You Can't Factor RSA Keys

General number field sieve In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10^100. Heuristically, its complexity for factoring an integer n (consisting of ⌊log₂ n⌋ + 1 bits) is of the form exp(((64/9)^(1/3) + o(1)) (log n)^(1/3)(log log n)^(2/3)) = L_n [1/3, (64/9)^(1/3)] O and L-notation. [1] It is a generalization of the special number field sieve: while the latter can only factor numbers of a certain special form, the general number field sieve can factor any number apart from prime powers (which are trivial to factor by taking roots). The principle of the number field sieve (both special and general) can be understood as an improvement to the simpler rational sieve or quadratic sieve. When using such algorithms for a large number n, it is necessary to search for smooth numbers (i.e. numbers with small prime factors) of order p^1/2. The size of these values is exponential in the size of n. fuck off, you can't factor RSA keys SO TRUE!!!!!!!!!! Lenstra–Lenstra–Lovász lattice basis reduction algorithm The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. [1] Given a basis B = {b₁, b₂, ..., b_d} with n-dimensional integer coordinates, for a lattice L (a discrete subgroup of R^d) with d ≤ n, the LLL algorithm calculates an LLL-reduced (short, nearly orthogonal) lattice basis in time O(δ^(d n log³ B)) where B is the largest length of b_i under the Euclidean norm, that is, B = max (||b₁||₂, ||b₂||₂, ..., ||b_d||₂) [2][3] The original applications were to give polynomial-time algorithms for factoring polynomials with rational coefficients, finding simultaneous rational approximations to real numbers, and for solving the integer linear programming problem in fixed dimensions.

The meme contrasts a serious mathematical explanation of the General Number Field Sieve and the Lenstra–Lenstra–Lovász lattice basis reduction algorithm with two exaggerated Wojak-style reactions. The upper character dismisses the claim that RSA keys can be factored, while the lower character enthusiastically agrees with the technical explanation, making the joke about smug confidence in cryptography knowledge. It is used as a reaction to complicated mathematical or programming content that feels obviously true to an expert. EN: The meme contrasts a serious mathematical explanation of the General Number Field Sieve and the Lenstra–Lenstra–Lovász lattice basis reduction algorithm with two exaggerated Wojak-style reactions. The upper character dismisses the claim that RSA keys can be factored, while the lower character enthusiastically agrees with the technical explanation, making the joke about smug confidence in cryptography knowledge. It is used as a reaction to complicated mathematical or programming content that feels obviously true to an expert.

• @gentoomemes / 8547 2024-01-07