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I'm trying to evaluate the correlation between key length and the number of messages that needs to be send to server during Cache timing Attack.

I read both D. Bernstein, “Cache-timing attacks on AES,” April 2005. Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago. Robert G. Salembier, "Analysis of Cache Timing Attacks against AES"

But it doesn't give me the answer. At the beginning Bernstein identified one byte of key after sending around 4,2 million 400-byte long messages. Attack described was done on the 128-bit AES key, and it required 32 million 800-byte packages, 32 million 600 byte packets, and 128 million 400-byte packets. But in conclusions (Future works) D.Bernstein write: "I wouldn't be surprised if the first million (2^20) 800-byte and 600-byte packets were sufficient to identify the key"

Additional information can be found in [7]. But there is still no direct correlation between key length and message numbers.

Is there any correlation ?

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Depends a lot on how well you can measure the timing. Bernstein used a setup with pretty accurate timing information. –  CodesInChaos Oct 12 '13 at 10:10

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