Cryptography and security
An honest note: classical cryptography rests on algebra, number theory and discrete structures, not on calculus. The connections that do exist are real but indirect.
2 topics
Calculus → cryptography: ★☆☆☆☆ indirect. Encryption works in finite sets — integers modulo , finite fields, lattices — where there are no limits, no derivatives and no integrals. This portal does not pretend otherwise. What is true:
- Elliptic curves were born in real and complex analysis; the chord-and-tangent formulas for adding points come from geometry and implicit differentiation over , and are then reused verbatim over finite fields.
- Side-channel attacks treat power consumption or electromagnetic emissions as signals: correlation, filtering and Fourier analysis recover secret keys from physical measurements.
- Analysis of algorithms (asymptotics, probability estimates such as the birthday bound ) is used to size keys and hashes, and it borrows tools from calculus.
Topics
Elliptic curve cryptography
Public-key cryptography on the group of points of over a finite field. The group law was derived geometrically over the reals (the tangent slope by implicit differentiation); security rests on the discrete logarithm problem, which has nothing to do with calculus.
Side-channel analysis
Recovering keys from physical leakage — power traces, EM emissions, timing — by treating it as a noisy signal. Correlation power analysis, filtering and spectral methods are signal-processing mathematics applied to security.