniformly at random at the apparatus of the signer, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n),
• where C2 is a parameter calculated at the user apparatus in accordance with the following relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed at the user apparatus to identify said user;
• and
• wherein the user apparatus comprises digital signature generating means for generating the digital signature of said message based on data obtained by the user apparatus from the apparatus of the signer during performance of said signature-issuing protocol.

A computer-readable medium encoded with a computer program executed by a computer which causes a user apparatus to participate in a fair blind digital signature scheme in which the user apparatus interacts with the apparatus of a signer in a signature-issuing phase to obtain a fair blind digital signature for a message, comprising:

• program code for providing the message;
• and
• program code for emitting to the apparatus of the signer a request for the digital signature of said message according to a predetermined signature-issuing protocol;
• wherein the user apparatus is configured to cooperate with the apparatus of the signer to perform said signature-issuing protocol;
• wherein performance of said signature-issuing protocol provides the user apparatus with data from the apparatus of the signer to enable said user apparatus to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of the public key of the signer and are generated at the apparatus of the signer,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random at the apparatus of the signer,
• t and xu are parameters chosen uniformly at random at the user apparatus,
• x is an intermediate value calculated at the user apparatus based on a parameter chosen uniformly at random at the user apparatus and on a parameter chosen uniformly at random at the apparatus of the signer, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n),
• where C2 is a parameter calculated at the user apparatus in accordance with the following relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed at the user apparatus to identify said user;
• and
• wherein the user apparatus comprises digital signature generating means for generating the digital signature of said message based on data obtained by the user apparatus from the apparatus of the signer during performance of said signature-issuing protocol.

Signer apparatus configured to participate in a fair blind digital signature scheme in which an apparatus of a user interacts with the signer apparatus in a signature-issuing phase to obtain a fair blind digital signature of a message, wherein the signer has a public key and anonymity of the digital signature is revocable by a trusted authority, the signer apparatus comprising:

• request receiving means for receiving, from the apparatus of the user, a request for the digital signature of said message;
• and
• signature-protocol-implementation means for cooperating with said apparatus of the user to perform a predetermined signature-issuing protocol;
• wherein the signature-protocol-implementation means is configured to perform a signature-issuing protocol which provides the apparatus of the user with data for enabling the apparatus of the user to generate said digital signature and for enabling said apparatus of the user to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of the public key of the signer and are generated at the signer apparatus,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random at the signer apparatus,
• t and xu are parameters chosen uniformly at random at the apparatus of the user,
• x is an intermediate value calculated at the apparatus of the user based on a parameter chosen uniformly at random at the apparatus of the user and on a parameter chosen uniformly at random at the signer apparatus, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n),
• where C2 is a parameter calculated at the user apparatus in accordance with the following relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed at the user apparatus to identify said apparatus of the user.

A computer-readable medium encoded with a computer program executed on a computer apparatus which causes the computer apparatus to function as a signer apparatus and participate in a fair blind digital signature scheme in which an apparatus of a user interacts with the signer apparatus in a signature-issuing phase to obtain the fair blind digital signature for a message, comprising:

• program code for receiving, from the apparatus of the user, a request for the digital signature of said message;
• and
• program code for cooperating with said apparatus of the user to perform a predetermined signature-issuing protocol;
• wherein the program code for cooperating with said apparatus of the user to perform the predetermined signature-issuing protocol causes execution of the signature-issuing protocol which provides the apparatus of the user with data for enabling the apparatus of the user to generate said digital signature and for enabling said apparatus of the user to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of a public key of a signer of the message and are generated at the signer apparatus,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random at the signer apparatus,
• t and xu are parameters chosen uniformly at random at the apparatus of the user,
• x is an intermediate value calculated at the apparatus of the user based on a parameter chosen uniformly at random at the apparatus of the user and on a parameter chosen uniformly at random at the signer apparatus, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n),
• where C2 is a parameter calculated at the user apparatus in accordance with the relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed at the user apparatus to identify said apparatus of the user.

Trusted authority apparatus configured to participate in a fair blind digital signature scheme in which an apparatus of a user interacts with an apparatus of a signer in a signature-issuing phase to obtain a fair blind digital signature for a message, the signer having a public key;

• wherein said trusted authority apparatus is configured to revoke anonymity of a digital signature issued according to a signature-issuing protocol whose performance provides the apparatus of the user with data from the apparatus of the signer for enabling said apparatus of the user to generate the digital signature and for enabling the apparatus of the user to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of the public key of the signer and are generated by the apparatus of the signer,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random by the apparatus of the signer,
• t and xu are parameters chosen uniformly at random by the apparatus of the user,
• x is an intermediate value calculated by the apparatus of the user based on a parameter chosen uniformly at random by the apparatus of the user and on a parameter chosen uniformly at random by the apparatus of the signer, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n),
• where C2 is a parameter calculated by the apparatus of the user in accordance with the relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed by the user to identify said apparatus of the user.

A computer-readable medium encoded with a computer program executed on a computer apparatus which causes the computer apparatus to function as a trusted authority apparatus and participate in a fair blind digital signature scheme in which an apparatus of a user interacts with an apparatus of a signer in a signature-issuing phase to obtain a fair blind digital signature for a message, wherein the signer has a public key, comprising:

• program code for revoking anonymity of a digital signature issued according to a signature-issuing protocol whose performance provides the apparatus of the user with data from the apparatus of the signer for enabling said apparatus of the user to generate the digital signature and for enabling the apparatus of the user to complete a 7-tuple in accordance with the relationship:
• Ae=a0a1xa2ma3xua4ta5s(mod n),
• where a0, a1, a2, a3, a4 and a5 and n are elements of the public key of the signer and are generated by the apparatus of the signer,
• m is said message to be signed,
• e and s are parameters chosen uniformly at random by the apparatus of the signer,
• t and xu are parameters chosen uniformly at random by the apparatus of the user,
• x is an intermediate value calculated by the apparatus of the user based on a parameter chosen uniformly at random by the apparatus of the user and on a parameter chosen uniformly at random by the apparatus of the signer, and
• A is a parameter calculated in accordance with the relationship:
• A=(a0C2a5sIdU)1/e(mod n)
• where C2 is a parameter calculated by the apparatus of the user in accordance with the relationship:
• C2=a1xa2ma4t(mod n), and
• IdU is a code computed by the user to identify said apparatus of the user.