Symmetric Key Cryptography

Summary

This script delves into the concept of block ciphers, a fundamental aspect of modern cryptography. It explains the evolution from historical ciphers to modern digital encryption, emphasizing the importance of encoding standards like UTF-8 over ASCII for comprehensive character representation. The speaker highlights the significance of block size in cipher security, advocating for a minimum of 128-bit keys for personal use and 256-bit for military applications. The script also introduces the principles of confusion and diffusion in cipher design, aiming to ensure that cipher text statistics are complex and that changes in plain text or key significantly affect the cipher text.

Takeaways

• 🗝️ Block ciphers are an important topic in modern cryptography, which encrypt data in fixed-size blocks of bits instead of individual characters or pairs of characters.
• 🔠 Historical ciphers were replaced due to their vulnerability to statistical techniques like frequency analysis, which is not a concern with block ciphers.
• 🌐 Communication parties must agree on an encoding standard, such as UTF-8, to represent letters, numbers, and symbols as strings of bits for digital communication.
• 📚 The ASCII encoding standard is widely known but does not include some special characters used in languages like Turkish, leading to the preference for UTF-8.
• 🔢 The number of bits used to represent characters is crucial; for instance, 8 bits allow for 256 different characters, which is why block sizes of 64 or 128 bits are common for encryption.
• 🔒 Block ciphers provide confidentiality by transforming plaintext into ciphertext using a secret key, which is essential for secure communication over potentially insecure channels.
• 🔑 Symmetric key encryption algorithms, including block ciphers, use the same key for both encryption and decryption, whereas asymmetric key algorithms use a public key for encryption and a private key for decryption.
• 🔄 Block ciphers involve a permutation of the input space (plaintext blocks) to the output space (ciphertext blocks), creating a complex relationship that is difficult for cryptanalysts to exploit.
• 🔍 The design of a good block cipher aims to provide confusion and diffusion, making it challenging to deduce any relationship between the ciphertext and the plaintext or the key.
• 🔧 The security of a block cipher is not absolute and can be compromised if a cryptanalyst develops a new technique to exploit weaknesses in the cipher.
• 📈 The size of the key space (e.g., 2^128 for a 128-bit key) is vast, and a good block cipher should act as if it is a randomly selected permutation from this large set.

Q & A

What is the primary difference between historical ciphers and modern block ciphers?

Historical ciphers typically operated on individual characters or pairs of characters, which could be easily broken using frequency analysis. In contrast, modern block ciphers operate on pairs of bytes or larger blocks of bits, making them much more secure against such attacks.

Why is encoding important in cryptography, especially in digital communication?

Encoding is crucial because it ensures that both communicating parties agree on a common way to represent data, such as letters, numbers, and symbols, as a string of bits. This standardization is necessary for effective encryption and decryption.

What are the limitations of the ASCII encoding standard mentioned in the script?

The ASCII encoding standard is limited because it only supports 128 characters, which is insufficient for languages with special characters, such as Turkish. This limitation can cause incorrect character representation in digital communication.

What is the significance of block size in block ciphers, and what are the commonly used block sizes?

The block size in block ciphers is significant because it determines how much data is encrypted at a time. Commonly used block sizes are 64 or 128 bits, with 128 bits being preferred for stronger security. Smaller block sizes, like 32 bits, are less secure and more vulnerable to attacks.

What is the role of secret keys in symmetric key cryptography?

In symmetric key cryptography, the same secret key is used for both encryption and decryption. The security of the system relies on keeping this key confidential, even if the encryption and decryption algorithms are known.

How do public key cryptography and symmetric key cryptography differ in terms of key usage?

In symmetric key cryptography, both parties use the same secret key for encryption and decryption. In public key cryptography, one key (public key) is used for encryption, and a different key (private key) is used for decryption, with the private key being kept secret.

What is meant by confusion and diffusion in the context of block cipher design?

Confusion refers to making the relationship between the cipher text and the key complex and non-linear, while diffusion involves spreading the influence of each bit of the plaintext and the key over many bits of the ciphertext to obscure statistical patterns.

Why is the choice of key size important in encryption, and what key sizes are recommended for different use cases?

The key size is important because it determines the security level of the encryption. For personal use, a 128-bit key is recommended, while military applications typically require a 256-bit key for stronger security. A larger key size provides more protection against brute-force attacks.

How does block cipher encryption work at a high level?

Block cipher encryption works by dividing the plaintext into fixed-size blocks (e.g., 128 bits) and encrypting each block separately using a secret key. This process creates ciphertext blocks, which together form the encrypted message.

What is the importance of selecting a good permutation in block cipher design?

Selecting a good permutation is crucial because it ensures that the encryption process maps plaintext blocks to ciphertext blocks in a way that is secure and resistant to cryptanalysis. A good permutation makes it difficult to find any relationship between related keys or ciphertexts.

Outlines

00:00

🔐 Understanding Block Ciphers and Data Encoding

This paragraph introduces the concept of block ciphers in cryptography, explaining the need to encrypt pairs of bytes instead of single characters in the modern era. The discussion highlights the importance of data encoding standards like ASCII and UTF-8, emphasizing their role in representing characters as bits for digital communication. The paragraph also addresses historical issues with encoding, particularly how ASCII failed to represent special characters in languages like Turkish. The explanation extends to the basics of data representation using bits and bytes, leading to a discussion on how block ciphers handle large amounts of data, such as megabytes or terabytes, in encryption.

05:01

🔑 Symmetric and Asymmetric Encryption Algorithms

This paragraph delves into the different types of cryptographic algorithms, focusing on symmetric key encryption, such as block ciphers and stream ciphers, and public key encryption, like RSA. It introduces the concept of authenticated encryption algorithms that provide both confidentiality and data authentication. The discussion includes the roles of hash functions and digital signatures in ensuring data integrity and origin non-repudiation. The paragraph outlines the broad scope of cryptography, touching on advanced topics like post-quantum cryptography and full homomorphic encryption, which are part of the larger cryptographic landscape.

10:04

🔍 Defining Cryptosystems and Cipher Text

This paragraph defines key cryptographic terms, such as plaintext, ciphertext, and cryptosystems. It clarifies the distinction between the terms 'cipher' and 'password,' which are often confused in some languages. The explanation covers the process of converting plaintext into ciphertext using encryption algorithms and the importance of keeping the decryption key secure. It also emphasizes that while the encryption algorithm can be public, the security of the system relies on the secrecy of the key, in line with Kerckhoffs's principle.

15:05

📦 How Block Ciphers Operate

This paragraph explains the operation of block ciphers, which encrypt fixed-size blocks of data using a secret key. It describes the importance of choosing an appropriate block size, such as 64 or 128 bits, to ensure security against attacks like frequency analysis. The discussion highlights how block ciphers map input blocks to output blocks through permutations, and the significance of designing a cipher that selects a secure subset of permutations. It introduces the concept of related-key attacks and stresses the need for different permutations when even a small change is made to the secret key.

20:07

🔐 Confusion and Diffusion in Cipher Design

This paragraph discusses the principles of confusion and diffusion, introduced by Claude Shannon, which are essential in designing secure block ciphers. Confusion makes the relationship between the plaintext, ciphertext, and key complex, preventing attackers from easily deducing the key. Diffusion ensures that a change in one part of the plaintext affects many parts of the ciphertext, making statistical attacks difficult. These abstract concepts are fundamental to creating effective cryptographic algorithms, although their security can't be definitively proven, only tested against known cryptanalysis techniques.

Keywords

💡Block Cipher

A block cipher is a method of encrypting text where a cryptographic key and algorithm are applied to a block of data (usually of fixed size) as a whole. This is a central concept in modern encryption, replacing earlier methods like character substitution. The video explains that block ciphers operate on b-bit blocks of data, transforming plain text into ciphertext using secret keys.

💡Encoding

Encoding is the process of converting data into a specific format for efficient transmission or storage. In the video, it refers to the agreement between communicating devices on how to represent data as bits. The choice of encoding, such as ASCII or UTF-8, impacts how characters are represented digitally, which is crucial for ensuring accurate communication and encryption.

💡ASCII

ASCII (American Standard Code for Information Interchange) is a character encoding standard that uses seven bits to represent text characters. The video mentions ASCII as a widely known standard but highlights its limitation in representing non-English characters, like certain Turkish letters, which is why UTF-8 is often preferred in modern applications.

💡Symmetric Key Cryptography

Symmetric key cryptography involves the use of the same key for both encryption and decryption. This method is foundational in the video’s discussion of block ciphers and other cryptographic techniques, where the security relies on keeping the shared key secret between the communicating parties.

💡Confusion and Diffusion

Confusion and diffusion are two principles introduced by Claude Shannon to design secure encryption algorithms. Confusion refers to making the relationship between the ciphertext and the key complex, while diffusion spreads the influence of each plaintext digit over many ciphertext digits. The video discusses how these principles are essential in the design of block ciphers to ensure security.

💡Permutation

In cryptography, a permutation refers to a rearrangement of elements in a set. The video explains that block ciphers operate by mapping input bits to output bits through a permutation, aiming to make it difficult to predict how the plaintext will be transformed into ciphertext. The concept is tied to the idea of creating a vast number of possible encryptions to ensure security.

💡Public Key Cryptography

Public key cryptography involves using two keys—a public key for encryption and a private key for decryption. Unlike symmetric key cryptography, the public key is openly shared, while the private key remains confidential. The video contrasts this method with symmetric key cryptography, highlighting its importance in modern secure communication, such as in the case of RSA.

💡Ciphertext

Ciphertext is the encrypted form of plaintext, which appears as a random sequence of bits. The video describes how encryption algorithms transform plaintext into ciphertext to protect data during transmission. Only someone with the correct decryption key can convert ciphertext back into its original plaintext form.

💡Message Authentication Code (MAC)

A Message Authentication Code (MAC) is used to verify the integrity and authenticity of a message, ensuring that it has not been altered. The video mentions MACs in the context of data authentication, distinguishing them from encryption algorithms and emphasizing their role in ensuring data security without necessarily encrypting the data.

💡Key Agreement Algorithm

A key agreement algorithm allows two parties to securely share a cryptographic key over an insecure channel. The video discusses the Diffie-Hellman key exchange as an example, explaining its significance in enabling secure communication over networks like the internet without prior sharing of secret keys.

Highlights

Introduction to block ciphers as a modern cryptographic technique to replace historical ciphers.

Explanation of the necessity to move from character pairs to bit pairs in encryption due to digital data handling.

The importance of agreeing on an encoding standard like UTF-8 for digital communication to avoid issues with character representation.

The limitations of ASCII encoding, particularly its inability to represent special characters in some languages like Turkish.

The concept of using bits to represent characters and the significance of the switch point at seven or eight bits for character representation.

The role of block ciphers in encrypting large amounts of data efficiently, such as one megabyte or even terabytes.

Cryptography's role in solving problems of confidentiality, authentication, and non-repudiation in digital communications.

Differentiation between symmetric key encryption algorithms like block and stream ciphers, and public key encryption algorithms like RSA.

The significance of choosing an appropriate block size in block ciphers to prevent vulnerability to frequency analysis.

The explanation of how block ciphers operate on fixed-size blocks of data, creating a permutation from input to output space.

The comparison of the vast number of possible permutations in block ciphers to the small subset actually used for encryption.

The importance of key size in block ciphers, with recommendations for different use cases, including personal and military standards.

The abstract concepts of confusion and diffusion in cipher design, introduced by Claude Shannon, to enhance security.

The definition of confusion as making the cipher text's relation to the key and plain text statistics complex for cryptanalysts.

The definition of diffusion as ensuring that changes in the plain text or key influence many bits in the cipher text.

The practical application of confusion and diffusion in the design of block ciphers to create a secure encryption method.

Transcripts

all right so today's topic is very

important which is called block ciphers

so we have seen the historical ciphers

so we understand why we need to replace

a pair of characters instead of a single

character right because it is easy to

break by using statistical techniques

like frequency analysis now uh we are in

the modern AG so instead of uh

encrypting pairs of characters we are

actually going to pairs of bites right

because we are dealing with zeros and

ones so first we have to agree on the

encoding okay in order to people or to

device to communicate they have to agree

in the language right so here encoding

is what we are going to tell it so

historical sers mostly operate on

letters since they are pen and paper

methods when working with digital data

we can represent letters number symbols

Etc a string of bits right thus the

communicating parties must first agree

on an

encoding this is why we have standards

right ask is the best known because it

is American Standard but generally we

prefer utf8 because ASI doesn't contain

the some of special Turkish characters

right so for this reason we cannot use

directly ask this is why years ago most

probably you remember whenever you chat

in a video game or in the general uh

chat program you could when you press a

Turkish character and send it you will

see a different symbol there this is

because of asky table okay they were

using asky okay so let me show you uh

the full ask key table so since we are

representing data as bits you know

Gathering bits together allows you to

represent more characters like because

with a single bit you can represent zero

or one so you can only represent two

character right you can say a is zero

and B is one and that's it but your

alphabet has more letters right so you

have to use

more uh bits so if you use two bits 2 to

the two is four so you can represent

four characters right so this way

actually if you look at the powers of

two you will realize that the switch

spot is something like seven or eight

because 2 to the 7 is

128 which is enough actually this part

of the table is 2 to the 7 which gives

you 128 characters

but if you add one more bit and make it

eight bits you can actually represent

two to

256 different characters right we are

starting from zero so this is why we end

up with

255

so first you have to agree on the

encoding and here as you can see uh

capital letters and then small letters

appear here we have the numbers and so

on and so forth at this extended part we

have have more Latin characters that are

used especially in French right but as

you can see we don't have some special

Turkish characters like sh or soft G

right this is why we cannot use it also

this picture shows explains one of the

problems when you see a list in a

Turkish web page or a database however

if your name starts with ch like

here and when you see a alphabetical

list you would expect to find your name

after C right but sometimes you don't

appear there the all alphabet ends with

the name Z and then you appear below it

this is because

128 is larger than these numbers okay

this is the whole reason they are using

asky table so CH comes a lot later than

Z this is the whole reason so this is

wrong database design if if you are

allowing Turkish characters then you

should be using a different encoding

this is the whole Li but here I'm only

talking this to say that we are going to

work on bits and we have a method to

represent every character in terms of

bits okay we agree on that then we will

talk about how we encrypt them okay

so in our case a single bite is 8 Bits

you know 1,24 by is 1 kiloby and so on

and so forth but uh we have very length

input in our cases for instance we are

going to encrypt maybe one megabyte or 2

terabytes we should have a method to do

that right block cers can do that this

is the whole idea

so let's remember where we are and then

we are going to talk about how block

ciphers work so as I mentioned before

cryptography solves a lot of problems

for the case of confidentiality which is

our current topic today we can provide

confidence confidentiality by encryption

algorithms like blog sers stream cers

these are symmetric key encryption

algorithms or you can use public

encryption algorithms like RSA or algama

which will'll be talking Weeks

Later nowadays we are we have

authenticated encryption algorithms

which provide both confidentiality but

also data

authentication also you can provide data

authentication with hash functions

message authentication codes moreover

you can obtain anti authentication with

digital signature zero knowledge proofs

or with digital signatures we also solve

the problem of origin non reputation so

this is actually the small picture of

all cryptography it doesn't contain

everything in order to talk about

everything in cryptography actually the

picture has to be a lot larger because a

lot of things are missing in this

picture like postquantum cryptography

full homomorphic full homomorphic

encryption multiparty computation

Randomness and so on and so forth so it

is a huge list and we are going to

actually cover almost everything that is

in this picture and some more

okay so let's talk about cryptographic

algorithms some algorithms use key and

some do not for instance cryptographic H

functions are keyless algorithms so you

don't have a secret information that is

shared between parties but for the case

of encryption we need keys so that

communic parties can agree right or for

also for message authentication and so

so we divide these key algorithms as

symmetric and asymmetric or secret key

and public key in the secret key case

secret key algorithms use the same key

material for both encryption and

decryption hence the name symmetric key

cryptography there are three types of

algorithms in this category blog ciphers

which is today's topic stream sers and

another way of encryption and message

authentication C this is not an

encryption algorithm as I mentioned this

is for data authentication okay here

you're not encrypting anything but you

are proving that the data didn't change

after you the person received okay so we

will see all of

them although these algorithms look very

different like log ciphers stream

ciphers they can actually uh in order to

understand one of them you have also

need to know the other so you cannot

simply learn block cers without learning

steam ciphers or hash functions and so

on so block ciphers and steam ciphers as

I mentioned are encryption Primitives

while the message authentication code is

used for data and data origin

authentication however as I mentioned

these topics are not completely

unrelated we can use a block CER to

build a b stream CER and the message

authentication code even we can turn a

block Cipher into a hash function

okay there are methods for that which

we'll be talking about when we talk

about HH functions a symmetri key crypto

system

part is uh relatively new compared to

symmetric key crypto systems because

symmetric key crypto systems actually

dates back to the invention of the you

know maybe the letters right but

asymmetric key cryptography thanks to Dy

Helman uh became famous around

1976 so there are different types of

algorithms here one of them is key

agreement algorithms like def key

exchange algorithm so this is important

because in key crypto systems we start

with the assumption that communicating

parties both securely shared the secret

key between each other right so they

need a secure channel to do that in the

key agreement algorithm we will do it on

an insecure Channel this is the nice

thing okay the whole internet actually

works with this principle okay okay and

imagine that you are adding a new device

to a network right so you initially want

to start communicating in an encrypted

way but you don't know other devices yet

so this is very very

important we have public encryption

algorithms like RSA or

ALG uh we have digital signature

algorithms like DSA which is digital

signature algorithm or standard DSS or

you can use the elliptic curve version

and you have ecdsa elliptic curve

digital signature algorithm which is

again very important and all Bitcoin or

cryptocurrency transactions are actually

elliptic C digital signature

okay so these are important

topics so let's remember the basic

definitions and terms we are going to

talk about the cipher or a crypto system

both are the same in my case but Cipher

is translated into Turkish in a wrong

way because whenever we say shifra which

is the Turkish translation of Cipher

actually people talk about

passwords okay here we are talking about

crypto systems this is

important so that mistake is actually

originating from maybe aund years ago

because whenever there's something

unknown people refer it to as shifra

Cipher but actually it is not so here

I'm going to talk about Cipher text in a

second we also call it the shif and so

so it is not in Turkish the there's a

confusion and I hope at one

point uh it will be corrected by

authorities okay so what is a crypto

system PL Tex is what you want to

protect so PL Tex can be an SMS message

a WhatsApp message a file in your

computer or your voice while you are

calling somebody and you're talking okay

so that is the plain text that is the

thing that you want to

protect a crypto system or a CER is just

a pair of algoritms that convert plain

text to Cipher text and back okay so a

cipher is not something that you can

press on your phone buttons and enter

that's is password okay this is cipher

so Cipher text is the encrypted version

of the plain text and Cipher text should

appear like a random sence so this is

the idea you have a plain text you want

to communicate or store that data but

you don't trust the medium that you are

using the communication Channel we

always assume that is insecure okay so I

need an

algorithm which we call encryption that

turns this plain text into Cipher text

which looks like just random zeros and

ones so in the communication Channel you

send this data and people receive that

every enemy or other people can listen

to this Communication channel and obtain

this but you still feel secure because

you know that if your algorithm is good

nobody can learn anything about the

plain text just by looking at the cipher

text okay but when you're the person you

want to communicate receive the cipher

text they have the decryption algorithm

and the secret key that they can decrypt

that is the whole idea

okay this is the nice thing so in the

symmetri key crypto systems you have a a

secret key and this is used for both

encryption and decryption sometimes you

use the identical key for encryption or

decryption sometimes you use in a

reverse order but important thing is

that encryption and decryption algorithm

are identical or closely related or if

we want a more scientific term we say

that one can be obtained from the other

in polinomial time okay in public key

cryptography this won't be the case Okay

because everybody will know the public

key and they will be allowed to encrypt

any message and sent to you but only you

have the private key where you can

decrypt it okay that's completely a

different scenario so symmetri case you

have to securely share this key between

parties before you want to communicate

maybe meet in person you know write it

into a paper and give it to them and so

but

uh however you do it we assume that the

both party have the secret key and also

this is the only thing that we keep

secret okay we don't care if the

algorithm is lost I mean if enemy knows

the this encryption and decryption

algorithm we don't care actually this is

casual principle saying that it should

be freely uh left to the uh enemy okay

we do we don't care as long as your

secret key is kept secure and secret

then enemy knowing everything about

about the algorithm shouldn't be a

problem and this is actually how modern

cryptography works because we have all

of these algorithms encryption and

decryption algorithms completely

detailed in the standard so you know how

the algorithm works it is not a secret

okay so how the block ciphers work block

ciphers operate on B bit blocks of data

so it is

fixed plain text is divided into b-bit

blocks each block is encrypted by secret

key K to produce B bit

output output blocks form the cipher

text so this is the whole idea instead

of working with a variable length data

you divide it into B bit blocks and then

work on

that th if you look at it in a

mathematical way a block Cipher and the

key you choose is actually a permutation

from 2 to the B elements to the two to

the B elements okay because you are your

input is bbits and you are mapping it to

to another bbits okay so you are

actually your input space is two to the

B output space is the same you are

mapping actual elements to each other so

this is just a

permutation nowadays we choose b as 64

or 128 depends actually on the use case

sometimes you can even choose as small

as 32 in some lightweight ciphers but if

you choose the block size as small as

that recall our historical ciphers we

said that you know replacing one bit

sorry one character with one character

didn't work due to frequency analysis

right so if you're choosing your bs32

bits divided by8 this means four bytes

right you are replacing four byes with

four bytes so as you can

imagine uh it is not that hard to attack

that kind of thing also you have to you

shouldn't be using that uh

Cipher for a very long time because

attacker May capture a lot of Cipher Tex

and pl Tex which actually covers the

whole Space so block size should be

large 64 is acceptable but generally we

use 128 so secret key size today we use

for instance Advanced encryption

standard allows three choices

128 this is for personal use so as a

individual person you shouldn't be

accepting any algorithm that has

security less than one 128 bits okay but

if you are military you should be using

256 bits and shouldn't accept anything

less

standard so you might ask what is the

point for 100 9 to2 nobody using it okay

so either choose this or CH choose that

you know I mean in libraries it is

implemented but nobody is using okay

even in papers when we obtain results

for all three cases we provide them in

the paper for 128 and 256 and put 192 K

in the appendix because of the page

limits okay so let's go back to our

initial claim I said that this is a

mapping from 2 to the B elements to the

two to the B element so this is just a

permutation so question is how many

permutations can you have and this

number is really huge you can have 2 to

the B factorial permutations mapping 2

to the B elements to the 2 to the B

elements and this number is really

really just imagine b equal to 128 right

2 to the power of 2 to the B is a huge

number so there are a huge number of

permutations but when you design a block

CER and when you choose a key you are

actually choosing a small sets from this

huge sets Okay so a block Cipher will

provide only a tiny fractional of all

these available permutations for typical

values of B and K namely 2 to the K so 2

to the

128 is a very small number compared to

two to the 2 to the

120 right so there are a huge number of

permutations in which looks like

Infinity a huge space so you're are

trying to design a cipher which actually

chooses a good subset of it for security

for any chosen key we expect a good

block Cipher to act like as if it is a

randomly selected permutation so encrypt

analysis this will make more

sense even more we expect no relation

between permutations that are obtained

by keys that are related

somehow we will return to this when we

are talking about related key Crypt

analysis but here the IDE is as follows

so you design the block Cipher you chose

a key so this key and the cipher

actually Maps two to the B elements to

the two to the B element right this is a

permutation if you make a small change

to your secret key maybe flipping the

rightmost bit let's say then it will

give you a completely different

permutation there shouldn't be a

relation between these two cases okay

that is the idea and if there is such a

relation then we can perform a related

key attack which breaks the system

okay so before moving on to uh examples

and see what kind of ciphers we have to

today we have to understand how we

design them or what makes a block

ciphers a good Cipher so there are some

abstract Concepts and there's not an

actually

a mathematical way to actually show that

this uh Cipher is good or not currently

what we are doing is when we design a

cipher we actually try to break it with

every non Crypt analysis techniques and

see if it is secure or not okay you

cannot prove that it is secure maybe one

year later somebody may come up with a

new crypto analysis technique and break

the

cipher so let's look at this abstract

Concepts K Channon is considered as the

father of information Theory and

contribut to the field of Crypt analysis

for USA defense during World War II his

Landmark paper communication theory of

secrecy systems introduced the t ideas

of confusion and diffusion for practical

Cipher design so we will be talking

about sboxes permutations and so on all

those come from these confusion and

diffusion ideas okay our aim is to

provide confusion and

diffusion confusion is defined by him as

follows to make the relation between the

simple statistics of the cipher text and

the simple description of the key a very

complex and invol

one and for the diffusion the

statistical structure of the plain text

which leads to its redundancy is

dissipated into long range statistics in

the

cryptogram so note that this concept

concepts of confusion and diffusion are

not measurable Concepts they're absolute

Concepts right they're abstract so must

try to give alternative definitions for

this so confusion the cipher T

statistics should depend on the plain T

statistics in a manner too complicated

to be exploited by the Crypt

analyst diffusion each digit of the pl

text and each digit of the secret key

should influence many digit of the cyer

text so these definitions are a lot

better or easier to understand let's say

because our aim is to you know map bbits

to bbits right so by confusion we are

trying to design it so that by looking

at the cipher text for instance last

bite of the cipher Tex this shouldn't

give you an idea about the last bite of

the pl text right you are causing a

confusion so you are

actually making some modifications like

substitutions so this try creates a

confusion but if you work on bytes for

instance then you'll be working on

individual B right diffusion says that

if you make a small change of one part

of the cipher like one bit it should

affect as many bits as possible so this

is the whole idea

actually uh in terms of mathematics when

we assume that you have a plain text and

we encrypted and obtain a cipher text so

if you flip one bit of the plain text we

actually expect half of the cipher text

bits to be changed this is the actually

uh how we Define it

okay