Patents by Inventor Adrian Antipa
Adrian Antipa has filed for patents to protect the following inventions. This listing includes patent applications that are pending as well as patents that have already been granted by the United States Patent and Trademark Office (USPTO).
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Patent number: 8284930Abstract: In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ, several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.Type: GrantFiled: July 6, 2011Date of Patent: October 9, 2012Assignee: Certicom Corp.Inventors: Adrian Antipa, Yuri Poeluev
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Publication number: 20120230494Abstract: Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as ?zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.Type: ApplicationFiled: May 23, 2012Publication date: September 13, 2012Inventors: Marinus Struik, Daniel R. Brown, Scott A. Vanstone, Robert P. Gallant, Adrian Antipa, Robert J. Lambert
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Patent number: 8204232Abstract: Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as ?zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.Type: GrantFiled: January 18, 2006Date of Patent: June 19, 2012Assignee: Certicom Corp.Inventors: Marinus Struik, Daniel R. Brown, Scott A. Vanstone, Robert P. Gallant, Adrian Antipa, Robert J. Lambert
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Publication number: 20120072975Abstract: An authentication system is provided. The authentication system comprises a first component configured to obtain information specific to an individual, a second component configured to dynamically formulate at least one challenge question based on the information, a third component configured to cause the at least one challenge question to be presented on a device when the device is used to perform an act that involves authentication, and a fourth component configured to judge authenticity based on an answer to the at least one challenge question.Type: ApplicationFiled: March 21, 2011Publication date: March 22, 2012Applicants: CERTICOM CORP., RESEARCH IN MOTION LIMITEDInventors: Christopher Labrador, Adrian Antipa, Russ F. Marsden
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Publication number: 20110261956Abstract: In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ, several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.Type: ApplicationFiled: July 6, 2011Publication date: October 27, 2011Applicant: CERTICOM CORP.Inventors: Adrian Antipa, Yuri Poeluev
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Patent number: 8045705Abstract: In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.Type: GrantFiled: November 3, 2006Date of Patent: October 25, 2011Assignee: Certicom Corp.Inventors: Adrian Antipa, Yuri Poeluev
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Patent number: 7412062Abstract: The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar. The applicants have also recognized that the representation of a scalar in a ?-adic representation may be optimized for each scalar that is needed. The applicants have further recognized that a standard rounding algorithm may be used to perform reduction modulo the truncator. In general terms, there is provided a method of reducing a scalar modulo a truncator, by pre-computing an inverse of the truncator. Each scalar multiplication then utilizes the pre-computed inverse to enable computation of the scalar multiplication without requiring a division by the truncator for each scalar multiplication.Type: GrantFiled: March 19, 2007Date of Patent: August 12, 2008Assignee: Certicom Corp.Inventors: Robert J. Lambert, Ashok Vadekar, Adrian Antipa
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Publication number: 20070217601Abstract: The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar. The applicants have also recognized that the representation of a scalar in a ?-adic representation may be optimized for each scalar that is needed. The applicants have further recognized that a standard rounding algorithm may be used to perform reduction modulo the truncator. In general terms, there is provided a method of reducing a scalar modulo a truncator, by pre-computing an inverse of the truncator. Each scalar multiplication then utilizes the pre-computed inverse to enable computation of the scalar multiplication without requiring a division by the truncator for each scalar multiplication.Type: ApplicationFiled: March 19, 2007Publication date: September 20, 2007Inventors: Robert Lambert, Ashok Vadekar, Adrian Antipa
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Patent number: 7215780Abstract: The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar. The applicants have also recognized that the representation of a scalar in a ?-adic representation may be optimized for each scalar that is needed. The applicants have further recognized that a standard rounding algorithm may be used to perform reduction modulo the truncator. In general terms, there is provided a method of reducing a scalar modulo a truncator, by pre-computing an inverse of the truncator. Each scalar multiplication then utilizes the pre-computed inverse to enable computation of the scalar multiplication without requiring a division by the truncator for each scalar multiplication.Type: GrantFiled: January 29, 2002Date of Patent: May 8, 2007Assignee: Certicom Corp.Inventors: Robert J. Lambert, Ashok Vadekar, Adrian Antipa
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Publication number: 20070098154Abstract: In computing point multiples in elliptic curve schemes (e.g. kP and sQ) separately using, for example, Montgomery's method for the purpose of combining kP+sQ several operations are repeated in computing kP and sQ individually, that could be executed at the same time. A simultaneous scalar multiplication method is provided that reduces the overall number of doubling and addition operations thereby providing an efficient method for multiple scalar multiplication. The elements in the pairs for P and Q method are combined into a single pair, and the bits in k and s are evaluated at each step as bit pairs. When the bits in k and s are equal, only one doubling operation and one addition operation are needed to compute the current pair, and when the bits in k and s are not equal, only one doubling operation is needed and two addition operations.Type: ApplicationFiled: November 3, 2006Publication date: May 3, 2007Inventors: Adrian Antipa, Yuri Poeluev
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Publication number: 20070064932Abstract: Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as ?zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.Type: ApplicationFiled: January 18, 2006Publication date: March 22, 2007Inventors: Marinus Struik, Daniel Brown, Scott Vanstone, Robert Gallant, Adrian Antipa, Robert Lambert
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Patent number: 7177423Abstract: A method of computing an exponent of a message m in an RSA cryptosystem having a private key d, a public key e and system parameters p, q where p and q are primes and ed=1 mod (p?1) (q?1). The method comprises the steps of obtaining a value r, and exponentiating the value r to the power e to obtain an exponent re mod p, combining said exponent re with the message m to obtain a combined value re m and mod p; selecting a value s and obtaining a difference (d?s), exponentiating the combined value with said difference to obtain an intermediate exponent (rem)d?s, multiplying the intermediate exponent by a value ms to obtain a resultant value equivalent to r1?es md and multiplying the resultant value by a value corresponding to r1?es to obtain an exponent corresponding to md mod p.Type: GrantFiled: June 9, 2004Date of Patent: February 13, 2007Assignee: Certicom Corp.Inventor: Adrian Antipa
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Publication number: 20050063548Abstract: A method of computing an exponent of a message m in an RSA cryptosystem having a private key d, a public key e and system parameters p, q where p and q are primes and ed=1 mod (p?1) (q?1). The method comprises the steps of obtaining a value r, and exponentiating the value r to the power c to obtain an exponent rc mod p, combining said exponent rc with the message m to obtain a combined value rc m and mod p; selecting a value s and obtaining a difference (d?s), exponentiating the combined value with said difference to obtain an intermediate exponent (rem)d?s, multiplying the intermediate exponent by a value ms to obtain a resultant value equivalent to r1?cs md and multiplying the resultant value by a value corresponding to r1?es to obtain an exponent corresponding to md mod p.Type: ApplicationFiled: June 9, 2004Publication date: March 24, 2005Inventor: Adrian Antipa
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Patent number: 6782100Abstract: A method for multiplication of a point P on elliptic curve E by a value k in order to derive a point kP comprises the steps of representing the number k as vector of binary digits stored in a register and forming a sequence of point pairs (P1, P2) wherein the point pairs differed most by P and wherein the successive series of point pairs are selected either by computing (2mP,(2m+1)P) from (mP,(m+1)P) or ((2m+1)P,(2m+2)P) from (mP,(m+1)P). The computations may be performed without using the y-coordinate of the points during the computation while allowing the y-coordinate to be extracted at the end of the computations, thus, avoiding the use of inversion operations during the computation and therefore, speeding up the cryptographic processor functions. A method is also disclosed for accelerating signature verification between two parties.Type: GrantFiled: October 2, 2000Date of Patent: August 24, 2004Assignee: Certicom Corp.Inventors: Scott Vanstone, Ronald Mullin, Adrian Antipa, Robert Gallant
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Publication number: 20030123655Abstract: The applicants have recognized an alternate method of performing modular reduction that admits precomputation. The precomputation is enabled by approximating the inverse of the truncator T, which does not depend on the scalar.Type: ApplicationFiled: January 29, 2002Publication date: July 3, 2003Inventors: Robert J. Lambert, Ashok Vadekar, Adrian Antipa