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# Public-Key Cryptography

Presentation for CSC 380 on Public-Key Cryptography based on my essay.
by

## Alex Dobson

on 12 April 2011

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#### Transcript of Public-Key Cryptography

Public-Key Cryptography Alex Dobson Cryptography helps answer the question How can two parties pass messages containing
a secret without the secret being revealed to a
third party? There is no way to guarentee our communication network can be "trusted", so we have to eliminate the need to trust the network. There are 4 basic elements to every Cryptosystem. 1 2 3 4 This is what cryptography tries to accomplish.
To eliminate the need to trust the network. The plaintext The plaintext is the original form of
the message, and can be understood
by anyone who reads it The encryption function The encryption function turns the plaintext
into the ciphertext by using an encrpytion
algorithm along with a key from the keyspace. The Ciphertext The ciphertext is the text that
results from the encryption
function being used on the
plaintext. The Decryption Algorithm The decryption algorithm turns the ciphertext back into plaintext so that it can be read, it also uses a key from the key space. There are 3 sets that
are used in cryptography 1 2 3 The plaintext space This set is all possible plaintexts
that can be used, in many cases
it is all binary numbers, all
the decimal numbers, or the all
the words in a particular human
language. The Keyspace The keyspace is the collection of all keys
that will be used with the encryption and
decryption algorithms Keys Keys in cryptography are used
by both the encryption and
decryption algorithm. Each key k from the keyspace
determines a particular pair of
encryption and decryption
functions. If we use the encryption algorithm
and then the decryption algorithm
with the same key, then we will
obtain the original plaintext. The Ciphertext Space The ciphertext space is determined by
applying the encryption algorithm for
every plaintext from the plaintext space
with every key from the keyspace. Classical Two-Way Cryptography Classical two way cryptography has a
major flaw with regards to the world we
live in today... In classical two-way cryptography, the two
parties have to meet at some point to exchange
keys in secret, so they know that no one else
has obtained the keys. In our modern world, we can't always meet
and exchange keys with the person we want
to exchange messages with. No one goes to
Amazon and exchanges keys with them when
they want to buy something from them over
the Internet. This is where Public-Key Cryptography comes in... Public-key cryptography eliminates the need to exhange
keys in private, it can now be done over an insecure
channel such as the Internet. Public-Key Cryptography
achieves this goal because In public-key cryptography, it is computationally
infeasable to be able to derive the decryption
algorithm if you know the encryption algorithm. This means that it won't matter if you make your
encryption algorithm public, because no one will
be able to derive your decryption algorithm from
the encryption algorithm. An everyday example of
Public-Key Cryptography Imagine that you have a phone book
for New York City. You create an
encryption algorithm where you write
out a message in English, and then for
each letter you pick a random last
name from the phone book that starts
with that letter. The phone number of
that person will then replace the letter
and this will create the ciphertext.
a trapdoor) will be that you have a
phone book that is sorted by phone
number. It will then be trivial for you
to to decrypt the ciphertext back to
plaintext, but for someone who does
not have the trap door, this task
could take decades. History Public-Key cryptography was
first introduced by Whitfield
Diffie and Martin Hellman in
their paper entitled, "New
Directions in Cryptography"
in May of 1975. They proposed an idea known as
Diffie-Hellman key exchange. It
was the first instance of public-key
cryptography. RSA We eliminate the need to trust the network
by making the message impossible to read
unless you know the secret of how to read
it. This process of disguising the message
is known as encrypting the message. History RSA is named after its inventors: Rivest, Shamir and Adleman. It is based on an amazingly simple (for a cryptographic system) number-theoretical idea. The idea is that while it is easy to multiply two large primes together, it is extremely difficult to factorize their product. Thus, the product can be used in the public key, and there is little risk that anyone will find out the primes used. This is possible because the encryption and decryption
algorithms don't share the same key, they each use a
different one. A public key to encrypt the message with
the encrytion algorithm, and a private key to decrypt
the ciphertext with the decryption algorithm. Diffie and Hellman wanted to solve two
problems, that of key distribution and that of digital signatures. They managed to solve both through public-key cryptography. They used one-way functions along with challenged and response identification to solve these two problems. Questions?
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