# Download Advances in Cryptology: Proceedings of Crypto 82 by Martin E. Hellman, Justin M. Reyneri (auth.), David Chaum, PDF

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

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Note that these are very conservative estimates. The presence of random multiples of m will increase the storage requirements and data expansion value drasticaUy. 6. Signature Capability Every ciphertext is an integer in the closed interval [ l , h ] . ;;t , j~n =( i

I constitute the user's secret decryption key. Matrix Cover Public-Key Cryptosystem 25 = 4 He computes bi/ aiiw r:10d m, 1 ::-:; i , j ::-:; n , i < j . Now, since the ai/s are all powers of 2 , it is possible that some of the bi/'s bear a simple relation to one another . To hide this, random multiples qii of m are added to each bii' to obtain bii. • Thus, bii =bi/ + % m , 1 ::-:; i , j ::-:; n , i < j , % ~ 0 . These bii 's constitute the above-diagonal elements of a matrix B. They form the user's publicly known encryption key.

To explain this cryptic solution, we must present more detail. We start subtracting multiples of C eleven steps after the multiplication procedure is started. So D, the accumulator, is a delayed carry register of length n + 11. , K is stored in only one register). t 1 and t 2 are two bits used as control bits. t 2 and t 1 are determined in essentially, but not precisely, the following manner. t 2 is set to l when the top 4 bits of D are greater than the top 4 bits of 2 11 C. t 1 is set to l when t 2 = 0 and the top 4 bits of D are greater than the top 3 bits of 2 1 °C.