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Quantum crypto,lattice based crypto, Neurocryptography and cellular automata based cryptography are alternatives to number theory based crypto. I need to know what are the other hard problems like Lattice problems and Number theory based problems that can be used for cryptography(For asymmetric crypto).

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Are you talking about asymmetric encryption, or symmetric encryption? For symmetric operations almost nobody number theory based crypto. –  CodesInChaos Apr 4 at 9:02
    
@CodesInChaos I am talking about asymmetric crypto –  deltaaruna Apr 4 at 9:27
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Code based cryptography like McEliece cryptosystem, is based on the hard problem of decoding linear codes. But i think it lies to the group of quantum based crypto since as far as we know it is still immune to quantum attacks

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