1 Tech Note 0002 2 How to avoid non-intrusive timing attacks with online computations 3 Tom St Denis 4 5 Introduction 6 ------------ 7 8 A timing attack is when an attacker can observe a side channel of the device (in this case time). In this tech note 9 we consider only non-intrusive timing attacks with respect to online computations. That is an attacker can 10 determine when a computation (such as a public key encryption) begins and ends but cannot observe the device 11 directly. This is specifically important for applications which transmit data via a public network. 12 13 Consider a Diffie-Hellman encryption which requires the sender to make up a public key "y = g^x mod p". Libtomcrypt 14 uses the MPI bignum library to perform the operation. The time it takes to compute y is controlled by the number 15 of 1 bits in the exponent 'x'. To a large extent there will be the same number of squaring operations. "1" bits in 16 the exponent require the sender to perform a multiplication. This means to a certain extent an attacker can 17 determine not only the magnitude of 'x' but the number of one bits. With this information the attacker cannot directly 18 learn the key used. However, good cryptography mandates the close scrutiny of any practical side channel. 19 20 Similar logic applies to the other various routines. Fortunately for this case there is a simple solution. First, 21 determine the maximum time the particular operation can require. For instance, on an Athlon 1.53Ghz XP processor a 22 DH-768 encryption requires roughly 50 milliseconds. Take that time and round it up. Now place a delay after the call. 23 24 For example, 25 26 void demo(void) { 27 clock_t t1; 28 29 // get initial clock 30 t1 = clock(); 31 32 // some PK function 33 34 // now delay 35 while (clock() < (t1 + 100)); 36 37 // transmit data... 38 39 } 40 41 This code has the effect of taking at least 100 ms always. In effect someone analyzing the traffic will see that the 42 operations always take a fixed amount of time. Since no two platforms are the same this type of fix has not been 43 incorporated into libtomcrypt (nor is it desired for many platforms). This requires on the developers part to profile 44 the code to determine the delays required. 45 46 Note that this "quick" fix has no effect against an intrusive attacker. For example, power consumption will drop 47 significantly in the loop after the operation. However, this type of fix is more important to secure the user of the 48 application/device. For example, a user placing an order online won't try to cheat themselves by cracking open their 49 device and performing side-channel cryptanalysis. An attacker over a network might try to use the timing information 50 against the user. 51 52 53
