- #1

shivajikobardan

- 674

- 54

- Homework Statement
- Is there some restrictions on values of p,q,d,e etc in RSA algorithm while trying to encrypt English Ciphertext?

- Relevant Equations
- RSA algorithm, modulus solving, Euler's formula for GCD calcualation

Is there some restrictions on values of p,q,d,e etc in RSA algorithm while trying to encrypt English Ciphertext?

I'll present few cases of RSA encryption:

##CT=(PT)^e mod \, n##

##PT=(CT)^d mod \, n##

CT= Cipher Text

PT=Plain Text

e*d/m should give remainder 1, where;

m=(p-1)*(q-1); where p, q are 2 prime numbers.

The value of e=3, d=7 satisfied the remainder=1 condition.

So, if sender wants to send "SELL":

S=19, CT=28

E=5. CT=26

L=12, CT=12

L=12, CT=12(? What to do to not get the cipher text same as plain text without making things too complex and still being able to do it in paper manually?)

e=3,d=7

I'll only write CT here(i.e S=17 means that 17 is a cipher text for S after RSA encryption):

S=17

E=15

L=12

L=12 (Same here? why? Because of d,e being the same?)

d=13, e=37

So,

S=95

E=93

L=12

L=12 (Again got the same value, what is this? Even with different values of p,q,d,e!)

I know e<m and e>1

And e should be relatively prime to m, i.e GCD(e,m)=1.

GCD(13,120)=1

For d,

de mod m=1

I'll present few cases of RSA encryption:

##CT=(PT)^e mod \, n##

##PT=(CT)^d mod \, n##

CT= Cipher Text

PT=Plain Text

e*d/m should give remainder 1, where;

m=(p-1)*(q-1); where p, q are 2 prime numbers.

**A) Sender takes p=3, q=11.**The value of e=3, d=7 satisfied the remainder=1 condition.

So, if sender wants to send "SELL":

S=19, CT=28

E=5. CT=26

L=12, CT=12

L=12, CT=12(? What to do to not get the cipher text same as plain text without making things too complex and still being able to do it in paper manually?)

**B) p=2, q=11**e=3,d=7

I'll only write CT here(i.e S=17 means that 17 is a cipher text for S after RSA encryption):

S=17

E=15

L=12

L=12 (Same here? why? Because of d,e being the same?)

**C) p=13, q=11**d=13, e=37

So,

S=95

E=93

L=12

L=12 (Again got the same value, what is this? Even with different values of p,q,d,e!)

**Questions:***a) Is there any restrictions if among p or q, anyone should be greater?*

b) Is there any restrictions like which of the d or e should be greater?b) Is there any restrictions like which of the d or e should be greate

I know e<m and e>1

And e should be relatively prime to m, i.e GCD(e,m)=1.

GCD(13,120)=1

For d,

de mod m=1

*c) Would there be any cases, where while decryption, we would not be able to get the plain text due to some reasons (like if not choosing values properly for d,e,p,q in english alphabet encryption? This is the main confusion that is making me ask this )*