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我們說，透過字詞出現的頻率來分析密文，稱為頻率分析，根據常見的有字典頻率分析的三原則，我們可以推導為明文。

前五名常出現的字母：e, t, a, o, i、最常出現的單字：the, to, of, and、常見的雙字母組合：st, ng, th, qu

Once, there was a young boy. This boy had problems controlling his anger. When he got angry, he would say the first thing the samethat came to mind, even if it affected people.

One day, his father gifted him a hammer and a bundle of nails, then said, “Whenever you get mad, hammer a nail into the backyard fence.”

The boy used up half of his nails in the first few days. Over the following weeks, he used up fewer nails until his temper was under control. The father then asked the young boy to remove a nail for each day he didn’t lose his temper.

On the day when the boy had removed his last nail, his father told him, “You have done good, boy. But can you see the holes in the wall? The fence is never going to be . Likewise, when you say mean things in anger, you’ll leave a scar.”

There once was a poor boy who spent his days going door to door selling newspapers to pay for school. The poor boy was starving, so he began to ask for nourishment at each home he stopped at.

The poor boy was denied every time until he reached the door of a young girl. He asked for a glass of water, but seeing his poor state, the girl returned with a glass of milk. The boy asked how much he owed her for the milk, but she refused payment.

Years later, the girl, who was now a grown woman, fell sick. She went from doctor to doctor, but no one could cure her. Finally, she went to the best doctor in town.

The doctor spent months treating her until she was finally cured. Despite her happiness, she was afraid she couldn’t afford to pay the bill. But, when the hospital handed her the bill, it read, “Paid in full, with a glass of milk.”

One bright autumn day, a family of ants was busy working in the warm sunshine. They were drying out the grain they had stored up during the summer when a starving grasshopper came up. With his fiddle under his arm, the grasshopper humbly begged for a bite to eat.

“What!” cried the ants, “Haven’t you stored any food away for the winter? What in the world were you doing all summer?”

“I didn’t have time to store any food before winter,” the grasshopper whined. “I was so busy making music that the summer flew by.”

The ants simply shrugged and said, “Making music, were you? Very well, now dance!” The ants then turned their backs on the grasshopper and returned to work.

邪惡的駭客總是從經驗中累積自己的破解實力，這次他知道了暴力破解法很耗時，決定採用頻率分析。
駭客已取得一篇文章，文章包含了上下段的明文，而中段的文字使用替換式加密，於是他決定依序下列步驟破解密文。

STEP 1. 首先，把「密文前後段的明文」做單字頻率分析，得出「表一、部分明文單字頻率」 。
STEP 2. 將「表二、字典字母頻率」與「表三、密文字母頻率」進行對照，並依據「表一、部分明文單字頻率」 推論密文中重複出現的單字。
STEP 3. 在「表四、解密後的明文」將加密段落回推為明文。

➢ 操作說明
請參考駭客提示的步驟，將你覺得可能的明文字母填入表四，並檢查解密後的明文是否通順，完成頻率分析。

文章

Once upon a time, a farmer had a goose that laid one golden egg every day. The egg provided enough money for the farmer and his wife to support their daily needs. The farmer and his wife continued to be happy for a long time. But, one day, the farmer thought, “Why should we take just one egg a day? Why can’t we take them all at once and make a lot of money?” The farmer told his wife his idea, and she foolishly agreed.

PHEF, PHE FEAP CLK, LB PHE GOOBE WLIC IPB GOWCEF EGG, PHE YLTUET DLB SZIVJ DIPH L BHLTN JFIYE. HE JIWWEC PHE GOOBE LFC VZP IPB BPOULVH ONEF, HONIFG PO YIFC LWW IPB GOWCEF EGGB.

But as he opened the stomach, he only found guts and blood. The farmer quickly realized his foolish mistake and proceeded to cry over his lost resource.

As the days went on, the farmer and his wife became poorer and poorer because of their foolishness.

明文

Once upon a time, a farmer had a goose that laid one golden egg every day. The egg provided enough money for the farmer and his wife to support their daily needs. The farmer and his wife continued to be happy for a long time. But, one day, the farmer thought, “Why should we take just one egg a day? Why can’t we take them all at once and make a lot of money?” The farmer told his wife his idea, and she foolishly agreed.

But as he opened the stomach, he only found guts and blood. The farmer quickly realized his foolish mistake and proceeded to cry over his lost resource.

As the days went on, the farmer and his wife became poorer and poorer because of their foolishness.

密文

PHEF, PHE FEAP CLK, LB PHE GOOBE WLIC IPB GOWCEF EGG, PHE YLTUET DLB SZIVJ DIPH L BHLTN JFIYE. HE JIWWEC PHE GOOBE LFC VZP IPB BPOULVH ONEF, HONIFG PO YIFC LWW IPB GOWCEF EGGB.

表一、明文單字頻率 (出現頻率前10高的單字)

表二、字典字母頻率

表三、密文字母頻率

表四、解密後的明文
按下「替換」後，出現橘底為解密正確的字母。

注意：同一格密文字母只能放入一個"藍色字母方塊"，以確保每一個明文字母只會對應到一個密文字母。
透過「表三、密文字母頻率」可以發現密文中沒有出現 MQRX 這四個字母，因此這四個密文字母的橘底答案僅供參考。

明文

密文

拖曳方塊

頻率分析 – 破解長文的方法

頻率分析 – 實作頻率分析 (由已知明文推論)