Secure user identification based on ring homomorphisms
First Claim
1. A method of communicating information between users of a communication system, the method comprising the steps of:
- transmitting from a first user to a second user a result ø
(g) of evaluating an element g in a ring R by a ring homomorphism ø
;
R→
B, wherein the element g satisfies a first set of predetermined conditions;
generating an element h in the ring R as a function of an element c in the ring R satisfying a second set of predetermined conditions, a private key element f of the first user in the ring R, wherein the element f satisfies a third set of predetermined conditions; and
transmitting the element h from the first user to the second user, such that the second user can authenticate the communication from the first user by verifying that the element h satisfies a fourth set of predetermined conditions and by comparing the result ø
(h) of evaluating the element h by the ring homomorphism o to a function of ø
(g), ø
(c), and a public key ø
(f) of the first user.
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Accused Products
Abstract
A method for authenticating, by a second user, the identity of a first user, that includes a challenge communication from the second user to the first user, a response communication from the first user to the second user, and a verification by the second user, includes the steps: selection by the first user of a private key f in a ring R and a public key that includes φ(f) in a ring B that is mapped from f using the ring homomorphism φ: R→B, and publication by the first user of the public key; generation of the challenge communication by the second user that includes selection of a challenge c in the ring R; generation of the response communication by the first user that includes computation of a response comprising h in the ring R, where h is a function of c and f; and performing of a verification by the second user that includes determination of φ(c) from c, φ(h) from h, and an evaluation that depends on φ(h), φ(c) and φ(f).
45 Citations
75 Claims
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1. A method of communicating information between users of a communication system, the method comprising the steps of:
-
transmitting from a first user to a second user a result ø
(g) of evaluating an element g in a ring R by a ring homomorphism ø
;
R→
B, wherein the element g satisfies a first set of predetermined conditions;
generating an element h in the ring R as a function of an element c in the ring R satisfying a second set of predetermined conditions, a private key element f of the first user in the ring R, wherein the element f satisfies a third set of predetermined conditions; and
transmitting the element h from the first user to the second user, such that the second user can authenticate the communication from the first user by verifying that the element h satisfies a fourth set of predetermined conditions and by comparing the result ø
(h) of evaluating the element h by the ring homomorphism o to a function of ø
(g), ø
(c), and a public key ø
(f) of the first user. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
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18. A method of communicating information between users of a communication system, the method comprising the steps of:
-
generating an element h in a ring R as a function of an element g in the ring R satisfying a first set of predetermined conditions, an element c in the ring R satisfying a second set of predetermined conditions, and a private key element f of a first user in the ring R satisfying a third set of predetermined conditions;
transmitting the element h from the first user to a second user, such that the second user can authenticate the communication from the first user by verifying that the element h satisfies a fourth set of predetermined conditions and by using a ring homomorphism ø
;
R+B and verifying that the quantity ø
(h), the quantity ø
(c), and a public key ø
(f) of the first user satisfy a fifth set of predetermined conditions. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
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38. A method for authenticating, by a second user, the identity of a first user, that includes a challenge communication from the second user to the first user, a response communication from the first user to the second user, and a verification by the second user, comprising the steps of:
-
selection by the first user of a private key f in a ring R and a public key that includes φ
(f) in a ring B that is mapped from f using the ring homomorphism φ
;
R→
B, and publication by the first user of the public key;
generation of the challenge communication by the second user that includes selection of a challenge c in the ring R;
generation of the response communication by the first user that includes computation of a response comprising h in the ring R, where h is a function of c and f, and performing of a verification by the second user that includes determination of φ
(c) from c, φ
(h) from h, and an evaluation that depends on φ
(h), φ
(c) and φ
(f). - View Dependent Claims (39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 67, 70, 71, 73)
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62. An authentication method that includes authenticating, by a second user, of a signed digital message of a first user communicated from said first user to said second user, comprising the steps of:
-
selecting by the first user, of a private key f in a ring R and a public key that includes φ
(f) in a ring B that is mapped from f using the ring homomorphism φ
;
R→
B, and publication by the first user of the public key;
selecting, by the first user, of an element g1 in the ring R, determining φ
(g1), and applying a hash function to at least a message m to produce an element c;
generating, by the first user, an element h which is a function of c and f;
communicating, from the first user to the second user, the message m and a digital signature comprising φ
(g1) and h;
determining, by the second user, of the element c, by applying a hash function to at least the message m, and determining, by the second user of φ
(c) from c and φ
(h) from h; and
authenticating, by the second user, of the digital signature, said authenticating including an evaluation that depends on φ
(h), φ
(f) and φ
(c). - View Dependent Claims (63, 64, 65, 66, 68, 69, 72)
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74. A method for use by a first user to prove its identity to a second user who sends a challenge to the first user and wishes to authenticate the identity of the first user, comprising the steps of:
-
selecting a private key f in a ring R and a public key that includes φ
(f) in a ring B that is mapped from f using the ring homomorphism φ
;
R→
B, and publication by the first user of the public key;
receiving the challenge communication from the second user that includes selection of a challenge element c in the ring R; and
generation of the response communication that includes computation of a response comprising h in the ring R, where h is a function of c and f;
whereby the second user can perform a verification that includes determination of φ
(c) from c, φ
(h) from h, and an evaluation that depends on φ
(h), φ
(c) and φ
(f).
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75. A method for producing and sending a signed digital message comprising the steps of:
-
selecting a private key f in a ring R and a public key that includes φ
(f) in a ring B that is mapped from f using the ring homomorphism φ
;
R→
B, and publication by the first user of the public key;
selecting an element g1 in the ring R, determining φ
(g1), and applying a hash function to at least a message m to produce an element c;
generating an element h which is a function of c and f; and
communicating the message m and a digital signature comprising φ
(g1) and h.
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Specification