2018-10-27

JavaのString.formatは、2進数表記が無いらしいけど。それはそれとして、Java.util.BitSetを使ってみる

Java

f:id:ts0818:20190507203513j:plain

JavaでDUKPTのサンプルを上げている人がいたんですよ～、な～に～！？やっちまったな！

github.com

⇧ その中で、Javaの標準のAPIであるBitSetっちゅうものを使っていたんですよ～、な～に～！？

名前からもお察しの通り、みんな大好きな bit 操作系のライブラリですかね。

java.lang.Object
- java.util.BitSet

すべての実装されたインタフェース:Serializable、Cloneable

public class BitSet extends Object implements Cloneable, Serializable

このクラスは、必要に応じて大きくなるビット・ベクトルを実装します。ビット・セットの各コンポーネントは、boolean値を持ちます。BitSetのビットには、負でない整数のインデックスが付けられます。インデックスが付けられた個別のビットは、試験したり、設定したり、クリアしたりできます。また、論理積、包含的論理和、および排他的論理和の演算を行うと、あるBitSetを使って別のBitSetの内容を変更できます。

導入されたバージョン:JDK1.0

BitSet (Java Platform SE 8)

⇧ 何がスゴいって、JDK1.0で導入されたAPIって、むっちゃ旧いのに堅牢な暗号アルゴリズムを実現してるってことですかね。まぁ、他のやり方もあるんでしょうが。

ちなみに、DUKPTのWikipediaさんの見解は、

In cryptography, Derived Unique Key Per Transaction (DUKPT) is a key management scheme in which for every transaction, a unique key is used which is derived from a fixed key. Therefore, if a derived key is compromised, future and past transaction data are still protected since the next or prior keys cannot be determined easily. DUKPT is specified in ANSI X9.24 part 1.

Derived unique key per transaction - Wikipedia

英語だからよく分からんけど、複雑なことをやってるらしいと...

Derived Key Generation Process[edit]

The following procedure is used for device initialization and encryption.

First: A key is irreversibly derived from the BDK (within a TRSM). This is known as the Initial PIN Encryption Key (IPEK).
Second: The IPEK is then injected into the devices, so any compromise of that key compromises only the device, not the BDK（Base Derivation Key）
Third:This IPEK creates yet another set of keys (inside the device) irreversibly derived from it (nominally called the Future Keys)
Fourth: Afterwards the IPEK is then immediately discarded. NOTE: This step contradicts "Session Keys" section where it indicates that only 21 "Future Keys" are generated. The IPEK must be retained by the terminal in order generate the next batch of 21 Future Keys.
Fifth: Future Keys are used to encrypt transactions in the DUKPT process.

Upon detection of compromise the device itself a new IPEK is derived inside the TRSM and the Derived Key Generation Process is restarted.

Derived unique key per transaction - Wikipedia

そして、全然関係ないけど、paizaで、

paiza.jp

f:id:ts0818:20181027145052p:plain

⇧ 機械学習が11月1日(木)まで無料で受講できるそうな。内容は第一弾の時と変わってないようです。

というわけで、今回は、bit について、レッツ、トライ～。

bitといえば、2進数らしい、でも量子コンピューターはさにあらず

例のごとく、Wikipediaさんに頼ります。

ビット (bit, b) は、ほとんどのデジタルコンピュータが扱うデータの最小単位。英語の binary digit （2進数字）の略であり、2進数の1けたのこと。量子情報科学においては古典ビットと呼ばれる。

1ビットを用いて2通りの状態を表現できる（二元符号）。これらの2状態は一般に"0"、"1"と表記される。

情報理論における選択情報およびエントロピーの単位も「ビット」と呼んでいるが、これらの単位は「シャノン」とも呼ばれる（詳細は情報量を参照）。

省略記法として、バイトの略記である大文字の B と区別するために、小文字の b と表記する。

ビット - Wikipedia

bit に関連して、bitの並び順を、

エンディアン（英: endianness）は、複数のバイトなどを並べる順序の種類である。一般的な用語による表現ではバイトオーダ（英: byte order）、ないしそれを一部訳して日本語ではバイト順とも言う。

エンディアン - Wikipedia

「エンディアン」または「バイトオーダ」というらしいですね。

例えば、十六進法で表現すると 1234ABCD という1ワードが4バイトのデータを、バイト毎に上位側から「12 34 AB CD」のように並べる順序はビッグエンディアン、下位側から「CD AB 34 12」のように並べる順序はリトルエンディアンである。

その他に「34 12 CD AB」あるいは「AB CD 12 34」のように並べる方式もあり、ミドルエンディアンなどという。またこのミドルエンディアンの2つのうちの前者は、DECのPDP-11で使われていたことからPDP エンディアンなどとも呼ばれる。

エンディアン - Wikipedia

⇧ 「エンディアン」の種類が多いですね。

1byte = 8bit = 1octet という関係になるそうですが、8bitを明示的に示したいときは、1octetというのが一般的らしいです。

ちなみに、量子コンピューターになってくると、「量子ビット」を利用してるため、様相が変わってくるようです。

量子ビット（りょうしビット、英: quantum bit）とは、量子情報の最小単位のことである。キュービット、キュビット、クビット（英: qubit）、Qビット（英: Qbit）ともいう。それに対して、従来のコンピュータのビットの事を古典ビット（英: classical bit）やCビット（英: Cbit）という。

量子ビット - Wikipedia

⇧ 「クアンタムビット」って読むんですかね？

仮想通貨に、「Quantum（クアンタム/QTUM)」ってものがおるそうな。

earnerk.com

⇧ 「ビットコイン」と「イーサリアム」のいいとこ取りらしいっす。

脱線しました。

量子情報では、従来の情報の取扱量の最小単位であるビットの代わりに、情報を量子力学的2準位系の状態ベクトルで表現する。

古典ビットは0か1かのどちらかの状態しかとることができないが、量子ビットは、0と1だけでなく0と1の状態の量子力学的重ね合わせ状態もとることができる。

量子ビット - Wikipedia

⇧ 「0」か「1」という2bitの概念で無くなるらしい。

ブラ-ケット記法では、1量子ビットは、 $\alpha |0\rangle +\beta |1\rangle$ と表現される。ここで、 $\alpha ,\beta$ は $|\alpha |^{2}+|\beta |^{2}=1$ の関係を満たす複素数である。これを観測した際に、状態 $|0\rangle$ を得る確率は $|\alpha |^{2}$ であり、状態 $|1\rangle$ を得る確率は $|\beta |^{2}$ である。同じ記法で古典ビットを表現すると、 $\alpha ,\beta$ は、どちらかが0で、もう一方が1である。

量子ビット - Wikipedia

⇧ 数学の知識が欲しいですね、サッパリ分からんです。

2進数表記の無いJavaのString.format

いや～、流石は、Java。2進数は知らんと。いや、2進数は知らんと言っているのはString.formatだけなんですけどね

ameblo.jp

⇧ 上記サイト様によりますと、String.format には、2進数表記のための方法が用意されとらんようなので、

Integer.toBinaryString(int i) メソッドを利用（もしくは、Long.toBinaryString）
独自のFormatter を作成
標準APIではないが、広く使われている Commons Lang を利用

のいずれかで対応していくしかないとのこと。

Java.util.BitSet ってを使ってみる

ExampleのDukptのアルゴリズムで利用されている、Java.util.BitSetを使ってみますか。

mocomei.hatenablog.com

⇧ Java.util.BitSetについては、上記サイト様が丁寧に説明してくれてます。

というわけで、Eclipseで、適当な「Javaプロジェクト」作成し、mainメソッドのあるクラスを作成。

f:id:ts0818:20181027140627p:plain

で、ファイルを編集。

package crypt;

import java.util.BitSet;

public class BitTest {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		BitSet oBitSetA = new BitSet(8);
        int result = 0;
        int value = 1;
        for(int index = 0; index < oBitSetA.size(); index++) {
        	oBitSetA.set(index);
           	System.out.println(oBitSetA.length());
           	System.out.println(oBitSetA);

        }

    	oBitSetA.set(9);
        for(int bitIndex = 0; bitIndex < oBitSetA.length(); bitIndex++) {
        	System.out.println(oBitSetA.length());
            if(oBitSetA.get(bitIndex)){
             System.out.print(result + " + 2の" + bitIndex +"乗は？ ===>");
                result += (value << bitIndex);

             System.out.println(result);
            }
        }
        oBitSetA.clear();
    	oBitSetA.set(10);

        for(int index = 0; index < oBitSetA.size(); index++) {
        	oBitSetA.set(index);
           	System.out.println(oBitSetA);

        }
        
        oBitSetA.clear();
    	oBitSetA.set(928979138);
    	oBitSetA.set(129894302);
    	oBitSetA.set(342113822);
     	oBitSetA.set(2147483647);
    	System.out.println(oBitSetA);

	}

}

で実行してみると、

f:id:ts0818:20181027141016p:plain

1
{0}
2
{0, 1}
3
{0, 1, 2}
4
{0, 1, 2, 3}
5
{0, 1, 2, 3, 4}
6
{0, 1, 2, 3, 4, 5}
7
{0, 1, 2, 3, 4, 5, 6}
8
{0, 1, 2, 3, 4, 5, 6, 7}
9
{0, 1, 2, 3, 4, 5, 6, 7, 8}
10
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
11
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
12
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
13
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
14
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
15
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
16
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
17
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
18
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}
19
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}
20
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}
21
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
22
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}
23
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22}
24
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23}
25
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}
26
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}
27
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}
28
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27}
29
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28}
30
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
31
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
32
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}
33
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}
34
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}
35
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34}
36
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35}
37
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}
38
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37}
39
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38}
40
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39}
41
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
42
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41}
43
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}
44
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43}
45
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44}
46
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45}
47
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46}
48
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47}
49
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
50
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
51
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50}
52
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51}
53
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52}
54
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53}
55
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54}
56
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55}
57
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56}
58
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57}
59
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58}
60
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59}
61
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60}
62
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61}
63
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63}
64
0 + 2の0乗は？ ===>1
64
1 + 2の1乗は？ ===>3
64
3 + 2の2乗は？ ===>7
64
7 + 2の3乗は？ ===>15
64
15 + 2の4乗は？ ===>31
64
31 + 2の5乗は？ ===>63
64
63 + 2の6乗は？ ===>127
64
127 + 2の7乗は？ ===>255
64
255 + 2の8乗は？ ===>511
64
511 + 2の9乗は？ ===>1023
64
1023 + 2の10乗は？ ===>2047
64
2047 + 2の11乗は？ ===>4095
64
4095 + 2の12乗は？ ===>8191
64
8191 + 2の13乗は？ ===>16383
64
16383 + 2の14乗は？ ===>32767
64
32767 + 2の15乗は？ ===>65535
64
65535 + 2の16乗は？ ===>131071
64
131071 + 2の17乗は？ ===>262143
64
262143 + 2の18乗は？ ===>524287
64
524287 + 2の19乗は？ ===>1048575
64
1048575 + 2の20乗は？ ===>2097151
64
2097151 + 2の21乗は？ ===>4194303
64
4194303 + 2の22乗は？ ===>8388607
64
8388607 + 2の23乗は？ ===>16777215
64
16777215 + 2の24乗は？ ===>33554431
64
33554431 + 2の25乗は？ ===>67108863
64
67108863 + 2の26乗は？ ===>134217727
64
134217727 + 2の27乗は？ ===>268435455
64
268435455 + 2の28乗は？ ===>536870911
64
536870911 + 2の29乗は？ ===>1073741823
64
1073741823 + 2の30乗は？ ===>2147483647
64
2147483647 + 2の31乗は？ ===>-1
64
-1 + 2の32乗は？ ===>0
64
0 + 2の33乗は？ ===>2
64
2 + 2の34乗は？ ===>6
64
6 + 2の35乗は？ ===>14
64
14 + 2の36乗は？ ===>30
64
30 + 2の37乗は？ ===>62
64
62 + 2の38乗は？ ===>126
64
126 + 2の39乗は？ ===>254
64
254 + 2の40乗は？ ===>510
64
510 + 2の41乗は？ ===>1022
64
1022 + 2の42乗は？ ===>2046
64
2046 + 2の43乗は？ ===>4094
64
4094 + 2の44乗は？ ===>8190
64
8190 + 2の45乗は？ ===>16382
64
16382 + 2の46乗は？ ===>32766
64
32766 + 2の47乗は？ ===>65534
64
65534 + 2の48乗は？ ===>131070
64
131070 + 2の49乗は？ ===>262142
64
262142 + 2の50乗は？ ===>524286
64
524286 + 2の51乗は？ ===>1048574
64
1048574 + 2の52乗は？ ===>2097150
64
2097150 + 2の53乗は？ ===>4194302
64
4194302 + 2の54乗は？ ===>8388606
64
8388606 + 2の55乗は？ ===>16777214
64
16777214 + 2の56乗は？ ===>33554430
64
33554430 + 2の57乗は？ ===>67108862
64
67108862 + 2の58乗は？ ===>134217726
64
134217726 + 2の59乗は？ ===>268435454
64
268435454 + 2の60乗は？ ===>536870910
64
536870910 + 2の61乗は？ ===>1073741822
64
1073741822 + 2の62乗は？ ===>2147483646
64
2147483646 + 2の63乗は？ ===>-2
64
{0, 10}
64
{0, 1, 10}
64
{0, 1, 2, 10}
64
{0, 1, 2, 3, 10}
64
{0, 1, 2, 3, 4, 10}
64
{0, 1, 2, 3, 4, 5, 10}
64
{0, 1, 2, 3, 4, 5, 6, 10}
64
{0, 1, 2, 3, 4, 5, 6, 7, 10}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 10}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62}
64
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63}
{129894302, 342113822, 928979138, 2147483647}

BitSetの中身の数は、最大で64までらしい。つまり、new BitSet(8)が最大サイズで、それ以降のnew BitSet(9)だったり、new BitSet(10)だったりは、全部変わらず64になってますかね。

BitSetの中に入れられうる値は、0以下は駄目なので、それ以外は、int型の値の範囲、つまり「-2147483648～2147483647」のうちの「0～2147483647」になるようです。

値の順番は昇順になるようです。

う～ん、bit系の操作も学習していかねばですかね...

今回はこのへんで。