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Is there something like a perfect asymmetric crypto-algo? Is there proof that there must be one or not. From a logical point of view it seems to be possible to design such algorithm if your keysize is high enough.

And please a mathematical solution and not some quantum-cryptography.

Thanks in advance

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  • $\begingroup$ The statement "From a logical point of view it seems to be possible to design such algorithm if your keysize is high enough" is misguided. To obtain perfect security, one needs something beyond high enough keysize, since keysize can only protect against computationally bounded adversaries. $\endgroup$
    – kodlu
    May 18 '15 at 1:32
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No there isn't. First, OTP is private-key encryption scheme. Second, Asymmetric key is public-key encryption and No public-key encryption scheme can ever be perfectly secret. This is because the public-key (used for encryption) is available to everyone and is related to the secret-key in some way. Thus, a certain negligible amount of information is leaked. However, this leakage implies it isn't perfectly secure. So, No such thing as asymmetric OTP.

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  • $\begingroup$ Can't you think of a non-asymmetric a method, that provides perfect security, like: A encrypts M with K[A] -> C[A]. A sends C[A] to B. B encrypts C[A] with own key K[B] -> C[A, B]. B sends C[A, B] to A. Now a 'removes' her key K[A] from C[A, B] -> C[B]. Now A can send it to B and B can decrypt it. $\endgroup$
    – olastor
    May 18 '15 at 19:42
  • $\begingroup$ The scheme you described isn't clear. Nevertheless, there is a diffecence between being secure (of which there are multiple tiers) and being "perfectly-secure". Perfect secrecy is a very tough standard. $\endgroup$
    – Gordon
    May 18 '15 at 19:54
  • $\begingroup$ The scheme is pretty simple: Alice has a box. Now Alice puts her lock on it (only Alice has the key to the lock). Then Alice sends this locked box to Bob. Bob puts his lock on the box. Now the box is locked with 2 different locks. He sends it back, so Alice can remove her lock with her key. If she sends the box now to Bob, he will be able to open it with his own, because it's only locked by Bobs lock. (thats a comparison used by Simon Singh to illustrate the idea behind diffie-hellman). Here we don't need a public key and the question is: Could an algorithm similiar to OTP work as the 'lock'? $\endgroup$
    – olastor
    May 19 '15 at 17:10
  • $\begingroup$ @olastor Why do alice and bob keep sending each other the box? And you need to formulate it more formally and rigorously. The vaguer the description the easier it is to fool your self into believing your schemes is secure. However, I'm very sure that there is no such thing as a perfectly secure public-key encryption scheme. Why are you so reluctant to accept this as an answer? $\endgroup$
    – Gordon
    May 19 '15 at 18:10
  • $\begingroup$ I've never disclaimed that there is a perfect public-key encryption scheme. I wanted to know, if there is an scheme that provides perfect security, when it comes to 2 persons communicating. Public-Key is only 1 way of solving the key-exchange-problem. Another way I tried to describe: Here is the original text from the book pastebin.com/dpsZ6t7C $\endgroup$
    – olastor
    May 20 '15 at 14:36

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