Final answer:
To implement a symmetric algorithm with 10 participants, you would need 45 unique keys since each pair requires a unique key. This is calculated using the combinations formula n(n - 1) / 2.
Step-by-step explanation:
The question pertains to the implementation of a symmetric algorithm in a scenario with 10 participants. In symmetric cryptography, each pair of users needs a unique key to communicate securely. To find the number of keys required, we can use the formula for the number of combinations of pairs that can be formed from a group of n participants, which is n(n - 1) / 2. For 10 participants, this would be 10(10 - 1) / 2, which simplifies to 10 x 9 / 2, resulting in 45. Therefore, 45 unique keys are needed for 10 participants to fully implement a symmetric algorithm, making option C the correct answer.