Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

## Algebraic Group on Fixed-length Bit Integer and its Adaptation to IDEA Cryptography

Yasushi Fuwa
Shinshu University, Nagano
Yoshinori Fujisawa
Shinshu University, Nagano

### Summary.

In this article, an algebraic group on fixed-length bit integer is constructed and its adaptation to IDEA cryptography is discussed. In the first section, we present some selected theorems on integers. In the continuous section, we construct an algebraic group on fixed-length integer. In the third section, operations of IDEA Cryptograms are defined and some theorems on these operations are proved. In the fourth section, we define sequences of IDEA Cryptogram's operations and discuss their nature. Finally, we make a model of IDEA Cryptogram and prove that the ciphertext that is encrypted by IDEA encryption algorithm can be decrypted by the IDEA decryption algorithm.

#### MML Identifier: IDEA_1

The terminology and notation used in this paper have been introduced in the following articles                       

#### Contents (PDF format)

1. Some Selected Theorems on Integers
2. Basic Operators of IDEA Cryptograms
3. Operations of IDEA Cryptograms
4. Sequences of IDEA Cryptogram's Operations
5. Modeling of IDEA Cryptogram

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