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Why is 128-bit encryption considered good enough for medium term security only? Because in the long term it is expected that mankind will be able to carry out $2^{128}$ operations because it's not physically as impossible as $2^{256}$ operations. Quantum computing or brute force attack? Assuming quantum computers work at a speed comparable to ...


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Let $\mathbb{Z}, +$ be the group integers, $\mathbb{Z}/n\mathbb{Z}, \times$ the multiplicative group of integers modulo $n$, and $\varphi(n)$ its order. Then $\varphi(n)\mathbb{Z}, +$, the additive group of multiples of $\varphi(n)$ is a subgroup of $\mathbb{Z}$. The function $f : \mathbb{Z} \rightarrow \mathbb{Z}/n\mathbb{Z} : x \mapsto a^x \mod n$ for ...


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Your best bet at the moment are probably the lattice-based key exchange described in the "Post-quantum key exchange – a new hope" paper. You can also find different implementations. C code can be found on Peter Schwabe's homepage. For signatures, if you want to use lattices, you will end-up with BLISS or BLISS-B both of which are implemented by various ...



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