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This tag refers to public-key algorithms based on problems that quantum computers can't solve efficiently. Existing algorithms such as RSA, Diffie-Hellman, and ECDSA are known to be breakable using Shor's algorithm on quantum computers. Symmetric-key algorithms generally don't fall under this category.

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Why the exponent is a power of 2 in Ring-LWE?

As @Raoul722 pointed out the polynomial should be irreducible. One should also add the fact that in the original Ring-LWE article security proofs hold by sampling the error with a spherical distribut …
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