Biomedical Engineering Reference
In-Depth Information
Introduction
Cryptography is the science which uses mathematics to encrypt and decrypt data.
This science enables you to store sensitive information or transmit it across
insecure networks so that it cannot be read by anyone except the intended reci-
pient. In conventional cryptography, also called secret-key or symmetric-key
encryption, one key is used both for encryption and decryption. In asymmetric
cryptography, the encryption and decryption keys are different on both the sides.
Hybrid cryptography is a combination of both symmetric and asymmetric cryp-
tographic techniques. Hybrid cryptography is very effective indeed in providing
high degree of security because whatever the problems associated with symmetric-
key cryptographic techniques were solved when asymmetric cryptographic
mechanism is used. So when both the types of algorithm are used in the protocol
architecture, the resulted new protocol architecture, is more immune against the
attacks and hence providing the high degree of security [
1
].
E-commerce and M-commerce transactions are growing at an explosive rate. The
success of these depends on how transactions are carried out in the most secured
manner. The prime requirements for any e-commerce and m-commerce transactions
are Privacy, Authentication, Integrity maintenance, and Non-Repudiation [
2
].
Cryptography helps us in achieving these prime requirements. Today, various
cryptographic algorithms have been developed [
3
,
4
].
The Cryptographic Algorithms Used
1. Advance Encryption Standard (AES) Algorithm
The Rijndael proposal for AES defined a cipher in which the block length and
the key length can be independently specified to be 128, 192, and 256 bits [
2
].
AES algorithm contains the following four different stages: (1) Substitution
bytes: Uses S box (substitution box) to perform byte-to-byte substitution. (2) Shift
rows: A simple permutation (3) Mix columns: A diffusion layer that makes use of
Finite field arithmetic. (4) Add Round Key: A simple bit-wise XOR of the current
block with the expanded key [
5
]. The beauty of AES is that all known attacks are
computationally infeasible to it.
2. Dual RSA
In practice, the RSA decryption computations are performed in p and q and then
combined via the Chinese remainder theorem (CRT) to obtain the desired solution
in Z N, instead of directly computing the exponentiation in Z N. This decreases the
computational costs of decryption in two ways. First, computations in Z p and Z q
are more efficient than the same computations in Z N since the elements are much
smaller. Second, from Lagrange's Theorem, we can replace the private exponent d
with dp = d mod (p - 1) for the computation in Z p and with dq = d mod (q - 1)
Search WWH ::
Custom Search