# Multiplication of Multidigit Numbers on Automata

##### Citations

13,597Â citations

### Cites background or methods from "Multiplication of Multidigit Number..."

...18 was known to Karatsuba and Ofman [661]....

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...A recursive algorithm due to Karatsuba and Ofman [661] reduces the complexity of multiplying two n-bit integers to O(n)....

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9,262Â citations

7,427Â citations

2,893Â citations

### Cites methods from "Multiplication of Multidigit Number..."

...268 B.2 URLs for standards bodies and working groups. . . . . . . . . . . . . . . 268 List of Figures 1.1 Basic communications model . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Symmetric-key versus public-key cryptography . . . . . . . . . . . . . . 4 2.1 Representing a prime-field element as an array of words . . . . . . . . . . 29 2.2 Depth-2 splits for 224-bit integers (Karatsuba-Ofman multiplication) . . . 33 2.3 Depth-2 splits for 192-bit integers (Karatsuba-Ofman multiplication) . . . 34 2.4 Representing a binary-field element as an array of words . . . . . . . . . 47 2.5 Right-to-left comb method for polynomial multiplication . . . . . . . . . 49 2.6 Left-to-right comb method for polynomial multiplication . . . . . . . . . 49 2.7 Left-to-right comb method with windows of width w . . . . . . . . . . ....

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...The multiplication method of Karatsuba-Ofman is due to Karatsuba and Ofman [239]....

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2,856Â citations