I assume this means that computer algorithms will compute faster, meaning software can be written that is faster and more efficient, speeding computers up without boosting IP the hardware.
One nightmare scenario is the ability to factor large numbers, where “large” means a number whose factorization would require a time scale comparable to a human lifetime or an economic cost much greater than the value of decryption. Decryption of military or financial messages can be very valuable. Breaking the Axis codes during World War II was literally worth billions of dollars, and at a small fraction of the cost.
Public key encryption depends on the fact that such factorization is impractical. There are murmurs that quantum computing could break this problem, but I do not understand quantum computing, and have not heard of any practical results (and why would I?). Multiplication might be used in brute force assaults, and suddenly high school kids could read top secret military transmissions.
I assume this means that computer algorithms will compute faster, meaning software can be written that is faster and more efficient, speeding computers up without boosting IP the hardware.
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I’m not sure. Don’t computers do something like bit shifting for multiplication? Too bad the article didn’t make it clear.
Applications of the SchönhageStrassen algorithm include mathematical empiricism, such as the Great Internet Mersenne Prime Search and computing approximations of π, as well as practical applications such as Kronecker substitution, in which multiplication of polynomials with integer coefficients can be efficiently reduced to large integer multiplication; this is used in practice by GMP-ECM for Lenstra elliptic curve factorization
I doubt it will have any practical effect on routine calculations. Computers use hardware multipliers that are effectively just like the multiplication tables you learned in school, just with bigger tables. The resolution of most practical calculations is far less than few score decades. For instance expressing the national debt to the nearest penny only requires sixteen digits, currently about $22,920,314,419,523.31. The total number of seconds since the birth of Christ can be express with 11 decimal places, currently 63,739,036,477.
The expense of applying “faster” algorithms probably will never be cost effect on these scales. This kind of math is only useful for things like number theory and its cousin cryptology.
Computers will just continue using the shift and add method required of binary numbers. It takes a maximum number of operations as there are bits in the number.