US6088798A
Expired / Lapsed
US
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Digital signature method using an elliptic curve, a digital signature system, and a program storage medium having the digital signature method stored therein
Assignee: Toshiba Corp
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Filing: 1997-09-26
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Granted: 2000-07-11
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Expires: 2017-09-26
Abstract
Abstract A digital signature method comprises the signature data generating step of, by the use of system information including an elliptic curve E/Fq over a finite field and a base point G on the elliptic curve E/Fq, a signer's public key Y defined by a point on the elliptic curve E/Fq, and the signer's secret key x generated so as to fulfill the public key Y=x·G, generating signature data including not only at least part of data on a point R on the elliptic curve E/Fq dependent on an arbitrarily generated random number k and the base point G on the elliptic curve E/Fq but also an integer s dependent on the plaintext data M, secret key x, and random number k, and the signature checking step of, by the use of an integer m dependent only on the plaintext data M, an integer r dependent on at least the point R of the point R on the elliptic curve E/Fq and the plaintext data M, at least part of data on the point R and the integer s that constitute the signature data, and the system information, and the signer's public key Y, checking a signature by using a relational equation defined as ±s·G=±m·Y±r·R over E/Fq (where the + and - signs are determined by a specific condition) or a relational equation equivalent to the above relational equation as a signature checking equation.
Inventors
- 👤 Atsushi Shimbo
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-09 12:56
CPC Classifications
H; H04; H04L; H04L9/00; H04L9/30; H04L9/3066; H04L9/32; H04L9/3247
Claims Analysis
Total Claims: 28
Claim 1
Independent Claim
146 words
A digital signature method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and checking a signature by confirming that a relational equation defined as ±s·G=±m·Y±r·R over E/Fq is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 2
Dependent Claim
146 words
A digital signature method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and checking a signature by confirming that a relational equation defined as ±s·G=±m·Y±r·R over E/Fq is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 3
Dependent Claim
160 words
A digital signature method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 4
Dependent Claim
160 words
A digital signature method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 5
Dependent Claim
175 words
A digital signature method for generating digital signature data for plaintext data M among n number of signers and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1,2,3, . . . n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i , and the random number k i ; and checking a signature by confirming that a relational equation defined as ±s·G=±m·(Y.sub.1 +Y.sub.2 + . . . +Y.sub.n)±r·R over E/Fq is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 6
Dependent Claim
175 words
A digital signature method for generating digital signature data for plaintext data M among n number of signers and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1,2,3, . . . n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i , and the random number k i ; and checking a signature by confirming that a relational equation defined as ±s·G=±m·(Y.sub.1 +Y.sub.2 + . . . +Y.sub.n)±r·R over E/Fq is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 7
Dependent Claim
200 words
A digital signature method for generating digital signature data for plaintext data M among n number of signers and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 8
Dependent Claim
200 words
A digital signature method for generating digital signature data for plaintext data M among n number of signers and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 9
Dependent Claim
217 words
A digital signature method for generating digital signature data for plaintext data M among n number of signers and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 10
Dependent Claim
217 words
A digital signature method for generating digital signature data for plaintext data M among n number of signers and checking a signature on the basis of the digital signature data, said digital signature method comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 11
Dependent Claim
168 words
A digital signature system for generating digital signature data for plaintext data M and for checking a signature based on the digital signature data, comprising: a signature data generating device comprising means for generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and a signature checking device comprising means for checking a signature by confirming that a relational equation defined by a specific arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 12
Dependent Claim
168 words
A digital signature system for generating digital signature data for plaintext data M and for checking a signature based on the digital signature data, comprising: a signature data generating device comprising means for generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and a signature checking device comprising means for checking a signature by confirming that a relational equation defined by a specific arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 13
Dependent Claim
209 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a signature data generating device comprising means for generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on a random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and a signature checking device comprising means for checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 14
Dependent Claim
209 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a signature data generating device comprising means for generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on a random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and a signature checking device comprising means for checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 15
Dependent Claim
225 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a signature data generating device comprising means for generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and a signature checking device comprising means for checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 16
Dependent Claim
225 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a signature data generating device comprising means for generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and a signature checking device comprising means for checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 17
Dependent Claim
177 words
A computer program storage device including a computer readable medium tangibly embodying a set of instructions from controlling a computing unit to perform a method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, comprising the steps of: generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 18
Dependent Claim
177 words
A computer program storage device including a computer readable medium tangibly embodying a set of instructions from controlling a computing unit to perform a method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, comprising the steps of: generating signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 19
Dependent Claim
212 words
A computer program storage device including a computer readable medium tangibly embodying a set of instructions from controlling a computing unit to perform a method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 20
Dependent Claim
212 words
A computer program storage device including a computer readable medium tangibly embodying a set of instructions from controlling a computing unit to perform a method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 21
Dependent Claim
229 words
A computer program storage device including a computer readable medium tangibly embodying a set of instructions from controlling a computing unit to perform a method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 22
Dependent Claim
229 words
A computer program storage device including a computer readable medium tangibly embodying a set of instructions from controlling a computing unit to perform a method for generating digital signature data for plaintext data M and checking a signature on the basis of the digital signature data, comprising the steps of: generating signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . , n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i ; and checking a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 23
Dependent Claim
159 words
A digital signature system for generating digital signature data for plaintext data M and for checking a signature based on the digital signature data, comprising: a computing unit configured to generate signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k, and to check a signature by confirming that a relational equation defined by a specific arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 24
Dependent Claim
159 words
A digital signature system for generating digital signature data for plaintext data M and for checking a signature based on the digital signature data, comprising: a computing unit configured to generate signature data satisfying public key Y=x·G including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an arbitrarily generated random number k, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x, and the random number k, and to check a signature by confirming that a relational equation defined by a specific arithmetic operation between a first term s·G, a second term m·Y, and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 25
Dependent Claim
200 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a computing unit configured to generate signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i , and to check a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 26
Dependent Claim
200 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a computing unit configured to generate signature data satisfying public key Y i =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R of an elliptic curve E/Fq over a finite field Fq dependent on an random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i , and to check a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term r·R is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 27
Dependent Claim
216 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a computing unit configured to generate signature data satisfying public key Y 1 =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i , and to check a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
Claim 28
Dependent Claim
216 words
A digital signature system for generating digital signature data for plaintext data M among n number of signers and for checking a signature on the basis of the digital signature data, comprising: a computing unit configured to generate signature data satisfying public key Y 1 =x i ·G for (i=1, 2, 3, . . . n) including at least part of data on a point R i of an elliptic curve E/Fq over a finite field Fq dependent on random number k i generated for each of the signers, base point G on the elliptic curve E/Fq, and an integer s dependent on the plaintext data M, secret key x i for each of the signers, and each random number k i , and to check a signature by confirming that a relational equation defined by an arithmetic operation between a first term s·G, a second term m·(Y 1 +Y 2 + . . . +Y n ), and a third term (r 1 ·R 1 +r 2 ·R 2 + . . . +r n ·R n ) is satisfied, wherein s and R constitute the signature data, m is an integer dependent only on the plaintext data M, and r is an integer dependent on at least point R of the elliptic curve E/Fq.
References Cited (Backward Citations)
US5146500A
Cited
JPH0695590A
Cited
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2003-07-11 | 2004-01-10 | 2004-07-11 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2007-07-11 | 2008-01-10 | 2008-07-11 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2011-07-11 | 2012-01-10 | 2012-07-11 | $7700.00 | Window Closed / Lapsed |