Abstract: The invention provides apparatus and methods for use in basis conversion involving a dual basis, such as a dual of a polynomial basis or dual of a normal basis. The invention in an illustrative embodiment includes basis generators for generating elements of a dual of a polynomial or a normal basis of a finite field GF(qm), where q is a prime number or power of a prime number and m is an integer greater than or equal to 2. The basis generators can be used in “import” basis conversion, such as converting a representation in an external basis to a representation in an internal dual of a polynomial basis or dual of a normal basis, as part of a generate-accumulate algorithm, or in “export” basis conversion, such as converting a representation in an internal dual of a polynomial basis or dual of a normal basis to a representation in an external basis, as part of a generate-evaluate algorithm.

Abstract: This invention provides for an apparatus and method to cause a stricture in a body passageway. For example, urinary incontinence and vesicoureteral reflux can be treated by inserting an energy-delivering probe into the body passageway of the urinary tract and applying energy to an arcuate segment of the wall of the body passageway to cause injury to the wall, hyperplasia of the tissue surrounding the wall, and stricture of the body passageway. Other applications for the apparatus and method of the present invention includes treatment of gastro-esophageal reflux and fecal incontinence.

Abstract: The invention relates to an antibiotic-free protective medium, comprising nutrients for tissue growth, which comprises a non-antibiotic preservative to prevent contamination, a method of producing said protective medium and the use of said medium for preserving vital tissue.