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Article #542

RSA keys

#542
From: Eric Weaver
Date: Thu, 30 Jul 1992 21:37
28 lines
1264 bytes
Summarized for those who haven't a Knuth Vol. II:

 Pick two primes, P and Q, which are NOT one greater than a multiple of 3
  (e.g. 37 won't do).  Probabilistic prime tests are good for this.

 Take a frame of bits F, no shorter than 1/3 the length of PQ (the
public, encryption key), and less than PQ.  

 Encrypt:  F[enc] = F^3 mod PQ.

 Let D (private, decryption key) = [(P-1)(Q-1)/6]+1

 Decrypt: F = F[enc]^D mod PQ.


 P and Q should be of approx. 25% difference in length, and of at
least 450 bits total.  1000 bits or more, if you can afford it, would
be best.

 Decryption is pretty expensive, obviously, so this technique is
commonly used only to exchange key and digest info.

Question for cognoscenti: How hard is it REALLY to guess or search D
from PQ?
-- 
Eric Weaver  Sony AVTC  677 River Oaks Pkwy, MS 35  SJ CA 95134  408 944-4904
& Eng. Asst., KFJC 89.7 -  Foothill College, Los Altos Hills, CA 94022
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From: weaver@sfc.sony.com (Eric Weaver)
Subject: RSA keys
Message-ID: <1992Jul30.213709.26515@sfc.sony.com>
Organization: Sony Advanced Video Technology Center
Date: Thu, 30 Jul 1992 21:37:09 GMT
Lines: 28