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Feasible? Sure, there are lattice algorithms that are competitive in performance with RSA. However, there are drawbacks, like: They've been studied less than RSA or ECC, especially the individual algorithms. No generic proof that I know of that there isn't a quantum algorithm to solve them. The first one is why I doubt TLS will move to lattices at least ...


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As Steth stated before, using system time as seed in cryptographic implementations is terrible idea for any PRNG because this may be simply very predictable. There are better solutions based on noise generated by device drivers in the system (see man urandom) What you want from PRNG in cryptography is to be uniform and unpredictable, so the entropy would be ...


1

I do not know why the OpenSSL implementation specifically does this. However, a branch-less (constant time) implementation of the RSA private key operation, might be slightly more efficient if the parameter $c = q^{-1} \bmod p$ is calculated for $p$ being the greatest prime of the two. Otherwise the value of $J_q = I^{d \bmod q-1} \bmod q$ has to be taken ...


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There's no real difference between $p$ and $q$ in RSA. It looks like OpenSSL just has the agreement "$p$ has to be bigger than $q$" for conveniences. One of the numbers has to be bigger than the other (otherwise they would be the same number, and $p = q$ is very bad in RSA). Just use two examples: $p = 13$ and $q = 11$. $p$ is bigger than $q$, all right. ...



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