200
Internet of Things (IoT)
factorization of vast numbers. RSA algorithm has three parts, specific encryption part, public key generation part, and decryption part. In the key generation part, two pairs of keys
are generated, namely private key and public key. Whereas the private key is a secret key
which is maintained by the sender, the public key can be shared with the receiver. Time
taken to generate a key is very slow, it is also said to be a disadvantage of the RSA algorithm.
There are five major steps involved in RSA key generation (Anonymous 2012).
1. Initially, generate two large prime numbers m and n. Make sure that m is not equal
to n.
2. Calculating product of generated prime number m and n, q = mn. The calculated
number q should be a larger number so that the generated number p and q cannot
be identified.
3. Calculate phi Φ = (m−1)(n−1).
4. Select a public key exponent e such that 1 < e < Φ and ensure that gcd (e, Φ) = 1.
5. To end, find the decryption key d by calculating d mod t = 1, where t is the plaint text.
Finally, generated public key {q, e} and private key {d} are used to encrypt the secure
plain text into cypher text as well as decrypt the cypher into plain text. RSA encipher
is constantly done by utilization of public key. Any individual who needs to send message to the receiver utilizing RSA encipher should first get its public key. It should be
possible by direct exchange of keys or by utilization of any accreditation power called
“CA.” If the message is larger than q then, split the message into two block of messages.
Then encrypt the plaint text “t” into scrambled text called cypher text “c” and generate
public key{q,e}. Unscrambling or deciphering process is carried out by the private key
generated by the RSA. Then the plain text can be obtained from the scrambled text.
Using RSA algorithm, public key digital signatures are generated. This signature can
be verified later by any receiver with the knowledge of generated public key (Qamar
and Hassan 2010).
RSA based signature is always computed over the hash of the original message. In order
to make a signature, the sender node will produce a hash of the message and then raise
it to the power of ”d mod q”, and then attach this to the original message. Receiver gets
the digitally signed message from the sender, and the same hash function is utilized to
compute the hash of the plain text. By verifying the signature, the receiver can ensure the
confidentiality of the message.
10.5.1.2 Elliptic Curve Cryptography
Elliptic curve cryptography (ECC) is a public key cryptography developed in 1985 by
Victor Miller and Niel Koblitz. ECC is a solid cryptographic algorithm compared to other
public key cryptographic algorithms like RSA. ECC is a mathematical structure of elliptic
curves over limited fields. Compared to the RSA public key algorithm, ECC is very secure.
It is difficult to discover huge prime numbers in RSA, whereas ECC is more secure and furnishes equal security while generating little key size. ECC is thought to be exceptionally
valuable for wearable devices, smart phones, and IoT implantable medical devices (IMDs).
ECC’s public key brings about data transfer capacity utilization and quick computation
capability. Algebraic formula of ECC is as shown below.
d 2 = b 3 + ab + c
Internet of Things (IoT)
factorization of vast numbers. RSA algorithm has three parts, specific encryption part, public key generation part, and decryption part. In the key generation part, two pairs of keys
are generated, namely private key and public key. Whereas the private key is a secret key
which is maintained by the sender, the public key can be shared with the receiver. Time
taken to generate a key is very slow, it is also said to be a disadvantage of the RSA algorithm.
There are five major steps involved in RSA key generation (Anonymous 2012).
1. Initially, generate two large prime numbers m and n. Make sure that m is not equal
to n.
2. Calculating product of generated prime number m and n, q = mn. The calculated
number q should be a larger number so that the generated number p and q cannot
be identified.
3. Calculate phi Φ = (m−1)(n−1).
4. Select a public key exponent e such that 1 < e < Φ and ensure that gcd (e, Φ) = 1.
5. To end, find the decryption key d by calculating d mod t = 1, where t is the plaint text.
Finally, generated public key {q, e} and private key {d} are used to encrypt the secure
plain text into cypher text as well as decrypt the cypher into plain text. RSA encipher
is constantly done by utilization of public key. Any individual who needs to send message to the receiver utilizing RSA encipher should first get its public key. It should be
possible by direct exchange of keys or by utilization of any accreditation power called
“CA.” If the message is larger than q then, split the message into two block of messages.
Then encrypt the plaint text “t” into scrambled text called cypher text “c” and generate
public key{q,e}. Unscrambling or deciphering process is carried out by the private key
generated by the RSA. Then the plain text can be obtained from the scrambled text.
Using RSA algorithm, public key digital signatures are generated. This signature can
be verified later by any receiver with the knowledge of generated public key (Qamar
and Hassan 2010).
RSA based signature is always computed over the hash of the original message. In order
to make a signature, the sender node will produce a hash of the message and then raise
it to the power of ”d mod q”, and then attach this to the original message. Receiver gets
the digitally signed message from the sender, and the same hash function is utilized to
compute the hash of the plain text. By verifying the signature, the receiver can ensure the
confidentiality of the message.
10.5.1.2 Elliptic Curve Cryptography
Elliptic curve cryptography (ECC) is a public key cryptography developed in 1985 by
Victor Miller and Niel Koblitz. ECC is a solid cryptographic algorithm compared to other
public key cryptographic algorithms like RSA. ECC is a mathematical structure of elliptic
curves over limited fields. Compared to the RSA public key algorithm, ECC is very secure.
It is difficult to discover huge prime numbers in RSA, whereas ECC is more secure and furnishes equal security while generating little key size. ECC is thought to be exceptionally
valuable for wearable devices, smart phones, and IoT implantable medical devices (IMDs).
ECC’s public key brings about data transfer capacity utilization and quick computation
capability. Algebraic formula of ECC is as shown below.
d 2 = b 3 + ab + c