Coppersmith method

<p>The Coppersmith method, proposed by <a href="/facts/Don_Coppersmith/T7zvXag6">Don Coppersmith</a>, is a method to find small integer <a href="/facts/Zero_of_a_function/mlK3dhoT">zeroes</a> of univariate or bivariate <a href="/facts/Polynomial/Lzak8VVx">polynomials</a>, or their small zeroes <a href="/facts/Modular_arithmetic/0wtRa5dU">modulo a given integer</a>. The method uses the <a href="/facts/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm/hadYSXGw">Lenstra–Lenstra–Lovász lattice basis reduction algorithm</a> (LLL) to find a polynomial that has the same zeroes as the target polynomial but smaller coefficients.
</p><p>In <a href="/facts/Cryptography/e94PEVau">cryptography</a>, the Coppersmith method is mainly used in attacks on <a href="/facts/RSA_(algorithm)/XTzyfHuq">RSA</a> when parts of the <a href="/facts/Public_key_cryptography/gowoFTxS">secret key</a> are known and forms a base for <a href="/facts/Coppersmith%27s_attack/wyQypHfq">Coppersmith's attack</a>.
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Coppersmith method open-in-new

Coppersmith method