Showing papers in "Sigact News in 1983"

Conjugate coding

Abstract: restrictions on measurement related to the uncertainty principal. Two concrete examples and some general results are given. The uncertainty principle imposes restrictions on the capacity of certain types of communication channels. This paper will show that in compensation for this \"quantum noise\", quantum mechanics allows us novel forms of coding without analogue in communication channels adequately described by classical physics.

Coin flipping by telephone a protocol for solving impossible problems

Abstract: Alice and Bob want to flip a coin by telephone. (They have just divorced, live in different cities, want to decide who gets the car.) Bob would not like to tell Alice HEADS and hear Alice (at the other end of the line) say "Here goes . . . I'm flipping the coin. . . . You lost!"Coin-flipping in the SPECIAL way done here has a serious purpose. Indeed, it should prove an INDISPENSABLE TOOL of the protocol designer. Whenever a protocol requires one of two adversaries, say Alice, to pick a sequence of bits at random, and whenever it serves Alice's interests best NOT to pick her sequence of bits at random, then coin-flipping (Bob flipping coins to Alice) as defined here achieves the desired goal:1. It GUARANTEES to Bob that Alice will pick her sequence of bits at random. Her bit is 1 if Bob flips heads to her, O otherwise.2. It GUARANTEES to Alice that Bob will not know WHAT sequence of bits he flipped to her.Coin-flipping has already proved useful in solving a number of problems once thought impossible: mental poker, certified mail, and exchange of secrets. It will certainly prove a useful tool in solving other problems as well.

A variant of a public key cryptosystem based on Goppa Codes

Abstract: This paper suggests a way in which an interesting Public Key Cryptosystem based on Goppa Codes introduced by R J McEliece can be modified and used in a classical way to yield several advantages The primary benefit is that the rate of the code (or data expansion reciporocal) can be increased by approximately 75% Secondly (for public key and classical versions), by using a polynomial with no linear or repeated factors instead of an irreducible one to generate the Goppa Code, the code parameters remain the same and the decoding apparatus can be used to test candidate generators Lastly, a wider range of transformations is made possible No degradation in security is incurred

A note on the functional estimation of values of hidden variables: an extended module for expert systems

Abstract: The paper describes an extension of our work on the Generalized Production Rules System. In its original form, it could estimate at a given point of time or space the value of hidden variables---variables that can be measured only intermittently or periodically. In contrast, open variables are readily measurable any time. The system establishes stochastic, causal relations, generalized production rules, between known values of hidden variables and certain mathematical properties of the open variables' behavior. These rules are then used to make the point estimates.We have now provided the system with the additional ability to estimate the functional behavior of the hidden variables. The system can serve as a domain-independent module to a knowledge-based expert system in need of such numerical estimates.

Learning context-free languages from their structured sentences

Abstract: There is never a unique grammar for L, so one aspect of the problem is establ i sh ing the nature of an in ferred G to be deemed an acceptable, or even best, resu l t . C r i te r ia for the choice and conveyance of sample in format ion, to ensure a desired resul t be obtained, may also be defined. Opt imal ly, an inference system or technique w i l l be appl icable to a l l contextf ree languages, so there must be some determination of the cases to which any so lut ion method appl ies.

An artificial intelligence technique to generate self-optimizing experimental designs

Abstract: The paper describes a completed and independent module of a large-scale system, the Quasi-Optimizer (QO). The QO system has three major objectives: (i) to observe and measure adversaries' behavior in a competitive environment, to infer their strategies and to construct a computer model, a descriptive theory, of each; (ii) to identify strategy components, evaluate their effectiveness and to select the most satisfactory ones from a set of computed descriptive theories; (iv) to combine these components in a quasi-optimum strategy that represents a normative theory in the statistical sense.The measurements on the input strategies can take place either in a sequence of confrontations unperturbed by the QO, or, for efficiency's sake, in a series of environments specified according to some experimental design. The module completed first, QO-I, can perform the experiments either in an exhaustive manner---when every level of a decision variable is combined with every level of the other decision variables---or, in relying on the assumption of a monotonically changing response surface, it uses the binary chopping technique.The module discussed here, QO-3, does not assume monotonic response surfaces and can deal also with multidimensional responses. It starts with a (loosely) balanced incomplete block design for the experiments and computes dynamically the specifications for each subsequent experiment. Accordingly, the levels of the decision variables in any single experiment and the length of the whole sequence of experiments depend on the responses obtained in previous experiments. In general, QO-3 is an on-line, dynamic generator of experimental design that minimizes the total number of experiments performed for a predetermined level of precision.

Survey on classes of interpretations and some of their applications

Abstract: We introduce classes of interpretations. We characterize the free and Herbrand interpretations for a class. We define the algebraic, equational, relational and first-order classes of interpretations, study their properties and relate them to the literature. We apply this study to derive complete proof systems for deducing (in some (in) equational logic) all (in) equalitions valid in a class.

Compact knapsacks are polynomially solvable

Abstract: l l (1) i = l The associated decision problem, i.e.,determining whether (i) has a solution, is Lb. the class of NP-Complete problems. Therefore it is believed that solving (I) is very hard tn general. Merkle and Hellman suggested a public key cryptographic system, which makes use of this difficu/ty. In their method a is the public key, x is the message and S is the cyphertext. The legitimate receiver knows "trapdoor" information embedded in a and hence can easily recover x. On the other hand the cryptanalyst must try to solve a knapsack problem of the form (i).

Iterative vs. regular factor algebras

Abstract: We characterize the free regular algebra in any variety of regular algebras as a factor algebra and prove that no similar characterization can be obtained for varieties of iterative or continuous algebras.

Time-memory-processor tradeoffs

Abstract: It is demonstrated that usual time-memory trade-offs offer no asymptotic advantage over exhaustive search. Instead, trade-offs be- tween time, memory, and parallel processing are proposed. Using this approach it is shown that most searching problems allow a trade-off between C,, the cost per solution, and C,,,, the cost of the machine: doubling C,,, increases the solution rate by a factor of four, halving C,. The machine which achieves this has an unusual architecture, with a number of processors sharing a large memory through a sorting/switching network. The implications for cryptanalysis, the knapsack problem, and multiple encryption are discussed.

On the necessity of cryptanalytic exhaustive search

Abstract: It is shown that the amount of computation required for a general cryptanalytic method is equivalent to an exhaustive search over the key space. In particular, any general time-memory tradeoff must do an exhaustive search as a part of the pre- or post-computation.

On the feasibility of computing discrete logarithms using Adleman's subexponential algorithm

Abstract: Some public key distribution systems, based on the difficulties in computing logarithms modulo a large prime, have been alleged to be insecure because of a statement that any logarithm modulo a 200 bit prime can be computed within a reasonable time by means of a subexponential algorithm due to Adleman.In this commentary said algorithm is examined from an algebraic and number-theoretical point of view. The scrutiny shows that the algebraic model for the algorithm contains several traps which seem to be hard to circumvent, and also, not least, that the presupposed abundance of so called round numbers will not be at hand in the computationally interesting cases.Hence it is concluded that the algorithm cannot be a serious threat to the mentioned public key distribution systems.

The solution of a general equation for the public key system

Abstract: Zz_ It is assumed that the reader is familiar with~$2ncept of the public key system, as developed, for example, by W. Diffie and M.E. Hellman [2]. The most common example of an one-way function is (I) z(x,a) _= xa(mod p), where a is the private key of an arbitrary, but fixed member of the key system, x is a primitive element of the finite field GF(p) and p a large prime number. The public keys of two such members of a public key system are then a x b x and (mod. p) ab ba and x = x is the common key used for encryption and decryption of the secret messages to be transmitted. We now derive a very general modification of this system. It is shown that the public key of any two members or the key system must obey a functional equation, which can be solved in a closed mathematical form: Let (a) and (b) be again two arbitrary members of a general public key system with a given fixed one-way function f(x,'). Let us suppose that (a) and (b) have the private keys a and b respectively that x is a common variable of the system, fixed,

On non-hierachical systems of binary operators

Abstract: In a previous paper [3] a system was described by which context-sensitive grammars could be used to specify balanced derivations of certain expressions; such derivations corresponding in a natural way to balanced semantic trees appropriate for parallel execution. The earlier work was only applicable to expressions involving a strictly ordered hierachy of binary operators. This note shows how under certain "reasonable" algebraic constraints the method can be extended to less well-behaved situations.

On a class of independent problems related to Rice theorem

Abstract: I. For many years-since the appearence of G~del Incom-Theorem ~3~-mathematicians have been looking for simple pleteness and natural mathematical examples of independent problems. The first significant such examples were found by Hartmanis and Hopcroft ~4] and by Paris and Harrington ~7~ (see also the preliminary discussion in L5]). In ~2~ the authors proved a general independence result (with respect to an arbitrary recursively axiomatizable, consistent, intuitively true and sufficiently rich formalized theory). As particular cases one obtains the existence of independent instances for some well-known undecidable problems including Hilbert's Tenth Problem , the Halting Problem, the Totality Problem, the Finiteness Problem , the Post Correspondence Problem (as well as all equivalent un-decidable problems in Formal Language Theory). In this note we construct a class of independent problems related to Rice Theorem C8] , L9] • To be more precise, let T be a formalized theory having the above four properties and let C be a non-empty proper subset of the set of all unary partial recursive functions. Then, th~ proble__~_____m whether the totally undefined function belon_~ to C i__~ independent of T. In this way we obtain a possible

The effect of paged memory upon algorithm performance: short note

Abstract: We investigate the effect of a common memory management scheme on the running times of some simple algorithms. We find that some otherwise comparable algorithms have markedly different performance under this new algorithm metric.