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Mathematical Hard Problems in Modern Public-Key Cryptosystem

In secure network communication public-key algorithms are designed to resist chosen-plaintext attacks; their security is based both on the difficulty of deducing the secret key from the public key and difficulty of deducing the plaintext from the ciphertext. In this paper the two general types of hard problems - number factoring and discrete logarithms are explained. These apply to cryptosystems such as RSA, ElGamal, elliptic curve, Diffie-Hellman key exchange, and they are used in digital signature algorithms