Blockchain tutorial 10: Diffie-Hellman key exchange Video Lecture | Blockchain Tutorial: A Fundamental Guide - Cryptocurrency

in this video al
Hellman key exchange works they see have
a key
a method to securely establish a shared
secret between two parties in this
example Alice and Bob over a public
Channel step 1 LSN Bob agrees on the
publicly shared domain parameters alpha
which is a generator at P which is the
modulus for example alpha is 3 P is 17
step 2
LS generates a random number this is LS
private key LS press the key must be a
failure in the range between 2 and P
minus 2 for example 15 step 3 Bob also
generates a random number this is Bob
private key also Bob private key must be
a fairly between 2 at P minus 2 for
example 13 step 4 LS calculates her
public key she uses her private key as
an exponent and using this equation step
5
Bob calculates his public key Bob uses
his private key as an exponent as you
can see in this equation
step 6 Ella sense of public key to Bob
of the public Channel
step 7 Bob senses public key to Ellis
also over the same public channel step 8
Ellis takes Bob public key and
calculates the secret key with this
equation here is Bob public key and this
is Ellis private key as an exponent and
the secret key is calculated with this
equation step 9 Bob takes Alice public
key and calculates the secret key this
secret key is the same as LS secret key
Bob takes LS public key and uses his
private key as an exponent step 10
Alice and Bob can use a secret key also
known as session key in symmetric key
algorithm for example a s to encrypt and
decrypt their messages so here's the
proof that Alice and Bob secret keys are
the same alpha ^ LS private key is
assigned to variable a alpha ^ Bob's
private key
if Santa Fairy will be this is the
equation of LS public key and here's the
equation of Bob public key LS calculate
the secret key using this equation so if
you look at the public key of Bob that
is this part and here is Bob public
this is Bob's public key equation if I
replace this exponent with P then you
get alpha B and then the private key of
LS that is a and the right way over here
if I do the same with Bob secret key
this is Bob secret key equation here is
the public key of LS this is the
equation of public key of Telus if I
replace this part with a so alpha a mod
P of a mod p and then the private key of
Bob that is B and if you look at this
equation alpha a B is the same as alpha
B a and if you look at both equations
over here that they are the same so this
is the proof that Alice and Bob secret
keys are the same the question is can if
calculate the secret key if is evil and
has intercepted Alice and Bob public key
and she also knows the generator and the
modulus so let's take LS public key and
this is the equation
she needs to calculate the discrete
logarithm which is very hard to do
especially if the modulus as thousand 24
bits or bigger to calculate LS private
key to write this equation private key
LS is log base alpha of public key LS
mod P in another form you can also write
it this way public key Ellis is alpha to
the power of private key LS mod p and if
you watch my previous video regarding
discrete logarithm you know that solving
a discrete logarithm is very hard to do
to answer the question can s calculate
the secret key the answer is No