The Mathematical Cryptography of the RSA Cryptosystem
نویسنده
چکیده
Invented in 1977 by Rivest, Shamir and Adleman, the RSA cryptosystem has played a very important role in the development of modern cryptography. Its various applications in industry, Internet, banking, online shopping, cell phones, smart cards, secure information transfers and electronic signatures have made RSA a standard at the heart of modern technologies. This chapter explores the mathematics behind the RSA cryptosystem including the encryption, decryption and signature schemes of RSA. We give a survey of the main methods used in attacks against the RSA cryptosystem. This includes the main properties of the continued fraction theory, lattices, the LLL algorithm of Lenstra, Lenstra and Lovász and the lattice reduction based technique of Coppersmith for solving modular polynomial equations.
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