I’m skeptical that we’ll prove P!=NP or even find a provably secure encryption scheme before making the world’s economy dependent on unproven schemes, etc.
Nitpick, but finding a provably secure encryption scheme is harder than proving P!=NP, since if P=NP then no secure encryption scheme can exist.
if P=NP then no [provably] secure encryption scheme can exist.
What? Why? Just because RSA would be broken? Shor’s algorithm would also do so, even in a proven P!=NP world. There may be other substitutes for RSA, using different complexity classes. There are other approaches altogether. Not to mention one-time pads.
As I understand it, if P=NP in a practical sense, then almost all cryptography is destroyed as P=NP destroys one-way functions & secure hashes in general. So RSA goes down, many quantum-proof systems go down, and so on and so forth, and you’re left with basically just http://en.wikipedia.org/wiki/Information-theoretic_security
Really, if P=NP, then encoding your messages would be quite low on the priority list … however we’re not debating the practical impact here, but that “finding a provably secure encryption scheme is harder than proving P!=NP”, which was raised as a nitpick, and is clearly not the case.
Happiness or unhappiness of life with one-time pads notwithstanding.
Nitpick, but finding a provably secure encryption scheme is harder than proving P!=NP, since if P=NP then no secure encryption scheme can exist.
What? Why? Just because RSA would be broken? Shor’s algorithm would also do so, even in a proven P!=NP world. There may be other substitutes for RSA, using different complexity classes. There are other approaches altogether. Not to mention one-time pads.
As I understand it, if P=NP in a practical sense, then almost all cryptography is destroyed as P=NP destroys one-way functions & secure hashes in general. So RSA goes down, many quantum-proof systems go down, and so on and so forth, and you’re left with basically just http://en.wikipedia.org/wiki/Information-theoretic_security
http://www.karlin.mff.cuni.cz/~krajicek/ri5svetu.pdf discusses some of this.
And life was so happy with just one-time pads?
Really, if P=NP, then encoding your messages would be quite low on the priority list … however we’re not debating the practical impact here, but that “finding a provably secure encryption scheme is harder than proving P!=NP”, which was raised as a nitpick, and is clearly not the case.
Happiness or unhappiness of life with one-time pads notwithstanding.