Algorithmic Strategies for Solving Complex Problems in Cryptography by Kannan Balasubramanian M. Rajakani

Author:Kannan Balasubramanian,M. Rajakani
Language: eng
Format: epub
Publisher: IGI Global

The following method strengthens a public key cryptosystem by appending to each ciphertext a tag that is correlated to the message to be enciphered. In this method tags are generated by the use of a one-way hash function.

Let us denote by G the cryptographically strong pseudo-random string generator based on the difficulty of computing discrete logarithms in finite fields. G stretches an n-bit input string into an output string whose length can be an arbitrary polynomial in n. This generator pro-duces O(log n) bits output at each exponentiation.

A user Alice's secret key is an element xA chosen randomly from [1, p- 1], and her public key is yA =It is assumed that all messages to be enciphered are chosen from the set , where P = P(n) is an arbitrary polynomial with P (n) n. Padding can be applied to messages whose lengths are less than n bits. In addition, let l= l(n) be a polynomial which species the length of tags. It is recommended that l should be at least 64 for the sake of security.

Assume that h is a one-way hash function compressing input strings into l-bit output strings. A user Bob can use the following enciphering algorithm to send in secret a P-bit message m to Alice.

Eowh(yA, p, g, m)

begin

1. x [1, p - 1].

2.

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