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A side-channel attack is any attack based on information gained from the implementation of Encryption protocol and by monitoring security-critical operations.
Almost every encryption had a side-channel attack.

What kind of side-channel attack are possible on RSA?

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One type of side channel attacks on RSA is timing attack. It explots the timing variability of operation implementation. To secure against RSA timing attack, constant-time operations are implemented.

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As far as I can find out there one of "Paul Carl Kocher" development was Timing Attack, that can break implementations of RSA, a timing attack is a side channel attack that attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms.

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    $\begingroup$ Actually, Paul's work was far more focused on various power side channel attacks (for one, those give far more information to the attacker than a simple timing measurement). $\endgroup$ – poncho Sep 22 '18 at 12:57

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