November 2019
Beginner to intermediate
408 pages
9h 29m
Korean
Content preview from 밑바닥부터 시작하는 비트코인
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.
밑바닥부터 시작하는 비트코인
48
1.6
유한체 곱셈과 거듭제곱
유한체에서 닫혀 있는 덧셈 (+
f
)을 정의했듯이 유한체에서 닫혀 있는 곱셈도 정의할 수 있습니
다. 이를 이용하여 같은 숫자를 여러 번 곱하는 거듭제곱도 정의할 수 있습니다. 이번 절에서는
나머지연산을 이용한 곱셈과 거듭제곱을 정의하겠습니다.
우리가 익숙한 정수집합에서의 곱셈은 ‘여러 번 더하기’입니다.
5
•
3
=
5
+
5
+
5
=
15
8
•
17
=
8
+
8
+
8
+
...
+
8
=
136
유한체에서 곱셈도 비슷하게 할 수 있습니다. 위수
19
의 유한체
F
19
에서 보면,
5
•
f
3
=
5
+
f
5
+
f
5
8
•
f
17
=
8
+
f
8
+
f
8
+
f
...
+
f
8
위 식의 오른쪽 계산을 어떻게 하는지는 이미 알고 있습니다. 결론적으로 계산은 정수집합의
곱셈을 유한체의 위수로 나눈 나머지이며 결과는 당연히 유한체
F
19
에 속합니다.
5
•
f
3
=
5
+
f
5
+
f
5
=
15
%
19
=
15
8
•
f
17
=
8
+
f
8
+
f
8
+
f
...
+
f
8
= (
8
•
17
)
%
19
=
136
%
19
=
3
위 두 번째 계산 결과는 그리 직관적이지 않습니다. 보통
8
•
f
17
=
3
이라고는 생각하지 않기 때
문입니다. 그러나 그 때문에 곱셈에 대해서 닫혀 있게 됩니다. 즉 곱셈의 결과는 항상 집합
{
0
,
1
, ..
p
-
1
}
에 속하게 됩니다.
거듭제곱
exponentiation
은 간단히 한 숫자를 여러 번 곱하는 것입니다.
7
3
=
7
•
7
•
7
=
343
유한체에서도 나머지연산을 이용하여 ...
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.