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If we instead select an aribtrary prime without such a special structure, there are still some optimizations we can do beyond the obvious 'perform a multiply, and then perform a generic modulo reduction'. We can implement Montgomery Multiplication, which replaces the modulo operation with some multiplies and shifts; the net result is that a modular reduction can be done in the time of approximately two bignum multiplications; in other words, modular reduction of a special form prime can be done approximately twice as fast as an arbitrary prime.  If this were the only consideration, the choice on whether we should use a prime with special structure would be an obvious one. However, there is another issue. Sometimes, Elliptic Curves are implemented by hardware that needs to do go  into hostile environments, and can be expected to be subject to side channel attacks, such as Differential Power Analysis; with this, Analysis, In this attack,  the attacker runs the system, performing the same operation repeatedly, and takes careful measurements of power consumed (or EM radiation emitted) on a cycle-by-cycle basis; by statistically combining these measurements, the attacker hopes to recover the internal states (and thus (which includes  the private key). To combat these sorts of attacks, one of the strategies that need to be employed is blinding; masking;  we include random data in our computations, and while the end results is independent of the random value, the intermediate values are strongly dependent, and thus the correlations between the internal states and anything that the attacker wants (such as the private key) is much weaker. One such method of blinding Elliptic Curve calculations (first published by Coron\cite{Coron_1999}) took advantage of a property of Elliptic Curve groups; we know an integer $n$ such that $nG = 0$ (this value $n$ is known as the order of the point $G$). Coron's method to compute $kG$ would be to select a random value $r$ and computing first $nr+k$, and then $(nr + k)G$. Everytime we would perform a point multiplication, we would select a random $r$, and hence the bits of the integer we're giving to the point multiplication logic are independent of the integer $k$ we're actually multiplying by.