# Kristin E. Lauter

## Kristin E. Lauter, Redmond, WA US

Patent application number | Description | Published |
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20100172491 | Computing Isogenies Between Genus-2 Curves for Cryptography - This cryptographic curve generation technique provides a faster way of constructing a genus 2 curve. The technique provides a procedure to compute isogenies between genus 2 curves over finite fields. Instead of looping over possible roots, as is typically done when solving Igusa class polynomials, the technique only finds one root and then applies the isogenies to find the others. The technique computes a set of polynomials that define all isogenies. To do this, for a given root of an Igusa class polynomial over a finite field, the technique computes a value of a small modular function ƒ. To the value of this function ƒ, the technique applies an isogeny to find an isogenous ƒ-value. The technique then transforms the ƒ-value back into an Igusa value. Once the Igusa class polynomials are solved they can be used to generate a genus 2 curve which can be used in cryptographic applications. | 07-08-2010 |

20120159179 | DIGITAL SIGNATURES WITH ERROR POLYNOMIALS - Representations of polynomials a, s, t, e | 06-21-2012 |

## Kristin E. Lauter, La Jolla, CA US

Patent application number | Description | Published |
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20080301448 | Security Against Corruption for Networked Storage - Systems and methods for security against corruption for networked storage are described. In one aspect, a destination device receives a linear combination of packets. The linear combination of packets represents digitally signed blocks of content and public information used to digitally sign segmented blocks of content. The destination device recombines the linear combination of packets to compute new valid signatures as linear combinations of received homomorphic digital signatures. The new valid signatures are for verifying by a requesting computing device recovering data associated with at least a subset of the linear combination of packets, integrity of the at least a subset. This provides the requesting node with security against corruption of data in networked storage. | 12-04-2008 |

20080301815 | Detecting Unauthorized Changes to Printed Documents - Systems and methods to detect unauthorized changes to a printed document are described. In one aspect, a digital signature of original content associated with electronic document is embedded into the original content to create a content signed document. The systems and methods use the embedded digital signature to automatically determine whether text-based content associated with a printout of the content signed document was changed from the original content associated with the electronic document. | 12-04-2008 |

20090287756 | Computing Modular Polynomials Modulo Large Primes - Systems and methods for computing modular polynomials modulo large primes are described. In one aspect, the systems and methods generate l-isogenous elliptic curves. A modular polynomial modulo a large prime p is then computed as a function of l-isogenous elliptic curves modulo p. | 11-19-2009 |

20090290705 | Algorithms for generating parameters for genus 2 hyperelliptic curve cryptography - An exemplary method includes defining a CM field, representing coefficients of a Frobenius element of a hyperelliptic curve over a prime field as non-linear polynomials that are functions of an integer x and selecting a value for x whereby the product of the Frobenius element and its complex conjugate is a prime number. Such a method may further include determining the order of the Jacobian of the hyperelliptic curve, for example, where the order is an almost prime number. Various other methods, devices, systems, etc., are also disclosed, which may be optionally used for cryptography. | 11-26-2009 |

20090290714 | Protocol for Verifying Integrity of Remote Data - An exemplary method for verifying the integrity of remotely stored data includes providing a key; providing a fingerprint, the fingerprint generated using the key in a keyed cryptographic hash function as applied to data of known integrity; sending the key to a remote storage location that stores a copy of the data of known integrity; receiving a fingerprint from the remote storage location, the fingerprint generated using the key in a keyed cryptographic hash function as applied to the remotely stored copy of the data; and verifying the integrity of the remotely stored copy of the data based at least in part on comparing the provided fingerprint to the received fingerprint. Other exemplary methods, systems, etc., are also disclosed. | 11-26-2009 |

20090290715 | Security architecture for peer-to-peer storage system - An exemplary method includes receiving a request to register a peer in a peer-to-peer system; generating or selecting a transaction key for the peer; storing the transaction key in association with registration information for the peer; transmitting the transaction key to the peer and, in response to a request to perform a desired peer-to-peer transaction by another peer, generating a token, based at least in part on the transaction key. Such a token allows for secure transactions in a peer-to-peer system including remote storage of data and retrieval of remotely stored data. Other exemplary techniques are also disclosed including exemplary modules for a peer-to-peer server and peers in a peer-to-peer system. | 11-26-2009 |

20100082992 | Cryptographic Applications of Efficiently Evaluating Large Degree Isogenies - Techniques are disclosed for representing and evaluating large prime degree isogenies for use in cryptographic signature and encryption schemes. An isogeny of prime degree 1 may be represented as an ideal in the form (1, A*alpha+B), where 1 comprises the degree of a prime number, the prime number is split into integers a and b, and alpha is a known endomorphism. For a given degree 1, integers a and b define a unique isogeny, allowing the isogeny to be stored with 3 log(1) bits of information. Techniques are also disclosed to evaluate the isogeny at a given point by decomposing the isogeny into an integer and a plurality of smaller degree isogenies, evaluating the smaller degree isogenies at the point with traditional means, and multiplying the results of the evaluations together and with the integer. | 04-01-2010 |

20110145198 | Contextual and Semantic Differential Backup - A backup system that utilizes contextual and semantic concepts is described. The backup system provides for the ability to create a version changes log for listing and tracking all the changes in the different versions of the file. The version changes log creates a contextual description around the changes, deletions and additions. The semantic concept log is created from the version changes log to create a log of all of the semantic concepts associated with each change. A visualization builder then creates visualizations that can be used by the user to search for changes, deletions and additions whether in a text file or an image file. | 06-16-2011 |