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British mathematician G. H. Hardy once said, \[OpenCurlyDoubleQuote]The \
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The significant increase in the availability and usefulness of computers in \
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In this chapter, you will learn about cryptography, a large and active field \
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Mathematical concepts form the basis of the techniques used in cryptography \
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Mathematics, computer science, electrical engineering, communication science \
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This is an encryption system where a single common key is used to encrypt and \
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This is an encryption system where a pair of keys is used to encrypt and \
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The history of cryptography can be divided into three distinct phases.\
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 "The most dramatic shift, occurring in the final two decades of the \
twentieth century (the third phase), was the adaptation of cryptology for the \
",
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 ". Modern cryptography relies heavily on various mathematical fields, such \
as information theory, computational complexity, statistics, combinatorics, \
abstract algebra, number theory and finite mathematics. Unlike classical \
ciphers, which only encrypted written text, computers enabled the encryption \
of any data in binary format."
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an apparently random form. Data is encrypted like a physical key securing a \
lock, requiring a matching decryption key for access."
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Cell[TextData[{
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A shared secret key, used by both sender and receiver, can be a password, \
code or secure random string of letters/numbers.\
\>", "Text",
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Cell["The Need for Asymmetric Cryptography", "Subsection",
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Symmetric algorithms allow for messages to be encrypted and decrypted \
quickly. Simply lengthening keys enhances the security offered by symmetric \
encryption.\
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However, there is a significant disadvantage. As you already know, in \
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Sharing keys over unsecured connections risks malicious interception by third \
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If you could find a method of encryption/decryption such that exchanging the \
keys does not reveal how to decrypt intercepted messages, then you would \
avoid this problem.\
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Using such a system, messages are encrypted with the receiver\
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Cell["\<\
The public key may be freely distributed and is used for encryption.\
\>", "Text",
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Cell["\<\
This system is so constructed that the calculation of the private key is \
computationally impossible from the public key, even though they are related.\
\
\>", "Text",
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Cell[TextData[{
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