Cryptography formula — definition, units and applicable conditions

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Cryptography

RSA modular exponentiation relationship

c\equiv m^e\pmod n,\quad m\equiv c^d\pmod n

shows the core mathematical relationship of RSA public and private key modular exponentiation.

Cryptography

y^2\equiv x^3+ax+b\pmod p

defines the set of points over a finite field for elliptic curve cryptographic operations.

Cryptography

K=(g^a)^b=(g^b)^a\pmod p

Both parties obtain the same shared group elements by exchanging public modular powers.

Cryptography

P_{\mathrm{coll}}\approx1-e^{-q(q-1)/(2N)}

estimates the probability of at least one collision when q random samples fall into N values.