| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Number Theory |
| Type | Cipher encoding/decoding |
| Difficulty | Easy -1.2 This is a straightforward application of cipher algorithms with no conceptual difficulty. Parts (i)-(iii) require only mechanical application of Caesar and Vigenère ciphers in sequence, with the keyword pattern repeating predictably. The arithmetic is simple modulo-26 addition/subtraction with no problem-solving or insight required beyond following the algorithm. |
| Spec | 8.02e Finite (modular) arithmetic: integers modulo n8.02f Single linear congruences: solve ax = b (mod n) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Evidence of intermediate H | B1 | |
| FACE | B3 | Evidence of intermediate HCEG – award 2 marks; Evidence of accurate application of one of the two decoding ciphers – award 1 mark |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(800=(3\times266)+2\); the second row gives T | M1 | Use of second row |
| so plaintext is R | A1 |
### Question 8:
**Part (i) & (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Evidence of intermediate H | B1 | |
| FACE | B3 | Evidence of intermediate HCEG – award 2 marks; Evidence of accurate application of one of the two decoding ciphers – award 1 mark |
**Part (iii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $800=(3\times266)+2$; the second row gives T | M1 | Use of second row |
| so plaintext is R | A1 | |8 A passage of plaintext is encoded by using the Caesar cipher corresponding to a shift of 2 places followed by the Vigenere cipher with keyword ODE.\\
(i) The first letter in the plaintext passage is $F$. Show that the first letter in the transmitted text is $V$.\\
(ii) The first four letters in the transmitted text are VFIU. What are the first four letters in the plaintext passage?\\
(iii) The 800th letter in the transmitted text is $W$. What is the 800th letter in the plaintext passage?\\
\hfill \mbox{\textit{OCR MEI C4 2010 Q8 [6]}}