the basics cryptography deals with techniques for secure communication in the presence of third parties (adversaries). modern cryptography uses mathematics,
the basics• cryptography deals with techniques for secure communication in the presence of third parties (adversaries).
• modern cryptography uses mathematics, computer science,and electrical engineering
• the word “cryptography” originatesfrom two Greek words: “hidden/secret” and “writing”
Alia
It's about protocols to overcome the influence of these adversaries.
serpent
cipher systems
• a cipher is the algorithm that transforms information
symmetric vs. asymmetric
Alia
It turns out that knowledge of the encryption key is not necessary for decoding the message. This simple observation made a big impact on cryptography and led to a natural division between symmetric and asymmetric cipher systems.
Alia
Asymmetric cryptography relies on the existence of a computational primitive called trapdoor functions. A trapdoor function takes a domain to a range in such a way that it is easy to go from the domain to range and it is hard to go from the range to the domain given a special string called the trapdoor.
Alia
The public key is used to go from the domain to the range and the private key is used to go from the range to the domain. Only one person has the private key. Also, the private and public keys are usually related by some function f such that "public key" = f("private key"). We make f one way so that it's very difficult to find the private key given the public key.
the olden days
• cryptography was basically encryptioninformation -> nonsense -> information
• whoever wrote the message provided the recipient with the decoding key
Alia
This was before the advent of computers. This method of encryption requires that the sender trust the recipient, because the sender must give the recipient the encryption key. In the example that same key is used by the sender and reciever. The idea that one could send a secure message to a distrusted party seemed impossible until more modern times.
Alia
The only assurance that this message remains private is that only the sender and recipient have access to the key. Knowledge of the key is the only thing that identifies the recipient, but if an adversary gets ahold of the key, he can pass off as the recipient.
exhaustive key search on a Caesar Cipher
code = XMZVH
modular arithmetic in a Caesar Cipher, a shift of 26 is the same as a shift of 0.
for example: 37 = 11(mod 26)
we want a large number of keys
(but having lots of keys is no guarantee of a strong system)
number of potential keys = number of ways 26 letters can be arranged
26! = 403,291,461,126,605,635,584,000,000
Mary, Queen of Scots
1542 - 1587
German Armed Forces, WWII
Enigma Machine
a large number of keys does not guarantee that a cipher is unbreakable
Alia
Used a variation of the substitution cipher to write secret letters detailing her plans to escape from imprisonment and to assassinate Queen Elizabeth of England so she could claim the English throne.
Alia
The German armed forces in the Second World War used a device called an Enigma machine to encrypt much of their military traffic. A basic Enigma machine had over 10^(20) possible keys (more than some modern algorithms). This made them think it was unbreakable, but the Allied Forces were able to break Enigma at various times during the war.
