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Abstract. We describe another key-exchange system which, while based on the general idea of the well-known scheme of Diffie and Hellman, seems to be more secure than that technique. The new system is based on the arithmetic of an imaginary quadratic field, and makes use, specifically, of the properties of the class group of such a field.

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Mathematical Society is collaborating with JSTOR to digitize, preserve and extend access to Mathematics of Computation.Abstract. A description is given of a modified version of Voronoi's algorithm for obtaining the regulator of a pure cubic field Q( 3D). This new algorithm has the advantage of executing relatively rapidly for large values of D. It also eliminates a computational problem which occurs in almost all algorithms for finding units in algebraic number fields. This is the problem of performing calculations involving algebraic irrationals by using only approximations of these numbers.The algorithm was implemented on a computer and run on all values of D (< 105) such that the class number of Q(./D) is not divisible by 3. Several tables summarizing the results of this computation are also presented.