Discretion

from SpinTunes 16 by Jocko Homomorphism

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about

This song is about modular arithmetic and elliptic curves in cryptography, which I'm teaching this semester! It's my second time writing math jazz.

Cryptography relies on one-way math problems to keep our secrets. It's easy to calculate powers, but taking roots is much more complicated. At least, it is in the discrete world, where the number line wraps around on itself. The chorus demonstrates counting powers of six and wrapping around at thirteen:

6^4 = 9 mod 13
6^3 = 8 mod 13
6^2 = 10 mod 13
6^1 = 6 mod 13.

To be practical, we have to wrap at a very large modulus. Anyone who knows how the modulus factors can calculate whatever root they like. Fortunately, factoring is hard; the best thing a code breaker can do is just guess and check. Encryption stacks the deck so that guessing takes a very, very long time.

lyrics

Count the hours
Master waiting
All my powers
Captivating
I know you just can't break me down

One two three four
Rounding back the contour
Nine eight ten six
Feeling my helix
One two three four
Rounding back the contour
Nine eight ten six
Feeling my helix

I don't fake it
If you wonder
It's my secret
By the number
I know you just can't break me down

One two three four
Rounding back the contour
Nine eight ten six
Feeling my helix
One two three four
Rounding back the contour
Nine eight ten six
Feeling my helix

Generators
Circulating
All you gators
Calculating
I know you just can't break me down

credits

from SpinTunes 16, released January 29, 2020

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Jocko Homomorphism Indiana

Electronic Musician

Jocko Homo + J-Homomorphism = Jocko Homomorphism

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