## 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 parameters 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

• The number q is predetermined and has the value 3.
• Find the modulus n = pq.
• Find the totient j(n).
• Assume that e = 5 (part of the public key).
• Find d so that  de  º 1 (mod j(n)) (part of the private key).
• Calculate  – 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.

Use the programs included with Homework 3 to calculate modular powers and inversions. Their Excel worksheets are shown below.

Examplary report on Exercise 4

My numerical data

My cryptographic data

1) alphabet S character table

2) link for quick conversion any ↔ any (especially hex ↔ dec)

Individual data can be found on the next page.

Report on Exercise 4

My numerical data

My cryptographic data

1) alphabet S character table

2) link for quick conversion any ↔ any (especially hex ↔ dec)

Individual data can be found on the next page.

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