Citation
Alfaris, Rand Qusay
(2009)
A New Cryptosystem Based on Decimal Numbers and Nonlinear Function.
PhD thesis, Universiti Putra Malaysia.
Abstract
We introduce a new cryptosystem, with new digital signature procedure. This
cryptosystem is based on decimal numbers and nonlinear function. Unlike other
cryptosystems, this system does not depend on prime or integer numbers and it
does not depend on group structure, ¯nite ¯eld or discrete logarithmic equation.
The idea is about using decimal numbers and thus the only integer number will
be the plaintext. A secret key is shared between Alice and Bob to construct their
decimal public keys, so that, we can say this cryptosystem is symmetric and asym
metric. We choose to distribute the secret key through the classic Di±eHellman
protocol after introducing some modi¯cation on it; this modi¯cation depends on
the extension of the theory of the modulus to be applicable on the real numbers.
We prove there is no loss of any bit of information when we use the decimal num
bers during the encryption and the decryption by introducing the rounding o® concept as a function. This function plays the primary role in proving a new the
orem called \Rounding theorem". A new theory for the security is established,
where basically, it depends on the properties of the decimal numbers and the cu
mulative and truncation errors that will occur during the attack, because every
attack requires solving a system of nonlinear equations. The decimal cryptosys
tem does not depend on large numbers because it deals with numbers between zero
and one. Therefore, this cryptosystem can be considered faster than the known
cryptosystems.
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