Public-key cryptography is based on the intractability of certain mathematical problems. Early public-key systems based their security on the assumption that it is difficult to factor a large integer composed of two or more large prime factors. For later elliptic-curve-based protocols, the base assumption is that finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point is infeasible: this is the "elliptic curve discrete logarithm problem" (ECDLP). The security of elliptic curve cryptography depends on the ability to compute a point multiplication and the inability to compute the multiplicand given the original and product points.

... is equivalent to proving that P != NP.

be playful

LOVE every minute of it

seek the Asymmetry in the Symmetry

use good tools (sagemath / pen & paper)

respect the ancients (Euclides, Diophantes, Fermat, Euler, Gauss, Galois, Erdos & co.)

contemplate the essence of main actors (p, n, ζ, ...) and their governing principles (quadratic reciprocity, (cyclotomic) polynomials, ...)

be ready that - if Truth demands it - You will fail as others (e.g. me) have failed