The most common proposals around non-commutative cryptography have been around braid groups. Its proponents have struggled to find parameter sets that are agreed to resist security analysis. Recent proposals have included the algebraic eraser key establishment system and WalnutDSA, a signature scheme that was entered in the NIST post-quantum crytpography ...


In case you would read Rusian: a Diffie-Hellman -like common key from non-commutative group operation. http://mi.mathnet.ru/dan5041 http://www.mathnet.ru/rus/person17348


fgrieu's answer in algorithmic shape: Given is prime $p$ and multiplicative group $(\Bbb Z_p^*, \cdot)$. 1.) Find all prime factors $\{p_1,p_2,...,p_k\}$ of $p-1$. 2.) Iterate through $g = 2,3,... $ until a generator is found, where $g$ is a generator of $(\Bbb Z_p^*, \cdot)$, iff \begin{equation}\forall i\in\{1,...,k\}: g^\frac{p-1}{p_i}\neq 1 \mod p \end{...

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