There are some reasons that we should not use the same key for encryption and signing.
1- We need to backup our secret key for encrypted data, later we want to decrypt some old encrypted messages but we don't need to backup our secret key for signing. If attacker finds the key we can tell CA and make it as expired key and get new secret key for signing without need of backup.
2- The second reason is more important, if. If we use the same key for encryption and signing, the attacker can use this for to decrypt our encrypted message, this is what he/she should do:
Attacker
The attacker must choose a random number r (r must have GDC(Nr, r) = 1 where
r must have GDC(N, r) = 1, N is
and N is the number use used for creating private and public key (N = p*q)N = pq) then he
Then the attacker chooses a new message (m′ = m^e.r^e ((e,n) is public key ) and send sends this message (m′) for signing to the sender, when:
m′ = m^e.r^e ....(here (e,n) is the public key)
When the sender sign m′ we signs m′ we get
m′^d ≡ (m^e.r^e)^d ≡ m.r (mod N) then attacket
Now the attacker only need needs to multiply "divide" it by r^-1 to r to get m m (the secret message).
There are some reasons that we should not use same key for encryption and signing.
1- We need to backup our secret key for encrypted data, later we want to decrypt some old encrypted messages but we don't need to backup our secret key for signing. If attacker finds the key we can tell CA and make it as expired key and get new secret key for signing without need of backup.
2- The second reason is more important, if we use same key for encryption and signing attacker can use this for decrypt our encrypted message, this is what he should do:
Attacker must choose random number r (r must have GDC(N, r) = 1, N is the number use for creating private and public key (N = p*q)) then he chooses new message m′ = m^e.r^e ((e,n) is public key) and send this message (m′) for signing to sender, when sender sign m′ we get m′^d ≡ (m^e.r^e)^d ≡ m.r (mod N) then attacket only need to multiply it by r^-1 to get m (the secret message).
There are some reasons that we should not use the same key for encryption and signing.
1- We need to backup our secret key for encrypted data, later we want to decrypt some old encrypted messages but we don't need to backup our secret key for signing. If attacker finds the key we can tell CA and make it as expired key and get new secret key for signing without need of backup.
2- The second reason is more important. If we use the same key for encryption and signing, the attacker can use this to decrypt our encrypted message, this is what he/she should do:
The attacker must choose a random number r, where
r must have GDC(N, r) = 1,
and N is the number used for creating private and public key (N = pq)
Then the attacker chooses a new message (m′ ) and sends this for signing to the sender:
m′ = m^e.r^e ....(here (e,n) is the public key)
When the sender signs m′ we get
m′^d ≡ (m^e.r^e)^d ≡ m.r (mod N)
Now the attacker only needs to "divide" it by r to get m (the secret message).
