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- W2278635504 abstract "All cryptographic systems require some form of key exchange. If there are only a few users engaged in a long-term relationship, then it may be possible to exchange keys over a secure private channel, such as by the use of a trusted courier. Then the security of the system is no better than the security of the private channel. If there are a great number of users in a network, however, and their relationships are unpredictable, unforeseen, and brief, then it is inappropriate to have a single shared key, and it is unreasonable to have an individual private key for each pair of users. Consequently, public-key cryptosystems are unavoidable. The keys must be exchanged, or created, over a public channel, but in a way that cannot be reproduced or broken by an adversary. The earliest public-key cryptographers used the fact that the factoring of large composite integers is apparently very hard. The historical evidence for this premise was compelling and remains so; mathematicians had been searching for suitable integer-factoring algorithms for hundreds of years with very limited success. Since the introduction of such public-key cryptosystems, there has been a continuing intense effort to find methods of factoring large composite integers. Accordingly, improved methods of factoring integers have been found, but these improvements are modest. For large n , even these improved methods of factoring are still impractical." @default.
- W2278635504 created "2016-06-24" @default.
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- W2278635504 date "2014-04-10" @default.
- W2278635504 modified "2023-09-26" @default.
- W2278635504 title "Cryptography based on the integer ring" @default.
- W2278635504 doi "https://doi.org/10.1017/cbo9781139013673.004" @default.
- W2278635504 hasPublicationYear "2014" @default.
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