https://github.com/sepandhaghighi/integer-squaring

Integer Squaring Algorithm
https://github.com/sepandhaghighi/integer-squaring

algorithm cryptographic cryptography integer-arithmetic integer-squaring multiplication product-scanning squaring

Last synced: about 1 month ago
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Integer Squaring Algorithm

• Host: GitHub
• URL: https://github.com/sepandhaghighi/integer-squaring
• Owner: sepandhaghighi
• Created: 2017-12-22T22:31:56.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2018-01-01T17:08:56.000Z (about 7 years ago)
• Last Synced: 2024-10-25T04:05:26.407Z (3 months ago)
• Topics: algorithm, cryptographic, cryptography, integer-arithmetic, integer-squaring, multiplication, product-scanning, squaring
• Language: Python
• Size: 1.78 MB
• Stars: 2
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Integer Squaring & Integer Multiplication (by product scanning) Algorithm #

### Sepand Haghighi & Mohammad Abassi

### Cryptographic Engineering Course Seminar At [Sharif University Of Technology](http://www.sharif.ir/ "Sharif University Of Technology") (Winter 2017)

### Instructor : [Dr.Siavash Bayat-Sarmadi](http://sharif.edu/~sbayat/ "http://sharif.edu/~sbayat/")

### Book : Cryptographic Engineering (Serdar S¨ uer Erdem, Tuˇ grul Yanık, and C ¸ etin Kaya Koc)	 

[![Build Status](https://travis-ci.org/sepandhaghighi/Integer-Squaring.svg?branch=master)](https://travis-ci.org/sepandhaghighi/Integer-Squaring)

[![Codacy Badge](https://api.codacy.com/project/badge/Grade/0f5fc6d4f3e84a06b004a716dc1ece6e)](https://www.codacy.com/app/sepand-haghighi/Integer-Squaring?utm_source=github.com&utm_medium=referral&utm_content=sepandhaghighi/Integer-Squaring&utm_campaign=Badge_Grade)

[Download Slides](files/Slides.pdf "Slides") (Format : PDF, Size : 1.1 MB)

----------

# Integer Multiplication

							

### Chapter : 5					

				

### Page : 79				





Fig1.Algorithm-2 Pseudocode



Fig2.Algorithm-2 Example


 


```

>>> IntegerMultiplication("1 1","1 1",Base=2)

>>> 1 0 0 1 

```

Complexity : `3` additions, `2` data read (Inner Loop)

# Integer Squaring

### Book : Cryptographic Engineering (Serdar S¨ uer Erdem, Tuˇ grul Yanık, and C ¸ etin Kaya Koc)				

				

### Chapter : 5					

				

### Page : 80				





Fig3.Algorithm-3 Pseudocode



Fig4.Algorithm-3 Example



* It seems this algorithm is wrong and `(U,H,L)` should be set to zero after each iteration and add shifted `(U,H,L)` outside of the loop (modified in code)

									

```

>>> IntegerSquaring("1 1","1 1",Base=2)

>>> 1 1 0 1 

```





Fig5.Algorithm-3(Modified) Pseudocode



Fig6.Algorithm-3(Modified) Example


 


```

>>> IntegerSquaringModified("1 1",Base=2)

>>> 1 0 0 1 

```

Complexity : `3` additions, `2` data read (Inner Loop)

# Run

1. Run `main.py` for automatic doctest --> `python main.py` or `python3 main.py`

2. Import `IntegerSquaring` and `IntegerMultiplication` and `IntegerSquaringModified` from `main.py` :

```

>>> from main import IntegerSquaring,IntegerMultiplication,IntegerSquaringModified

>>> IntegerSquaring("1 6",Base=10)

'3 8 6'

>>> IntegerSquaringModified("1 6",Base=10)

'2 5 6'

>>> IntegerMultiplication("1 6","1 6",Base=10)

'2 5 6'

```

* Enter digits with one space, for example : `"31 12"` in base `32`