# Can someone explain the timing attack on RSA with Montgomery multiplication?

I have read several articles on the temporal attack against Montgomery multiplication to speedup RSA computations. However, I do not quite get the principle.

I understood that there is a additional reduction when performing Montgomery multiplication when the multiplication is greater than the modulus.

What I don't understand is how to choose the message sets. Or how to go from one key bit to another. And how many messages should be taken for each bit.

Edit : i'm still wondering on how we get the two sets of messages. The first set should not include a reduction in contrary to the second set. How can we know if there is a reduction or not ?

• Have you seen this question yet? Commented May 10, 2020 at 3:44
• Please indicate if you did. Your question could be closed as a duplicate if you don't. As it stands, it is unclear what part you don't get. There are 3 questions (I had to remove the "how to attack a little" because that's not really a good question). If you read the other answer, then where are you stuck? Commented May 10, 2020 at 15:22
• Yes i do, i'm still wondering on how we get the two sets of messages. The first set should not include a reduction in contrary to the second set. How can we know if there is a reduction or not ? Commented May 10, 2020 at 16:22
• Does this answer your question? RSA Timing Attack on "Extra" Montgomery Reduction Commented May 10, 2020 at 22:05
• I read it several times, but i dont understand this part "plays all messages" in the first answer. Commented May 11, 2020 at 0:58