Homework Practise. Decryption of RSA ciphertext LAND USING 53261 CYPHER TEXT : PO- Run of the Exercise You get a ciphertext resulting from the operation of the RSA algorithm on the plaintext, the content of which you are to restore. You also get some data on the basis of which you define the necessary param- eters for the cipher service. Following steps: 1. Remember the year of the battle between the troops of the Polish king Ladislaus the Short (or "Elbow-high" and the Teutonic Order in the 14th century. Mark it as R. 2. Determine in the table below the leftmost prime to R and consider it as p. Table of 300 initial prime numbers 3 5 1113 17 lalala 1 H | | 379 397 701 719 2 7 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 383 389 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 709 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 883 887 907 911 919 937 941 947 953 967 971 977 983 991 997 1009 1013 1019 1021 1031 | 1033 1039 1049 | 1051 1061 1063 1069 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193 1201 1213 1217 1223 12291231 1237 12491259 | 127712791283 | 1289 1291 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 1429 1433 1439 1447 1451 1453 1459 | 1471 1481 1483 1487 1489 1493 1499 1511 1523 1531 1543 | 1549 1553 1559 1567 1571 15791583 15971601 1607 1609 16131619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811 1823 1831 1847 | 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 881 929 H 3. The number q is predetermined and has the value 3. 4. Find the modulus n= pq. 5. Find the totient (n). 6. Assume that e = 5 (part of the public key). 7. Find d so that de = 1 (mod o(n)) (part of the private key). e In n In N 8. Calculate k = log n] = where n is a modular number, and N= 16 (the length of the alphabet narrowed down to letters from A to P). The numbers k and k + 1 have the following meanings: k+1 -length of the block being decrypted simultaneously (= number of letters in the ciphertext being decrypted at once). k - number of letters in the plaintext block after decryption. Examplary report on Exercise 4 Private key de = 1 (mod o(n)) ? put proper value My numerical data Y-year of Alphabet Modulus Totient k - the length Public key the battle length N of plaintext n o(n) e block ? ? ? ? ? ? put proper put proper put proper put proper put proper put proper value value value value value value My cryptographic data Plaintext to be encrypted people k-element blocks of cipher- text letters pe ople (separated by space or Decimal values of every plaintext block 244 239 180 (separated by space or G - decimal ciphertext value of every block 3301 3158 483 (separated by space or ) Conversion dec. to hex.2) CE5 056 1E3 (separated by space or ) Corresponding letters from the table" in hex, system mof mfg apd (separated by space or) Ciphertext letter by letter m 0 f m f g a d Dec alphabet character table 01 2 3 0 1 2 3 4 4 | 5 5 f 6 6 g 7 7 h 8 8 9 9 j alo 10 A k || 11 B 1 12 13 14 15 C D E F m n b d e link for quick conversion any any (especially hex dec) https://fin-calc.org.ua/en/calculator/conversionotation/any/ Report on Exercise4 My numerical data Y-year of Alphabet the battle length N Modulus n Public key Totient (n) k-the length of plaintext block Private key de = 1 (mod on)) e My cryptographic data Plaintext to be encrypted k-element blocks of cipher- text letters (separated by space or ) Decimal values of every plaintext block (separated by space or ) c-decimal ciphertext value of every block (separated by space or ) Conversion dec. to hex.?) (separated by space or Corresponding letters from the table" in hex. System (separated by space or Ciphertext letter by letter alphabet & character table Dec 0 1 2 3 Hex 0 1 2 3 b d 4 4 e 5 67 5 67 f g 8 8 i 9 9 j 10 A k |-|:|E 11 B 1 12 m 13 D 14 E Two 15 F | n 2) link for quick conversion any any (especially hex dec) https://fin-calc.org.ua/en/calculator/conversionotation/any/