Cracking RSA by listening to the wires and radio waves

A recent paper showed that it is possible to determine the private key of RSA by simply listening to the radio waves emitted from a mobile phone. This is because the RSA method uses multiply and square operations. This can then be observed on a power trace as the processor consumes different amounts of electrical power as it performs the calculations.

Performing the RSA decryption operation

In RSA we decrypt by taking the cipher, and then raising it to the power of d:

Message = Cipherᵈ (mod N)

and where N is the multiplication of two prime numbers. Our decryption key is (d,N). Thus if we find d, we crack RSA. We know N, as the public key is (e,N).

In order to perform the exponent operation (Cipherᵈ), we normally use the square and multiply method. So 5⁴ (where 4 is the exponent) becomes:

5² = 25

25²= 625

If we can to multiply 5⁸ that is 5² squared to give 5⁴, and then if we square again we get 5⁸. It has thus taken us six operations to find a power of 8. For 5⁶⁴, we will need four operations:

5² →5⁴ →5⁸ → 5¹⁶→ 5³²→ 5⁶⁴

But let’s say we want 5⁹. For this we square as we did before to give us 5⁸, and…