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Elliptic-curve cryptography
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<p>Elliptic-curve cryptography (ECC) is an approach to <a href="/facts/Public-key_cryptography/gowoFTxS">public-key cryptography</a> based on the <a href="/facts/Algebraic_structure/TkuXca24">algebraic structure</a> of <a href="/facts/Elliptic_curve/60jvaHSA">elliptic curves</a> over <a href="/facts/Finite_field/UkMGJo3m">finite fields</a>. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in <a href="/facts/Finite_field/UkMGJo3m">Galois fields</a>, such as the <a href="/facts/RSA_(cryptosystem)/XTzyfHuq"> RSA cryptosystem</a> and <a href="/facts/ElGamal_encryption/sKDVyMyR"> ElGamal cryptosystem</a>. </p><p>Elliptic curves are applicable for <a href="/facts/Key_agreement/W1DErngS">key agreement</a>, <a href="/facts/Digital_signature/tY7e2pnW">digital signatures</a>, <a href="/facts/Cryptographically_secure_pseudorandom_number_generator/Kew9SdpN">pseudo-random generators</a> and other tasks. Indirectly, they can be used for <a href="/facts/Encryption/16q29Fdv">encryption</a> by combining the key agreement with a <a href="/facts/Symmetric-key_algorithm/5zfe0b76">symmetric encryption</a> scheme. They are also used in several <a href="/facts/Integer_factorization/EjMCTz2t">integer factorization</a> <a href="/facts/Algorithm/fnl5NmRt">algorithms</a> that have applications in cryptography, such as <a href="/facts/Lenstra_elliptic-curve_factorization/PwdIdtQW">Lenstra elliptic-curve factorization</a>. </p>