Patents by Inventor Richard E. Crandall
Richard E. Crandall 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: 7603560Abstract: 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.Type: GrantFiled: May 27, 2004Date of Patent: October 13, 2009Inventor: Richard E. Crandall
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Patent number: 7587047Abstract: A chaos generator for accumulating stream entropy is disclosed. The chaos generator includes a random source coupled to an entropy accumulator that is configurable for generating a binary random input sequence. The entropy accumulator is configurable for accumulating entropy of the input sequence and providing a binary random output sequence based on the accumulated entropy. The binary random output sequence is reduced by a modular reduction operation having a modulus that is set equal to a cryptographic prime (e.g., the order of an elliptic curve). The number of iterations performed by the entropy accumulator on the binary random input sequence is selected to provide a binary random output sequence having a desired cryptographic strength. The chaos generator can be part of a signing and verification system that uses fast elliptic encryption for small devices.Type: GrantFiled: June 22, 2005Date of Patent: September 8, 2009Assignee: Apple Inc.Inventors: Richard E. Crandall, Douglas P. Mitchell, Scott Krueger, Guy Tribble
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Publication number: 20090138721Abstract: A method of generating a digital signature includes generating a first random number from a finite field of numbers, and generating field elements defining a first point on an elliptic curve defined over the finite field of numbers by performing elliptic curve arithmetic on the first random number and an initial public point on the elliptic curve. The method continues by generating a product from a field element, a private key, and a second random number received from a challenger seeking verification of a digital signature, and generating a signature component by summing the product and the first random number. The signature component is reduced using one or more modular reduction operations, using a modulus equal to an order of the elliptic curve, and then the reduced signature component and the field elements are sent to the challenger as a digital signature for verification by the challenger.Type: ApplicationFiled: January 16, 2009Publication date: May 28, 2009Inventors: Richard E. Crandall, Douglas P. Mitchell
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Patent number: 7206001Abstract: Rapid dithering of an RGB image from a higher order to a lower order number of bits is provided while introducing fewer undesirable artifacts than are visible in conventional dithering technology. A compact, deterministic method enables the elimination of banding, for example as is seen in 24-bit monitors when viewing color images with greater color depth. A fractal dithering engine selects a threshold matrix appropriate for an input stream, and using the threshold matrix, dithers images of the input stream to output images having a lower order number of color bits. In one embodiment, the threshold matrix is obtained by traversing 2-by-2 sub-regions of an N-by-N matrix according to a traversal pattern, and then applying a reverse binary function to the values in the original matrix to yield the threshold matrix. The threshold matrix preferably tessellates the pixel plane, subject to certain constraints.Type: GrantFiled: June 22, 2004Date of Patent: April 17, 2007Assignee: Apple Computer, Inc.Inventors: Richard E Crandall, Evan T Jones, Jason Klivington
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Patent number: 6998217Abstract: Systems and methods for gray scale lithography for defining edges such as on microelectronic device patterns during integrated circuit fabrication are disclosed. Methods for critical dimension edge placement and slope enhancement utilize central pixel dose addition or modulated inner pixels. A method for gray scale lithography for defining edges of features generally comprises identifying a center pixel of a feature, exposing the general width of the feature including the identified center pixel with full doses, and enhancing the identified center pixel by exposing the identified center pixel with additional dose to accurately place the edge of the feature, whereby the edge of the feature is defined and moved by exposing the center pixel with the additional dose.Type: GrantFiled: January 6, 2003Date of Patent: February 14, 2006Assignee: Applied Materials, Inc.Inventors: Jerry Martyniuk, H. Christopher Hamaker, Matthew J. Jolley, Peter Pirogovsky, Asher Klatchko, Richard E. Crandall
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Patent number: 6912323Abstract: A fast convolution method applicable to convolving a signal (indicative of an n-dimensional pattern, where n is greater than or equal to two) with a smooth kernel that can be approximated by a separated-spline kernel, and a system configured to perform such method using software or signal processing circuitry. Unlike Fourier-based convolution methods which require on the order of N log N arithmetic operations for a signal of length N, the method of the invention requires only on the order of N arithmetic operations to do so. Unlike wavelet-based convolution approximations (which typically also require more arithmetic operations than are required in accordance with the invention to convolve the same signal), the method of the invention is exact for convolution kernels which are spline kernels.Type: GrantFiled: May 29, 2001Date of Patent: June 28, 2005Assignee: Applied Materials, Inc.Inventors: David Jeremy Copeland, Richard E. Crandall, Ulrich Hofmann, Richard L. Lozes
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Publication number: 20040250081Abstract: 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.Type: ApplicationFiled: May 27, 2004Publication date: December 9, 2004Inventor: Richard E. Crandall
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Publication number: 20040131977Abstract: Systems and methods for gray scale lithography for defining edges such as on microelectronic device patterns during integrated circuit fabrication are disclosed. Methods for critical dimension edge placement and slope enhancement utilize central pixel dose addition or modulated inner pixels. A method for gray scale lithography for defining edges of features generally comprises identifying a center pixel of a feature, exposing the general width of the feature including the identified center pixel with full doses, and enhancing the identified center pixel by exposing the identified center pixel with additional dose to accurately place the edge of the feature, whereby the edge of the feature is defined and moved by exposing the center pixel with the additional dose.Type: ApplicationFiled: January 6, 2003Publication date: July 8, 2004Applicant: Applied Materials, Inc.Inventors: Jerry Martyniuk, H. Christopher Hamaker, Matthew J. Jolley, Peter Pirogovsky, Asher Klatchko, Richard E. Crandall
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Patent number: 6751318Abstract: 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.Type: GrantFiled: September 4, 2001Date of Patent: June 15, 2004Assignee: NeXT Software, Inc.Inventor: Richard E. Crandall
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Patent number: 6701028Abstract: A fast convolution method applicable to convolve a signal with a smooth kernel that can be approximated by a spline kernel, and a system configured to perform such method using software or signal processing circuitry. Unlike Fourier-based convolution methods which require on the order of N log N arithmetic operations for a signal of length N, the method of the invention requires only on the order of N arithmetic operations to do so. Unlike wavelet-based convolution approximations (which typically also require more arithmetic operations than are required in accordance with the invention to convolve the same signal), the method of the invention is exact for convolution kernels which are spline kernels. Moreover, convolution in accordance with the invention can be acyclic convolution (achieved without zero-padding) or cyclic convolution, and in both cases the invention imposes no restriction (such as evenness) on signal length.Type: GrantFiled: January 11, 2000Date of Patent: March 2, 2004Assignee: Applied Materials, Inc.Inventor: Richard E. Crandall
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Publication number: 20020122555Abstract: 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.Type: ApplicationFiled: September 4, 2001Publication date: September 5, 2002Applicant: NEXT COMPUTER, INC.Inventor: Richard E. Crandall
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Patent number: 6433707Abstract: A universal method and system for compression of general, digitized analog data utilizing Laplacian integer input encoding with space maps is disclosed. The method and system combine and reblock data for more efficient encoding without having to calculate or transmit data-specific frequency tables.Type: GrantFiled: December 3, 1999Date of Patent: August 13, 2002Assignee: Pixar Animation StudiosInventor: Richard E. Crandall
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Publication number: 20010051860Abstract: A fast convolution method applicable to convolving a signal (indicative of an n-dimensional pattern, where n is greater than or equal to two) with a smooth kernel that can be approximated by a separated-spline kernel, and a system configured to perform such method using software or signal processing circuitry. Unlike Fourier-based convolution methods which require on the order of N log N arithmetic operations for a signal of length N, the method of the invention requires only on the order of N arithmetic operations to do so. Unlike wavelet-based convolution approximations (which typically also require more arithmetic operations than are required in accordance with the invention to convolve the same signal), the method of the invention is exact for convolution kernels which are spline kernels.Type: ApplicationFiled: May 29, 2001Publication date: December 13, 2001Applicant: Applied Materials, Inc.Inventors: David Jeremy Copeland, Richard E. Crandall, Ulrich Hofmann, Richard L. Lozes
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Patent number: 6307935Abstract: The present invention takes advantage of a quadratic-only ambiguity for x-coordinates in elliptic curve algebra as a means for encrypting plaintext directly onto elliptic curves. The encrypting of plaintext directly onto elliptic curves is referred to herein as “direct embedding”. When performing direct embedding, actual plaintext is embedded as a “+” or “−” x-coordinate. The sender specifies using an extra bit whether + or − is used so that the receiver can decrypt appropriately. In operation their are two public initial x-coordinates such that two points P1+ and P1− lie respectively on two curves E+ and E−. A parcel of text xtext is selected that is no more than q bits in length. The curve (E+ or E−) that contains xtext is determined. A random number r is chosen and used to generate a coordinate xq using the public key of a receiving party.Type: GrantFiled: July 18, 1997Date of Patent: October 23, 2001Assignee: Apple Computer, Inc.Inventors: Richard E. Crandall, Blaine Garst
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Patent number: 6285760Abstract: 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.Type: GrantFiled: April 6, 2000Date of Patent: September 4, 2001Assignee: NeXT Software, Inc.Inventor: Richard E. Crandall
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Patent number: 6154542Abstract: A method and apparatus for simultaneously encrypting and compressing data identifies an encryption key and uses the encryption key to identify one compression algorithm from a set of compression algorithms. The data is then compressed according to the one compression algorithm.Type: GrantFiled: December 17, 1997Date of Patent: November 28, 2000Assignee: Apple Computer, Inc.Inventor: Richard E. Crandall
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Patent number: 6049610Abstract: 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.Type: GrantFiled: September 9, 1998Date of Patent: April 11, 2000Assignee: NeXT Software, Inc.Inventor: Richard E. Crandall
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Patent number: 5805703Abstract: 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.Type: GrantFiled: November 27, 1996Date of Patent: September 8, 1998Assignee: NeXT Software, Inc.Inventor: Richard E. Crandall
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Patent number: 5581616Abstract: 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.Type: GrantFiled: June 7, 1995Date of Patent: December 3, 1996Assignee: NeXT Software, Inc.Inventor: Richard E. Crandall
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Patent number: 5463690Abstract: The present invention is an elliptic curve cryptosystem that uses elliptic curves defined over finite fields comprised of special classes of numbers. Special fast classes of numbers are used to optimize the modulo arithmetic required in the enciphering and deciphering process. The class of numbers used in the present invention is generally described by the form 2.sup.q -C where C is an odd number and is relatively small, for example, no longer than the length of a computer word (16-32 bits). When a number is of this form, modulo arithmetic can be accomplished using shifts and adds only, eliminating the need for costly divisions. One subset of this fast class of numbers is known as "Mersenne" primes, and are of the form 2.sup.q -1. Another class of numbers that can be used with the present invention are known as 14 "Fermat" numbers of the form 2.sup.q +1. The present invention provides a system whose level of security is tunable.Type: GrantFiled: December 14, 1993Date of Patent: October 31, 1995Assignee: Next Computer, Inc.Inventor: Richard E. Crandall