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.

This will be your public key. Your private key (sometimes called

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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# Public-Key Cryptography

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

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