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*To*: Network Demon <[email protected]>*Subject*: Re: Total RSA in PGP*From*: [email protected] (Scott Collins)*Date*: Sat, 28 Aug 1993 21:13:26 -0800*Cc*: [email protected]

>Am I mistaken in believing RSA is more secure than the present hybrid? .....SHORT ANSWER..... You are mistaken. .....MEDIUM ANSWER..... You are mistaken not because the statement 'RSA is more secure than the present hybrid' is false, but because it is a mistake to put your belief in this statement, which has not been proved true. RSA alone would represent a great increase in computational effort, without risk of a decrease in security, after which you couldn't prove you were any better off (though, in practice, against currently known attacks, and with a large key, you might be). .....LONG ANSWER..... RSA alone is no _less_ secure than the PGP's combination of RSA and IDEA: if you can break RSA, you can extract the IDEA key and decipher the message; if you can break IDEA, you don't need the key. I am guessing that you share a widely echoed predjudice that public-key ciphers are better than secret-key ciphers (I apologize if I have mis-labeled you :). Public-key ciphers have gained a reputation for being more secure, as a class, than secret-key ciphers. Perhaps because public-key ciphers afford 'better' key management, the world at large has gotten the impression that they provide 'better' security. Public-key ciphers as a class are _not_ more secure than secret-key ciphers. One counter example, which periodically rears its ugly head here, is the (truly random) one-time-pad. This secret-key cipher offers perfect security in the Shannon sense. No public-key cipher can make that claim. To prove RSA _more_ secure than the hybrid, RSA must be proved more secure than IDEA. Unfortunately, we don't really know how secure the RSA algorithm is (or IDEA, for that matter). It is known that RSA is no _more_ secure than factoring a component of the public key (readily available to an attacker). To my knowledge, it has not been proved that either a) RSA is at least this secure; or b) factoring is hard. Despite a paucity of formal proof, I know of know better attack on a message enciphered with well chosen keys than factoring, which both man and machine currently find taxing. RSA with well chosen keys is 'empirically' computationally secure. While IDEA has been designed specifically to resist differential cryptanalysis (thanks to those who pointed me to the IDEA papers explaining this), more formal proof of its security awaits further understanding of the information theory aspects of its foundation: mixing operations from incompatible groups. In the end, IDEA is also 'empirically' computationally secure. I know of no comparisons of the security offered by RSA and IDEA against practical attacks. .....FINAL ANSWER..... In theory: theory is as good as practice; but in practice... it isn't. Hope this helps, Scott Collins | "Few people realize what tremendous power there | is in one of these things." -- Willy Wonka ......................|................................................ BUSINESS. voice:408.862.0540 fax:974.6094 [email protected] Apple Computer, Inc. 1 Infinite Loop, MS 301-2C Cupertino, CA 95014 ....................................................................... PERSONAL. voice/fax:408.257.1746 1024/669687 [email protected]

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