Modular multiplication is a widely used operation in cryptography. Several well-known applications, such as the decipherment operation of the RSA algorithm, the Diffie-Hellman key exchange algorithm, as well as some applications currently under development, such as the Digital Signature Standard and elliptic curve cryptography, all use modular multiplication and modular...
Modular multiplication is a mathematical operation fundamental to the RSA cryptosystern,
a public-key cryptosystem with many applications in privacy, security, and authenticity.
However, cryptosecurity requires that the numbers involved be extremely large,
typically ranging from 512-1024 bits in length. Calculations on numbers of this magnitude
are cumbersome and lengthy; this...
Modular exponentiation and modular multiplication are the most used operations in current cryptographic systems. Some well-known cryptographic algorithms, such as RSA, Diffie-Hellman key exchange, and DSA, require modular exponentiation operations. This is performed with a series of modular multiplications to the extent of its exponent in a certain fashion depending...
The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2ⁿ), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware implementations to compute the...
Information security is an important concern in today’s communication and business world. To achieve these security functions, cryptography is utilized. RSA and the Diffie Hellman key exchange are some examples of cryptography algorithms that use modular multiplication to compute modular exponentiations. Modular multiplication requires division operations which becomes very time...