A cryptographer investigates the relationship between the bit-length of an encryption key, LLL, and the time, TTT ms, required for a hardware-accelerated brute-force attack to penetrate the cipher. He believes that there is a positive correlation between key length and decryption time. He decides to test this hypothesis at the 2.5%2.5\%2.5% level of significance.
The cryptographer correctly calculates the product moment correlation coefficient (PMCC) for a random sample of 404040 different ciphers to be r=0.321r = 0.321r=0.321.
The table below shows the critical values for the PMCC for a sample size of 404040 for various significance levels.
| 1-tailed test significance level | 5% | 2.5% | 1% | 0.5% |
|---|---|---|---|---|
| 2-tailed test significance level | 10% | 5% | 2% | 1% |
| Critical values | 0.2638 | 0.3120 | 0.3665 | 0.4026 |
Determine the conclusion of the cryptographer's investigation, justifying your answer.
