This course will introduce you to the foundations of modern cryptography, with an eye toward practical applications.

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From the course by University of Maryland, College Park

Cryptography

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This course will introduce you to the foundations of modern cryptography, with an eye toward practical applications.

From the lesson

Week 1

Introduction to Classical Cryptography

- Jonathan KatzProfessor, University of Maryland, and Director, Maryland Cybersecurity Center

Maryland Cybersecurity Center

[SOUND].

Â In the last lecture, we talked about the importance of definitions in general.

Â In this and the next lecture we'll look specifically at defining security for

Â private key encrytion schemes building up to a definition called perfect secrecy.

Â In this lecture we're going to build up to an informal definition of security.

Â And we'll make everything more formal in the next lecture.

Â In general cryptographic definitions have two components.

Â The first component specifies the threat model which is meant to

Â capture the real world capabilities that the attacker's assumed to have.

Â As we'll see, there can be many different threat models.

Â And the right one to use depends,

Â in part, on the environment in which the scheme will be used.

Â The second component of any cryptographic definition is the security guarantee.

Â You can view this alternately as the goal we're trying to

Â achieve by using the scheme.

Â Or is what it is we're trying to prevent the attacker from doing.

Â Since it's been awhile since we've looked at private key encryption let me

Â briefly remind you of the setting.

Â We have two parties, Bob and Alice, who have shared a key k in advance.

Â When Bob say, has some message m that he wants to send to Alice.

Â He'll encrypt that message, using the encryption scheme and their shared key K.

Â This results in a ciphertext that bob sends across the channel to Alice.

Â Upon receiving this message, Alice will use her key to decrypt the cypher-text and

Â recover the original message.

Â At a high level, the parties are trying to ensure secrecy of

Â their communication against an eavesdropper who can

Â observe everything being sent across the channel between Alice and Bob.

Â There are several different threat models we could consider here.

Â I'll describe them informally for now.

Â The most basic and the one implicit in the figure on

Â the previous slide is known as a ciphertext-only attack.

Â Here the attacker only gets to observe ciphertext being sent by the parties and

Â nothing else.

Â Even within this threat model, there are choices we can make.

Â In particular do we assume the attacker observes only a single ciphertext or

Â do we assume that the parties encrypt multiple messages using the same key and

Â the attacker gets to observe multiple ciphertexts.

Â As we'll see later on, this distinction makes a big difference.

Â A stronger threat model is the so-called known-plaintext attack.

Â Here, the attacker will again observe one or

Â more ciphertext whose underlying plaintext is unknown.

Â But, in addition to this, the attacker was able to obtain a bunch of

Â ciphertext encrypted using the same key along with the corresponding plaintext.

Â This might seem unrealistic, but

Â there are many real world scenarios in which such an attack is possible.

Â For a simple example, imagine that every day Alice and

Â Bob begin by sending encrypted hello messages back and forth.

Â If the attacker observes those ciphertext, it knows the underlying plain text.

Â An even stronger threat model is a chosen plaintext attack.

Â The attacker will again observe one or

Â more ciphertexts, whose underlying plaintext is unknown.

Â But in addition, the attacker is now assumed to be able to obtain cipher text,

Â encrypted using the same key,

Â corresponding to plaintext of the attacker's choice.

Â This may really seem unreasonable, but again, there are many natural

Â scenarios where some form of chosen-plaintext attack is possible.

Â For one thing actions of an attacker might influence the messages that parties send

Â even if the attacker can't control them completely.

Â In other cases,

Â the attacker might be able to have complete control over what gets encrypted.

Â For example, imagine an attacker typing at a terminal where anything that's

Â typed gets encrypted using a key unknown to the attacker.

Â In that case, the attacker really does have the ability to mount a complete

Â Chosen-plaintext attack.

Â The strongest threat model typically considered is a Chosen-ciphertext attack.

Â Now in addition to having the ability to carry out a Chosen-plaintext attack

Â like before.

Â We also assume the attacker is able to get the parties to decrypt certain cipher

Â texts of that attacker's choice.

Â This may sound totally unrealistic but

Â we'll see later on in the course that the ability to carry out some limited form of

Â chosen cipher text attack is actually very common and must be defended against.

Â For concreteness let's assume from now on the simplest threat model, a ciphertext

Â only attack where the attacker only gets to observe a single ciphertext.

Â Even within this setting, how should we define security?

Â Before I continue, you may want to pause the video for a few minutes.

Â To think about how you would define security in this setting.

Â One suggestion people sometimes come up with is that it should be impossible for

Â the attacker to determine the key shared by the parties.

Â A little thought,

Â however, should convince you that this is not really the right definition.

Â For starters, the key is just a means to an end.

Â But protecting the key is not the goal in itself.

Â In any case, maintaining secrecy of the key is at best necessary, but

Â not at all sufficient to ensure that the parties communication remains secret.

Â In particular it's easy to come up with a trivial encryption scheme

Â that protects the key completely but

Â doesn't ensure secrecy of the messages being encrypted at all.

Â How about this possibility?

Â Say the encryption scheme is secure if and

Â only if it is impossible for the attacker to learn the plain text.

Â This is better but still has problems.

Â For one, what if I come up with a scheme in which the attacker cannot learn

Â the entire plaintext but is able to learn 90 percent of the plaintext?

Â Such a scheme would be considered secure by this definition, but hopefully you

Â would agree that we don't really want to consider such a scheme secure.

Â This means we have to keep looking for the right definition.

Â [SOUND] We can follow the problem I just mentioned by the following definition.

Â Say a scheme is secure if it is impossible for

Â the attacker to learn any character of the plain text.

Â This is a step in the right direction but it ignores the possibility that

Â the attacker might be able to learn other information about the plaintext.

Â For example, what if I encrypt someone's salary and

Â the attacker can't figure out any digit in the salary but can tell whether or

Â not they make more than $60,000.

Â That would satisfy this definition but,

Â again we really wouldn't want to consider such a scheme secure.

Â Furthermore, it's not entirely clear what it means to learn a character.

Â What if an attacker is able to guess a character correctly,

Â does that count as learning a character?

Â It shouldn't, but how do we rule that out?

Â Cryptographers have thought about the problem of defining secure encryption for

Â many years.

Â The definition they have converged upon,

Â which takes in to account all the previous considerations, is this one.

Â An encryption scheme is secure if the following is true.

Â Regardless of any prior information the attacker has

Â about the plaintext the ciphertext observed by

Â the attacker should leak no additional information about the plaintext.

Â Note first of all that this rules out learning 90 percent of the plaintext.

Â Or characters of the plaintext, or

Â even any other type of information about the plaintext.

Â On the other hand, blindly guessing some character of the plaintext is not

Â considered a violation of security, because the attacker could have

Â guessed the character of the plaintext without seeing the ciphertext at all.

Â That is, as long as seeing the ciphertext does not make it any easier for

Â the attacker to guess a character of the plaintext.

Â It's not to be considered a violation of security.

Â This definition was first proposed in the early 1980s.

Â And by now has become the generally accepted definition of security.

Â The question we'll turn to next time is how to mathematically formalize

Â this definition.

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