Richard A Crandall

US Patent:

6751318, Jun 15, 2004

Filed:

Sep 4, 2001

Appl. No.:

09/946967

Inventors:

Richard E. Crandall - Redwood City CA

Assignee:

NeXT Software, Inc. - Redwood City CA

International Classification:

H04L 930

US Classification:

380 30, 380 28

Abstract:

The present invention improves speed and reduces complexity in a digital signature scheme that uses elliptic algebra. The signature scheme generates two points that are compared. If the points do not match, the signature is not authentic. The present invention reduces computations by comparing only the x coordinates of the two generated points. The invention provides a scheme for deducing the possible values of the x-coordinate of a sum of two points using only the x coordinates of the original two points in question. The present invention provides a scheme that limits the possible solutions that satisfy the equation to two (the authentic signature and one other). Because of the large number of possible inauthentic solutions, the chance of a false authentic signature is statistically insignificant.

US Patent:

8484236, Jul 9, 2013

Filed:

Jun 29, 2007

Appl. No.:

11/771911

Inventors:

Mark Andrews - Orinda CA, US
Richard Crandall - Portland OR, US
Karl Schiffmann - Montecito CA, US

Assignee:

Robert T. Jenkins and Virginia T. Jenkins - Sacramento CA

International Classification:

G06F 7/00
G06F 17/30
G06F 7/50

US Classification:

707763, 707736, 707713, 708671

Abstract:

Embodiments of methods, apparatuses, devices and/or systems for manipulating character expressions to determine relationships among such character expressions. In particular embodiments, a character expression may be represented as a concatenation of binary representations of individual characters in the character expression to provide a binary string. The binary string may then be processed by applying a binary arithmetic operator to provide a comparison.

US Patent:

6049610, Apr 11, 2000

Filed:

Sep 9, 1998

Appl. No.:

9/149876

Inventors:

Richard E. Crandall - Redwood City CA

Assignee:

NeXT Software, Inc. - Redwood City CA

International Classification:

H04L 930

US Classification:

380 30

Abstract:

The present invention improves speed and reduces complexity in a digital signature scheme that uses elliptic algebra. The signature scheme generates two points that are compared. If the points do not match, the signature is not authentic. The present invention reduces computations by comparing only the x coordinates of the two generated points. The invention provides a scheme for deducing the possible values of the x-coordinate of a sum of two points using only the x coordinates of the original two points in question. The present invention provides a scheme that limits the possible solutions that satisfy the equation to two (the authentic signature and one other). Because of the large number of possible inauthentic solutions, the chance of a false authentic signature is statistically insignificant.

US Patent:

58057030, Sep 8, 1998

Filed:

Nov 27, 1996

Appl. No.:

8/758688

Inventors:

Richard E. Crandall - Redwood City CA

Assignee:

NeXT Software, Inc. - Redwood City CA

International Classification:

H04L 930

US Classification:

380 30

Abstract:

The present invention improves speed and reduces complexity in a digital signature scheme that uses elliptic algebra. The signature scheme generates two points that are compared. If the points do not match, the signature is not authentic. The present invention reduces computations by comparing only the x coordinates of the two generated points. The invention provides a scheme for deducing the possible values of the x- coordinate of a sum of two points using only the x coordinates of the original two points in question. The present invention provides a scheme that limits the possible solutions that satisfy the equation to two (the authentic signature and one other). Because of the large number of possible inauthentic solutions, the chance of a false authentic signature is statistically insignificant.

US Patent:

62857606, Sep 4, 2001

Filed:

Apr 6, 2000

Appl. No.:

9/544530

Inventors:

Richard E. Crandall - Redwood City CA

Assignee:

NeXT Software, Inc. - Redwood City CA

International Classification:

H04L 930

US Classification:

380 30

Abstract:

The present invention improves speed and reduces complexity in a digital signature scheme that uses elliptic algebra. The signature scheme generates two points that are compared. If the points do not match, the signature is not authentic. The present invention reduces computations by comparing only the x coordinates of the two generated points. The invention provides a scheme for deducing the possible values of the x-coordinate of a sum of two points using only the x coordinates of the original two points in question. The present invention provides a scheme that limits the possible solutions that satisfy the equation to two (the authentic signature and one other). Because of the large number of possible inauthentic solutions, the chance of a false authentic signature is statistically insignificant.

US Patent:

55816169, Dec 3, 1996

Filed:

Jun 7, 1995

Appl. No.:

8/484264

Inventors:

Richard E. Crandall - Redwood City CA

Assignee:

NeXT Software, Inc. - Redwood City CA

International Classification:

H04L 930

US Classification:

380 28

Abstract:

The present invention improves speed and reduces complexity in a digital signature scheme that uses elliptic algebra. The signature scheme generates two points that are compared. If the points do not match, the signature is not authentic. The present invention reduces computations by comparing only the x coordinates of the two generated points. The invention provides a scheme for deducing the possible values of the x-coordinate of a sum of two points using only the x coordinates of the original two points in question. The present invention provides a scheme that limits the possible solutions that satisfy the equation to two (the authentic signature and one other). Because of the large number of possible inauthentic solutions, the chance of a false authentic signature is statistically insignificant.