בוב רצה לשלוח מסר מוצפן לאליס. הוא החליט להשתמש בסכמה קריפטוגרפית מוכרת. לשם כך, הוא מצא ברשת קוד פתוח המממש ווריאציה לסכמה זו (ראו קובץ מצורף). כצעד ראשון, הוא קידד הודעה (בעזרת קוד ASCII) לתוך פולינום, הצפין אותו וקיבל את התוצאה ב-c1. אליס קיבלה את ההודעה המוצפנת, פענחה אותה וקיבלה הודעה (p1) שהיא מאוד קרובה ל-c1. לאחר מכן, היא שלחה את p1 לחברתה אמבר שעיגלה את רשימת המספרים חזרה לערכי ASCII. איב יירטה את ההודעות c1 ו-p1 ולאחר מספר ימים איב יירטה טקסט מוצפן נוסף (c2) והיא מאוד רוצה לקרוא אותו.
האם תוכלו לעזור לאיב לשחזר את ההודעה המוצפנת ב-c2?
q = 524287
scale = 100
c1:
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
p1:
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
c2:
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