Describe in about 200-300 words the RSA encryption algorithm,
Including:
*the method of encryption and decryption
*the three key theorems on which the algorithm depends
*the reason for the security of the algorithm
Thank you!
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Describe in about 200-300 words the RSA encryption algorithm,
Including:
*the method of encryption and decryption
*the three key theorems on which the algorithm depends
*the reason for the security of the algorithm
Thank you!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I understand,
I have done this so fay from my notes but i dont understand what is what.
SO
1) Choose two distinct primes, p and q
2) Find n such that n=pq
3) Use Q(n)= (p-1)(q-1) Q = phi, (*****)
4)Choose e such that 1
one key aspect of the totient function is that it is a multiplicative function so long as the factors of a number are relatively prime.; there is a more complicated method for finding the phi value of any number. The phi value is simply the number of relatively prime values that are less the number; for example:
the number 8: 1 2 3 4 5 6 7 8
^ ^ ^ ^
there are 4 numbers less than 8 that are relatively prime
to 8; (a,8)=1
the phi value of 8 is 4
the number 9: 1 2 3 4 5 6 7 8 9
^ ^ ^ ^ ^ ^
i count 6 of them
the phi value of 9 is 6
the phi value of a prime number is simply all the numbers less than it; phi(7) = 6, phi(13)=12, phi(17)=16 why? because a prime number is prime ....
now to explain what it means to be a multiplicative function:
f(ab) = f(a) * f(b) simple enough; and this is true for phi given that a and b are relatively prime.
since 8 and 9 are relatively prime then,
phi(72) = phi(8*9) = phi(8) phi(9) = 4 * 6 = 24
the reason for picking 2 large primes for the "n" is so that you can construct this phi value in a simple manner i believe
another thrm is that \[a^{\phi(n)}\cong a~(mod~n)\]
proof:
let "n" be a number with the set of relatively primes: {r1,r2,r3,...,r phi(n)}, since there are phi(n) relatively primes by definition.
the product of these numbers is then: r1 r2 r3 ... r phi(n) = k
therefore \(k\cong 1~(mod~n)\)
lets take a number a such that (a,n) = 1; and multiply each r value in the set
\[a r_1~ a r_2 ~ a r_3 ... ar_{ phi(n)} = a^{\phi(n)}k\]
since (k,n)=1; and (a,n)=1; therefore a^(phi(n)) = 1 (mod n)