1. A method comprising:
identifying data to be signed;
establishing parameter data for use with signature generating logic that encrypts data based on a Jacobian of a curve, said Jacobian having a genus exceeding one, said parameter data causing said signature generating logic to select at least one Gap Diffie-Hellman (GDH) group of elements relating to said curve;
determining private key data and corresponding public key data using said signature generating logic; and
signing said identified data with said private key data using said signature generating logic to create a corresponding digital signature.
2. The method as recited in claim 1, wherein said identified data includes a message m \u2208 {0, 1}*.
3. The method as recited in claim 2, wherein said parameter data establishes a base group G and a generator g as system parameters for said signature generating logic.
4. The method as recited in claim 3, wherein determining said private key data and said public key data includes:
picking
x
\u2062
\u2190
R
\u2062
Z
p
*
;
and
computing \u03bd\u2190gx, wherein said public key data includes \u03bd and said private key data includes x.
5. The method as recited in claim 4, wherein signing said identified data using with said private key data using said signature generating logic further includes:
determining h\u2190h(m), and \u03c3\u2190hx, using at least one hash function, said private key data x and said message m, wherein said digital signature includes \u03c3.
6. The method as recited in claim 5, wherein said hash function includes a full-domain hash function h: {0, 1}*\u2192G.
7. The method as recited in claim 5, wherein said hash function includes a hash function h\u2032: {0, 1}*\u2192G \u222a {\u22a5}, that outputs an element of G or \u22a5 indicating a failure.
8. The method as recited in claim 1, further comprising:
outputting said digital signature.
9. The method as recited in claim 8, further comprising:
determining if said digital signature is valid using signature verifying logic.
10. The method as recited in claim 9, wherein said signature verifying logic is configured using said parameter data and said parameter data establishes a base group G and a generator g as system parameters for said signature verifying logic.
11. The method as recited in claim 10, wherein:
said public key data includes public key data \u03bd;
said identified data includes a message m;
said digital signature includes signature \u03c3; and
determining if said digital signature is valid using said signature verifying logic further includes:
determining h\u2190h(m) using at least one hash function, and
verifying that (g, \u03bd, h, \u03c3) is a valid Gap Diffie-Hellman tuple.
12. The method as recited in claim 1, wherein said digital signature is included in a product ID.
13. A computer-readable medium having computer implementable instructions for causing at least one processing unit to perform acts comprising:
providing signature generating logic capable of digitally signing identified data;
configuring said signature generating logic using parameter data, said signature generating logic being configured to digitally sign said identified data based on a Jacobian of a curve, said Jacobian having a genus greater than one, said parameter data causing said signature generating logic to select at least one Gap Diffie-Hellman (GDH) group of elements relating to said curve;
determining private key data and corresponding public key data using said signature generating logic; and
signing said identified data with said private key data using said signature generating logic to create a corresponding digital signature.
14. The computer-readable medium as recited in claim 13, wherein said identified data includes a message m \u2208 {0, 1}*.
15. The computer-readable medium as recited in claim 14, wherein said parameter data establishes a base group G and a generator g as system parameters for said signature generating logic.
16. The computer-readable medium as recited in claim 15, wherein determining said private key data and said public key data includes:
picking
x
\u2062
\u2190
R
\u2062
Z
p
*
;
and
computing \u03bd\u2190gx, wherein said public key data includes \u03bd and said private key data includes x.
17. The computer-readable medium as recited in claim 16, wherein signing said identified data using with said private key data using said signature generating logic further includes:
determining h\u2190h(m), and \u03c3\u2190hx, using at least one hash function, said private key data x and said message m, wherein said digital signature includes \u03c3.
18. The computer-readable medium as recited in claim 17, wherein said hash function includes a full-domain hash function h: {0, 1}*\u2192G.
19. The computer-readable medium as recited in claim 17, wherein said hash function includes a hash function h\u2032: {0, 1}*\u2192G \u222a {\u22a5}, that outputs an element of G or \u22a5 indicating a failure.
20. The computer-readable medium as recited in claim 13, further comprising:
outputting said digital signature.
21. The computer-readable medium as recited in claim 20, further comprising:
determining if said digital signature is valid using signature verifying logic.
22. The computer-readable medium as recited in claim 21, wherein said signature verifying logic is configured using said parameter data and said parameter data establishes a base group G and a generator g as system parameters for said signature verifying logic.
23. The computer-readable medium as recited in claim 22, wherein:
said public key data includes public key data \u03bd;
said identified data includes a message m;
said digital signature includes signature \u03c3; and
determining if said digital signature is valid using said signature verifying logic further includes:
determining h\u2190h(m) using at least one hash function, and
verifying that (g, \u03bd, h, \u03c3) is a valid Gap Diffie-Hellman tuple.
24. An apparatus comprising:
memory configured to store identifying data that is to be signed;
signature generating logic that encrypts data based on a Jacobian of a curve, said Jacobian having a genus greater than one, said signature generating logic being operatively coupled to said memory and configurable using parameter data, 11said parameter data causing said signature generating logic to select at least one Gap Diffie-Hellman (GDH) group of elements relating to said curve, and wherein said signature generating logic determines private key data and corresponding public key data, and then signs said identified data with said private key data to create a corresponding digital signature.
25. The apparatus as recited in claim 24, wherein said identified data includes a message m \u2208 {0, 1}*.
26. The apparatus as recited in claim 25, wherein said parameter data establishes a base group G and a generator g as system parameters for said signature generating logic.
27. The apparatus as recited in claim 26, wherein said signature generating logic determines said private key data and said public key data by: picking
x
\u2062
\u2190
R
\u2062
Z
p
*
;
and
computing \u03bd\u2190gx, wherein said public key data includes \u03bd and said private key data includes x.
28. The apparatus as recited in claim 27, wherein said signature generating logic is further configured to:
determine h\u2190h(m), and \u03c3\u2190hx, using at least one hash function, said private key data x and said message m, wherein said digital signature includes \u03c3.
29. The apparatus as recited in claim 28, wherein said hash function includes a full-domain hash function h: {0, 1}*\u2192G.
30. The apparatus as recited in claim 28, wherein said hash function includes a hash function h\u2032: {0, 1}*\u2192G \u222a {\u22a5}, that outputs an element of G or \u22a5 indicating a failure.
31. The apparatus as recited in claim 24, wherein said signature generating logic is further configured to output said digital signature.
32. The apparatus as recited in claim 31, further comprising:
signature verifying logic operatively coupled to receive said output digital signature and determine if said digital signature is valid.
33. The apparatus as recited in claim 32, wherein said signature verifying logic is configured using said parameter data and said parameter data establishes a base group G and a generator g as system parameters for said signature verifying logic.
34. The apparatus as recited in claim 33, wherein:
said public key data includes public key data \u03bd;
said identified data includes a message m;
said digital signature includes signature \u03c3; and
said signature verifying logic determines if said digital signature is valid by determining h\u2190h(m) using at least one hash function, and verifying that (g, \u03bd, h, \u03c3) is a valid Gap Diffie-Hellman tuple.
35. The apparatus as recited in claim 24, wherein said digital signature is included in a product ID.
36. A method comprising:
receiving message data and a corresponding digital signature and public key data;
using parameter data configure signature verifying logic that performs cryptography operations based on a Jacobian of a curve, said Jacobian having a genus greater than one, said parameter data causing said signature verifying logic to select at least one Gap Diffie-Hellman (GDH) group of elements relating to said curve; and
with said signature verifying logic, determining if said digital signature is valid using said public key data and said message data.
37. The method as recited in claim 36, wherein said message data includes a message m \u2208 {0, 1}*.
38. The method as recited in claim 37, wherein said parameter data establishes a base group G and a generator g as system parameters for said signature verifying logic.
39. The method as recited in claim 38, wherein:
said public key data includes public key data \u03bd;
said digital signature includes signature \u03c3; and
determining if said digital signature is valid further includes:
determining h\u2190h(m) using at least one hash function, and
verifying that (g, \u03bd, h, \u03c3) is a valid Gap Diffie-Hellman tuple.
40. The method as recited in claim 39, wherein said hash function includes a full-domain hash function h: {0, 1}*\u2192G.
41. The method as recited in claim 39, wherein said hash function includes a hash function h\u2032: {0, 1}*\u2192G \u222a {\u22a5}, that outputs an element of G or \u22a5 indicating a failure.
42. A computer-readable medium having computer implementable instructions for causing at least one processing unit to perform acts comprising:
receiving message data and a corresponding digital signature and public key data;
using parameter data configure signature verifying logic that performs cryptography operations based on a Jacobian of a curve, said Jacobian having a genus greater than one, said parameter data causing said signature verifying logic to select at least one Gap Diffie-Hellman (GDH) group of elements relating to said curve; and
with said signature verifying logic, determining if said digital signature is valid using said public key data and said message data.
43. The computer-readable medium as recited in claim 42, wherein said message data includes a message m \u2208 {0, 1}*.
44. The computer-readable medium as recited in claim 43, wherein said parameter data establishes a base group G and a generator g as system parameters for said signature verifying logic.
45. The computer-readable medium as recited in claim 44, wherein:
said public key data includes public key data \u03bd;
said digital signature includes signature \u03c3; and
determining if said digital signature is valid further includes:
determining h\u2190h(m) using at least one hash function, and
verifying that (g, \u03bd, h, \u03c3) is a valid Gap Diffie-Hellman tuple.
46. The computer-readable medium as recited in claim 45, wherein said hash function includes a full-domain hash function h: {0, 1})*\u2190G.
47. The computer-readable medium as recited in claim 45, wherein said hash function includes a hash function h\u2032: {0, 1}*\u2192G \u222a {\u22a5}, that outputs an element of G or \u22a5 indicating a failure.
48. A method comprising:
identifying data to be signed;
establishing parameter data for use with signature generating logic that encrypts data based on a Weil pairing on a Jacobian of at least one super-singular curve having a genus greater than one;
determining private key data and corresponding public key data using said signature generating logic; and
signing said identified data with said private key data using said signature generating logic to create a corresponding digital signature.
49. The method as recited in claim 48, wherein said identified data includes a message m \u2208 {0, 1}*.
50. The method as recited in claim 49, wherein said signature generating logic establishes EFpl as an algebraic curve having genus g equal to at least two, J being a corresponding Jacobian, such that P, Q \u2208 J are linearly independent points of order q and P\u2208 JFpl and Q\u2208 JFpla.
51. The method as recited in claim 50, wherein determining said private key data and said public key data includes:
picking
x
\u2062
\u2190
R
\u2062
Z
q
*
,
and
computing R\u2190xQ, wherein said public key data includes R and said private key data includes x.
52. The method as recited in claim 51, wherein signing said identified data using with said private key data using said signature generating logic further includes:
determining Pm\u2190h(m)\u2208 JFpl, and Sm\u2190xPm, wherein said digital signature includes \u03c3, which is an x-coordinate of g points in a representation of Sm as a reduced divisor.
53. The method as recited in claim 48, further comprising:
outputting said digital signature.
54. The method as recited in claim 53, further comprising:
determining if said digital signature is valid using signature verifying logic.
55. The method as recited in claim 54, wherein said signature verifying logic is configured to:
receive said public key as R, said identified data as a message m, and said digital signature as \u03c3,
determine that said digital signature is valid for message m using said public key data R, if u=\u03bd after letting S be a point on JFpl whose x-coordinates is in \u03c3 and whose y-coordinate is y for some y\u2208 Fpl, and by setting u\u2190e(P,S) and \u03bd\u2190e(R, \u03c6(h(m)));
otherwise determining that said digital signature \u03c3 is invalid.
56. The method as recited in claim 48, wherein said digital signature is included in a product ID.
57. A computer-readable medium having computer implementable II instructions for causing at least one processing unit to perform acts comprising:
identifying data to be signed;
establishing parameter data for use with signature generating logic that encrypts data based on a Weil pairing on a Jacobian of at least one super-singular curve having a genus greater than one;
determining private key data and corresponding public key data using said signature generating logic; and
signing said identified data with said private key data using said signature generating logic to create a corresponding digital signature.
58. The computer-readable medium as recited in claim 57, wherein said identified data includes a message m \u2208 {0, 1}*.
59. The computer-readable medium as recited in claim 58, wherein said signature generating logic establishes EFpl as an algebraic curve having genus g equal to at least two, J being a corresponding Jacobian, such that P, Q \u2208 J are linearly independent points of order q and P\u2208 JFpl and Q\u2208 JFpla.
60. The computer-readable medium as recited in claim 59, wherein determining said private key data and said public key data includes:
picking
x
\u2062
\u2190
R
\u2062
Z
q
*
,
and
computing R\u2190xQ, wherein said public key data includes R and said private key data includes x.
61. The computer-readable medium as recited in claim 60, wherein signing said identified data using with said private key data using said signature generating logic further includes:
determining Pm\u2190h(m)\u2208 JFpl, and Sm\u2190xPm, wherein said digital signature includes \u03c3, which is an x-coordinate of g points in a representation of Sm as a reduced divisor.
62. The computer-readable medium as recited in claim 57, further comprising:
outputting said digital signature.
63. The computer-readable medium as recited in claim 62, further comprising:
determining if said digital signature is valid using signature verifying logic.
64. The computer-readable medium as recited in claim 63, wherein said signature verifying logic is configured to:
receive said public key as R, said identified data as a message m, and said digital signature as \u03c3,
determine that said digital signature is valid for message m using said public key data R, if u=\u03bd after letting S be a point on JFpl whose x-coordinates is in \u03c3 and whose y-coordinate is y for some y\u2208 Fpl, and by setting u\u2190e(P,S) and \u03bd\u2190e(R, \u03c6(h(m)));
otherwise determining that said digital signature \u03c3 is invalid.
65. An apparatus comprising:
memory configured to store identifying data to be signed;
signature generating logic that is configured using parameter data such that said signature generating logic encrypts data based on a Weil pairing on a Jacobian of at least one super-singular curve having a genus greater than one, and determines private key data and corresponding public key data and signs said identified data with said private key data using said signature generating logic to create a corresponding digital signature.
66. The apparatus as recited in claim 65, wherein said identified data includes a message m \u2208 {0, 1}*.
67. The apparatus as recited in claim 66, wherein said signature generating logic establishes EFpl as an algebraic curve having genus g equal to at least two, J being a corresponding Jacobian, such that P, Q \u2208 J are linearly independent points of order q and P\u2208 JFpl and Q\u2208 JFpla.
68. The apparatus as recited in claim 67, wherein said signature generating logic is further configured to:
pick xR\u2190Zq*, and
determine R\u2190xQ, wherein said public key data includes R and said private key data includes x.
69. The apparatus as recited in claim 68, wherein said signature generating logic is further configured to:
determine Pm\u2190h(m)\u2208 JFpl, and Sm\u2190\u2192xPm, wherein said digital signature includes \u03c3, which is an x-coordinate of g points in a representation of Sm as a reduced divisor.
70. The apparatus as recited in claim 65, wherein said signature generating logic is further configured to:
output said digital signature.
71. The apparatus as recited in claim 70, further comprising:
signature verifying logic configured to receive said output digital signature and determine if said digital signature is valid.
72. The apparatus as recited in claim 71, wherein said signature verifying logic is configured to:
receive said public key as R, said identified data as a message m, and said digital signature as \u03c3;
determine that said digital signature is valid for message m using said public key data R, if u=\u03bd after letting S be a point on JFpl whose x-coordinates is in \u03c3 and whose y-coordinate is y for some y\u2208 Fpl, and by setting u\u2190e(P,S) and \u03bd\u2190e(R, \u03c6(h(m)));
otherwise determining that said digital signature \u03c3 is invalid.
73. The apparatus as recited in claim 65, wherein said digital signature is included in a product ID.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method of transmitting response information, comprising:
determining, by a base station, at least two Physical Uplink Control Channel (PUCCH) transmission carriers and notifying a User Equipment (UE) of the at least two PUCCH transmission carriers;
determining, by the base station, configuration information for PUCCH transmission by the UE and transmitting the configuration information to the UE; and
receiving, by the base station, in a sub-frame n, response information transmitted from the UE over at least one PUCCH transmission carrier;
wherein the PUCCH transmission carrier for transmission of the response information is determined from the at least two PUCCH transmission carriers of which the UE is notified by the base station.
2. The method according to claim 1, wherein notifying, by the base station, the UE of the at least two PUCCH transmission carriers comprises:
notifying, by the base station, the UE of the at least two PUCCH transmission carriers in higher-layer signaling.
3. The method according to claim 1, wherein transmitting, by the base station, the configuration information to the UE comprises:
transmitting, by the base station, the configuration information to the UE in higher-layer signaling andor downlink control signaling.
4. The method according to claim 1, wherein the at least two PUCCH transmission carriers determined by the base station comprise a first PUCCH transmission carrier, wherein the first PUCCH transmission carrier is an uplink primary carrier or a carrier with a largest coverage radius among a plurality of uplink carriers aggregated for the UE.
5. (canceled)
6. The method according to claim 1, wherein the configuration information comprises:
information about a set of downlink carriers corresponding to each of the at least two PUCCH transmission carriers; andor
priority information corresponding respectively to the at least two PUCCH transmission carriers.
7. A method of transmitting response information, comprising:
obtaining, by a User Equipment (UE), at least two Physical Uplink Control Channel (PUCCH) transmission carriers;
determining, by the UE, at least one of the at least two PUCCH transmission carriers in a sub-frame n for transmission of response information; and
transmitting, by the UE, the response information over the determined PUCCH transmission carrier in the sub-frame n.
8. The method according to claim 7, wherein before the response information is transmitted over the determined PUCCH transmission carrier in the sub-frame n, the method further comprises:
receiving, by the UE, configuration information transmitted from a base station, wherein the configuration information comprises PUCCH resources over the PUCCH transmission carriers; andor
determining, by the UE, PUCCH resources over the PUCCH transmission carriers according to Control Channel Element (CCE) indexes, wherein the CCE indexes are indexes of CCEs occupied by a Physical Downlink Control Channel (PDCCH) by which the base station schedules a Physical Downlink Shared Channel (PDSCH).
9. The method according to claim 7, wherein before the UE determines at least one of the at least two PUCCH transmission carriers in the sub-frame n for transmission of response information, the method further comprises:
determining, by the UE, sub-frames to transmit response information corresponding to respective downlink sub-frames over each downlink carrier, wherein different downlink carriers correspond to one or more response information feedback timing relationships.
10. The method according to claim 7, wherein the obtaining, by the UE, the at least two PUCCH transmission carriers comprises: receiving, by the UE, the at least two PUCCH transmission carriers notified of by a base station in higher-layer signaling.
11. (canceled)
12. The method according to claim 7, wherein the at least two PUCCH transmission carriers obtained by the UE comprises a first PUCCH transmission carrier, wherein the first PUCCH transmission carrier is an uplink primary carrier or a carrier with a largest coverage radius among a plurality of uplink carriers aggregated for the UE.
13. (canceled)
14. The method according to claim 7, wherein the method further comprises:
receiving, by the UE, configuration information transmitted from the base station, wherein the configuration information comprises:
information about a set of downlink carriers corresponding to each of the at least two PUCCH transmission carriers; andor
priority information corresponding respectively to the at least two PUCCH transmission carriers.
15. The method according to claim 7, wherein determining, by the UE, the at least one of the at least two PUCCH transmission carriers in the sub-frame n for transmission of response information comprises:
selecting, from the at least two PUCCH transmission carriers, a PUCCH transmission carrier with the sub-frame n being an uplink sub-frame and with a highest priority as a PUCCH transmission carrier for transmission of response information; or
obtaining, by the UE, sets of downlink carriers corresponding to respective PUCCH transmission carriers and selecting, from the at least two PUCCH transmission carriers, a PUCCH transmission carrier, corresponding to the set of downlink carriers comprising carriers for which response information needs to be fed back in the sub-frame n and with a highest priority, as a PUCCH transmission carrier for transmission of response information; or
obtaining, by the UE, sets of downlink carriers corresponding to respective PUCCH transmission carriers, and when response information needs to be fed back in the sub-frame n for carriers in a set of downlink carriers, determining the PUCCH transmission carriers corresponding to the set of downlink carriers to be a PUCCH transmission carrier for transmission of response information;
wherein the priorities of the PUCCH transmission carriers are determined according to configuration information transmitted from a base station or preset by a system.
16. (canceled)
17. (canceled)
18. The method according to claim 1, wherein receiving, by the base station, in the sub-frame n, the response information transmitted from the UE over the at least one PUCCH transmission carrier comprises:
when feedback response information corresponding to scheduled downlink data is transmitted in the sub-frame n, the base station receiving the feedback response information over the PUCCH transmission carrier with the sub-frame n being an uplink sub-frame and with a highest priority among the at least two PUCCH transmission carriers, wherein the priorities are configured by the base station in higher-layer signaling or preset by a system; or
the base station receiving feedback response information over the PUCCH transmission carrier with a highest priority among PUCCH transmission carriers corresponding to sets of downlink carriers over which data transmission is scheduled and for which corresponding feedback response information is transmitted in the sub-frame n, wherein the priorities are configured by the base station in higher-layer signaling or preset by a system; or
the base station receiving the response information respectively over PUCCH transmission carriers corresponding to sets of downlink carriers over which data transmission is scheduled and for which corresponding feedback response information is transmitted in the sub-frame n.
19. An apparatus for transmitting response information, comprising:
a first PUCCH transmission carrier determination unit configured to determine at least two Physical Uplink Control Channel (PUCCH) transmission carriers;
a PUCCH transmission carrier notification unit configured to notify a User Equipment (UE) of the at least two PUCCH transmission carriers determined by the PUCCH transmission carrier determination unit;
a configuration information determination unit configured to determine configuration information for PUCCH transmission by the UE;
a configuration information transmission unit configured to transmit the configuration information determined by the configuration information determination unit to the UE;
a second PUCCH transmission carrier determination unit configured to determine at least one PUCCH transmission carrier for transmission of response information by a UE, wherein the PUCCH transmission carrier for transmission of response information is determined from the at least two PUCCH transmission carriers of which the UE is notified by a base station; and
an response information reception unit configured to receive the response information transmitted from the UE over the at least one PUCCH transmission carrier in a sub-frame n.
20. (canceled)
21. (canceled)
22. The apparatus according to claim 19, wherein the first PUCCH transmission carrier determination unit is configured to determine that the at least two PUCCH transmission carriers comprise a first PUCCH transmission carrier, wherein the first PUCCH transmission carrier is an uplink primary carrier or a carrier with a largest coverage radius among a plurality of uplink carriers aggregated for the UE.
23. (canceled)
24. The apparatus according to claim 19, wherein the configuration information determination unit is configured to determine information about a set of downlink carriers corresponding to each of the at least two PUCCH transmission carriers; andor to determine priority information corresponding respectively to the at least two PUCCH transmission carriers.
25. An apparatus for transmitting response information, comprising:
an obtainment unit configured to obtain at least two Physical Uplink Control Channel (PUCCH) transmission carriers;
a PUCCH transmission carrier determination unit configured to determine at least one of the at least two PUCCH transmission carriers, obtained by the obtainment unit, in a sub-frame n for transmission of response information; and
a response information transmission unit configured to transmit the response information over the PUCCH transmission carrier determined by the PUCCH transmission carrier determination unit in the sub-frame n.
26-29. (canceled)
30. The apparatus according to claim 25, wherein the obtainment unit is configured to obtain the at least two PUCCH transmission carriers comprising a first PUCCH transmission carrier, wherein the first PUCCH transmission carrier is an uplink primary carrier or a carrier with a largest coverage radius among a plurality of uplink carriers aggregated for a UE.
31. (canceled)
32. The apparatus according to claim 25, wherein the obtainment unit is further configured to receive configuration transmitted from a base station, wherein the configuration information comprises: information about a set of downlink carriers corresponding to each of the at least two PUCCH transmission carriers; andor priority information corresponding respectively to the at least two PUCCH transmission carriers.
33-35. (canceled)
36. The apparatus according to claim 19, wherein the response information reception unit is configured:
when feedback response information corresponding to scheduled downlink data is transmitted in the sub-frame n, to receive the feedback response information over the PUCCH transmission carrier with the sub-frame n being an uplink sub-frame and with a highest priority among the at least two PUCCH transmission carriers, wherein the priorities are configured by the base station in higher-layer signaling or preset by a system; or
to receive the response information over the PUCCH transmission carrier with a highest priority among PUCCH transmission carriers corresponding to sets of downlink carriers over which data transmission is scheduled and for which corresponding feedback response information is transmitted in the sub-frame n, wherein the priorities are configured by the base station in higher-layer signaling or preset by a system; or
to receive the response information respectively over PUCCH transmission carriers corresponding to sets of downlink carriers over which data transmission is scheduled and for which corresponding feedback response information is transmitted in the sub-frame n.
37. (canceled)