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Is there any technique that could secure a public document from being counterfeited, given the constraint that the documents shall be available to cracker and hence an unlimited number of ciphertext and plaintext pairs shall be available to cracker to crack the encryption.

i.e. Does there exist a system wherein the encryption key can be made indecipherable despite making arbitrarily many plaintext and ciphertext pairs available to the cracker? If so, how strong is such a system, what kind of key and algorithms should be used? I'm assuming if such a system is possible, then it must rely on strong prime number arithmetic; a simple XOR encryption, it seems to me, should be decipherable.

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    Perhaps ask here instead: http://security.stackexchange.com/ – 2017-02-26
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    Have you looked at [digital signatures](https://en.wikipedia.org/wiki/Digital_signature)? Plus, what Ethan Bolker said. – 2017-02-26
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    @FabioSomenzi However digital signatures are not foolproof - for example consider Diginotar and spoofed certificates. – 2017-02-26
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    @unseen_rider Agreed. I was asking the OP to provide more context. – 2017-02-26

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