By Martin E. Hellman, Justin M. Reyneri (auth.), David Chaum, Ronald L. Rivest, Alan T. Sherman (eds.)
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Extra resources for Advances in Cryptology: Proceedings of Crypto 82
Implementation Of The Public-key Cryptosystem A public-key cryptosystem based on the matrix cover problem could be designed as described below. 2. 1. Generation Of The Encryption and Decryption Keys At the time of joining the network , each user creates his encryption and decryption keys as follows : 1 . He constructs an n-rt secret matrix A= (a;,i) having the following properties : (i) A is symmetric. (ii) all elements of A are nonnegative and are positive powers of 2. (iii) the above-diagonal elements of A are all distinct.
A 1n . Algorithm F : begin f(i) +- 1 for j +- 2 step 1 until n do begin if ali is in Ap then f (j) else f (j) end end +- I +- - ( 1) f (1) Note that the values of I (j) , 2 :=; j :=;n, depend on the value of 1 ( 1). We could equally well have chosen f (1) to be -1.
It might be possible to determine if a given multiple of C, say 2 1c, should be subtracted from D before the multiplication procedure has finished many steps. In examining this idea closely, there are two problems that arise. C might be negative after step j, but positive after step i, for some i > j. c. When using delayed carry or carry-save arithmetic, magnitude comparison is always much slower than addition. To determine the sign of D-2Lc, we must find E = D-2 1C in the redundant number system and then essentially convert E to binary.
Advances in Cryptology: Proceedings of Crypto 82 by Martin E. Hellman, Justin M. Reyneri (auth.), David Chaum, Ronald L. Rivest, Alan T. Sherman (eds.)