Richard A. DeMillo

Cryptographic protocols

A cryptographic transformation is a mapping f from a set of cleartext messages, M, to a set of ciphertext messages. Since for m e M, f(m) should <underline>hide</underline> the contents of m from an enemy, f<supscrpt>-1</supscrpt> should, in a certain technical sense, be difficult to infer from f(m) and public knowledge about f. A <underline>cryptosystem</underline> is a model of computation and communication which permits the manipulation of messages by cryptographic transformations.

Some connections between mathematical logic and complexity theory

However difficult the fundamental problems of theoretical computer science may seem, there is very little to suggest that they are anything more than knotty combinatorial problems. So, when we look for reasons for our inability to resolve P &equil; NP and related questions, we most likely find them dealing with a lack of understanding of particular computational problems and their lower bounds. This is the sense of Hopcrofts prediction: “...within the next five years, nobody will prove that any of these problems takes more than lets say n2 time. I think thats a reasonably safe conjecture and it also illustrates how little we know about lower bounds.” [MT]. Hopcrofts guess is uncanny in its accuracy—after six years and considerable effort by many researchers, his conjecture remains unchallenged. The results in this paper offer a possible explanation for our failure to resolve these problems. Roughly, the main result of the sequel links lower bounds and a branch of mathematical logic known as model theory. In particular, we prove that the existence of nonpolynomial lower bounds is equivalent to the existence of nonstandard models of a sizable fragment of arithmetic. Since these are deep logical issues and there are very few techniques for handling them, and since the nonstandard models in question are non-effective, it seems plausible that this linking of complexity theory and logic explains our failure to obtain nontrivial lower bounds. One of the aims of mathematical logic is to clarify the relation between mathematical theories and their interpretations—or models.

Protecting Shared Cryptographic Keys

In this paper, we present a scheme for distributing a key to n users in such a way as to require at least k of them (k < n) to be present to construct the original key. The scheme has the property that up to k - 1 defections can be tolerated. It can be implemented simply and efficiently.

Can structured programs be efficient

By using a new method for comparing the power of control structures, we give evidence that there are provable quantitative differences among various control structures. The key result discussed in this note states that there are natural <u>goto</u> programs which can only be simulated by structured programs that are either very large or very slow.

The complexity of control structures and data structures

The running time or computational complexity of a sequential process is usually determined by summing weights attached to the basic operations from which the process is derived. In practice, however, the complexity is often limited by how efficiently it can access its data structures and how efficiently it can control program flow. Furthermore, it has been extensively argued [4] that certain limitations on the process sequencing mechanisms available to the programmer result in more “efficient” representations for the underlying processes. In this paper we will examine these issues in an attempt to assess the “power” of various data and control structures.

Theory in the Computer Science and Engineering Curriculum: Why, What, When, and Where

Theory plays several different roles in the undergraduate curriculum. In recognition of this, both the IEEE Computer Society1 and ACM,2,3 have recommended a substantial theoretical component in the computer science/engineering curriculum.

NSF workshop on a software research program for the 21 st century

Workshop Participants: Professor Victor R. Basili, University of Maryland (Chairman) Mr. Laszlo Belady, Belady Enterprises Professor Barry Boehm, University of Southern California Professor Frederick Brooks, University of North Carolina Professor James Browne, University of Texas Dr. Richard DeMillo, Bellcore Dr. Stuart I. Feldman, IBM Dr. Cordell Green, Kestrel Institute Dr. Butler Lampson, Microsoft Corporation Professor Duncan Lawrie, University of Illinois Professor Nancy Leveson, Massachusetts Institute of Technology Professor Nancy Lynch, Massachusetts Institute of Technology Dr. Mark Weiser, Xerox Corporation Professor Jeannette Wing, Carnegie Mellon Institute

Parallel scheduling of programs in a restricted model of computation

The purpose of this paper is to present the basis of an automata-theoretic model which treats the concept of “schedule” for programs which admit a (predefined) degree of parallelism. After a brief review of notational conventions (Section 2), the class of representing automata will be introduced as a device for treating a programs control structure. In Section 4, since the definition of schedules is non-constructive in the sense that no procedure is given for passing from a representing automaton to a schedule, a particular kind of schedule with such an effective presentation is given and shown to be optimal in the natural sense of optimality defined in Section 6. Section 5 presents one of the many possible interpretation schemes for our model; this scheme is used to justify some of the claims we have made in this section. Finally, we examine some elementary conditions, on a programs control structure which affect the existence of optimal schedules which have finite, explicit presentation.