By Martin E. Hellman, Justin M. Reyneri (auth.), David Chaum, Ronald L. Rivest, Alan T. Sherman (eds.)

ISBN-10: 1475706022

ISBN-13: 9781475706024

ISBN-10: 1475706049

ISBN-13: 9781475706048

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**Extra resources for Advances in Cryptology: Proceedings of Crypto 82**

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R. Blakley and La if Swanson 40 Probability (the message is t) Probability (the message is intercepted). tj given that p + s is It is also true that Probability (the message is t) Probability (the message is known) tl given that p is somehow A priori probabilities are the same as a posteriori probabilities, in other words. You need both p and p + s to find s. Knowing just one of them is knowing nothing about s you didn't already know just before the sender composed the message. Is it possible to retain Shannon perfect security when some messages s are infinitely more probable than others?

Notice that the output bits satisfy do = 0. 53 A Fast Modular Multiplication Algorithm o = xy X y d =x Figure 1. ~ y Half Adder MODULAR MULTIPLICATION USING DELAYED CARRY NUMBERS Let A and B be two delayed carry integers of length n. The product D = A·B can be computed by executing the following n steps. D ,_ Bo • B + a 1 • 2B Since atat+t = 0, either at • 21 B or at+! • 21 +lB is 0. Each step requires only a shift of B and the addition of at most two delayed carry integers. One reason for using delayed carry rather than carry save should now be apparent.

The problem is difficult. However, as shown below, for our special choice of A i';. is easy. Before proceeding further we state two lemmas. The proofs appear in Appendix A. LEMMA 1 : Let A be symmetric matrix in which all elements are nonnegative and are positive powers of 2. Also, let the above-diagonal elements be distinct. Then, the Characteristic Difference d is always nonzero. LEMMA 2 : If A is chosen as in lemma 1. then for a given Characteristic Difference d, the partition (Ap , AN) is unique.

### Advances in Cryptology: Proceedings of Crypto 82 by Martin E. Hellman, Justin M. Reyneri (auth.), David Chaum, Ronald L. Rivest, Alan T. Sherman (eds.)

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