Abstract
The key exchange problem occurs with symmetric cipher systems because the same key is used for both enciphering and deciphering messages. This means that both the sender and receiver must have the same key and it must be distributed to them via a secure method. While this is merely inconvenient if there are only two correspondents, if there are tens or hundreds of people exchanging secret messages, then distributing keys is a major issue. Public-key cryptography eliminates this problem by mathematically breaking the key into two parts, a public key and a private key . The public key is published and available to anyone who wants to send a message and the private key is the only key that can successfully decipher a message enciphered with a particular public key. This chapter investigates the mechanisms used to implement public-key cryptography .
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The characteristic of a field is the smallest number of times one must use the field’s multiplicative identity element (1) in a sum to get the additive identity element (0). The field has a characteristic of zero if the sum never reaches the addition identity. E.g. the characteristic of F is the smallest positive integer n such that 1 + 1 + 1 + … + 1 = 0, if such an n exists, and zero otherwise.
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Dooley, J.F. (2018). Alice and Bob and Whit and Martin: Public-Key Cryptography. In: History of Cryptography and Cryptanalysis. History of Computing. Springer, Cham. https://doi.org/10.1007/978-3-319-90443-6_11
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DOI: https://doi.org/10.1007/978-3-319-90443-6_11
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