Obfuscation.htm
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<title>Obfuscation method for DDR</title>
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<div class=Section1>
<h1><b>Obfuscation method for DDR<o:p></o:p></b></h1>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>This is implemented in RI for all memory accesses. It
consists of two parts, the address obfuscation and data masking. Both are
associated with keys, which are dynamically generated and change for every run
of the game. The address obfuscation is an invertible scrambling and addition
(xor)<span style="mso-spacerun: yes"> </span>on addresses to</p>
<ul style='margin-top:0in' type=disc>
<li class=MsoNormal style='mso-list:l1 level1 lfo1;tab-stops:list .5in'>Make
it difficult to infer the layout of code and data on DDR in run time</li>
<li class=MsoNormal style='mso-list:l1 level1 lfo1;tab-stops:list .5in'>Make
it difficult to run third party code from DDR.</li>
</ul>
<p class=MsoNormal>The data masking is a simple data transformation to hide
data on the chip- DDR interface.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><b>Address obfuscation</b>:</p>
<p class=MsoNormal>Address obfuscation consists of a permutation and xor.
(Substitution is not feasible).</p>
<p class=MsoNormal>There are 24 address bits that reference 16MB of DDR memory.
Of these the lower order 7 bits represent 128 bit blocks which cannot be
scrambled, so we safely assume we scramble 16 higher bits. </p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>In order to reduce complexity we do not allow the entire set
of 16! permutations of these 16 bits. We break up into 4 sets of 4 bits each.
So we need </p>
<ul style='margin-top:0in' type=disc>
<li class=MsoNormal style='mso-list:l0 level1 lfo2;tab-stops:list .5in'>two
bits for each set to describe its ordering (total = 2*4 = 8) </li>
<li class=MsoNormal style='mso-list:l0 level1 lfo2;tab-stops:list .5in'>two
bits per address bit for its ordering within the group (total = 2*4*4 = 32
for all four groups)</li>
</ul>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>With just the bits within each group scrambled, it will give
us 4! * 4! *4! *4! orderings = 331776 possibilities of address scrambling,
which means that one would need to observe 331776 known plaintext (actual
address values) to derive the keys. Adding the permutations of groups itself,
there are 4! Ways of ordering the 4 groups, so that results in 7962624 orderings,
which is about 8 million known plaintext, assuming all permutations are equally
likely. </p>
<p class=MsoNormal><span style="mso-spacerun: yes"> </span>(For comparison, 16!
is 20 x 10^12.)</p>
<p class=MsoNormal>For simplicity I will denote these address lines A0-A16.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><b>Remember the software generated select bits should be
valid permutations with no repetitions</b>.</p>
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<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>For example, a resulting permutation using the above result
G1, G0, G2, G3 could be</p>
<p class=MsoNormal>A4, A6, A7,A5, A0,A1, A3,A2, A10,A11,A7,A8, A12,A14,A13,A15</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<ul style='margin-top:0in' type=disc>
<li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'><b>Addition<o:p></o:p></b></li>
</ul>
<p class=MsoNormal>In order to add some more confusion into the address
obfuscation, we bitwise xor a random 16 bit key to the bits on the address bus
after permutation.</p>
<p class=MsoNormal>New A0-A16 = A0-A16 xor K1-K16 </p>
<p class=MsoNormal>Where K0-K16 is a random 16 bit pattern.</p>
<p class=MsoNormal>This adds 65536 possibilities to deciphering this key.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<h2>Data masking</h2>
<p class=MsoNormal><b><![if !supportEmptyParas]> <![endif]><o:p></o:p></b></p>
<p class=MsoNormal>Data masking is achieved by calculating a mask which is
xored to data bits after the data bits are read. This mask is a function of
the scrambled address, and another key used in the following scrambling circuit
based on a feedback shift register PN generator to create a mask for data. This
logic could be exercised in parallel with the data fetched/written<span
style="mso-spacerun: yes"> </span>from/to<span style="mso-spacerun: yes">
</span>DDR.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<h2>Mask generation circuit</h2>
<p class=MsoNormal>Two possibilities, depending on what we can implement, are
shift register based and substitution table based:</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><b>Shift register based</b>:</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>For the purpose of creating 64 bit shift registers, here are
few connections which will lead to primitive polynomials</p>
<ul style='margin-top:0in' type=disc>
<li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>(59,
6,5,4,3,1,0) (that is x^59 + x^6 + x^5 + x^4 + x^3 + x^1 +<span
style="mso-spacerun: yes"> </span>1)</li>
<li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>(54,
6,5,4,3,2,0)</li>
<li class=MsoNormal style='mso-list:l2 level1 lfo3;tab-stops:list .5in'>(48,7,5,4,2,1,0)</li>
</ul>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>Since we plan to hardwire the connections, we could pick one
of these.</p>
<p class=MsoNormal>We generate 48 bits of random key to be used as a constant
for one run of the game. We use the 16 bits of scrambled address bits and input
this as state to the feedback shift register. If we clock through this FSR 64
times we get 64 bits as output. (Or implement the equivalent as a table
lookup). This is a cheap way of accomplishing hash(key, address). This is the
mask for the data read from the DDR, or to be written to DDR.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
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<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><b>Matrix based substitution</b>:</p>
<p class=MsoNormal>A substitution based scheme would be to take the 64 bits
from the (key, address) combination and store into a 4x4 array, each element
being 4 bits</p>
<p class=MsoNormal>(This is an AES like scheme).</p>
<p class=MsoNormal>[d15 d14 d13 d12] = r0</p>
<p class=MsoNormal>[d11 d10 d9 d8] = r1</p>
<p class=MsoNormal>[d7 d6 d5 d4] = r2</p>
<p class=MsoNormal>[d3 d2 d1 d0] = r3</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>Then shift r1 by one bit to the right, r2 by two, r3 by
three.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>Then lookup a 16 entry table (generated once for each game)
to lookup and substitute each value.</p>
<p class=MsoNormal>Resulting in: </p>
<p class=MsoNormal>[s15 s14 s13 s12]</p>
<p class=MsoNormal>[s11 s10 s9 s8]</p>
<p class=MsoNormal>[s7 s6 s5 s4]</p>
<p class=MsoNormal>[s3 s2 s1 s0]</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>The resulting mask is copied out columnwise as:</p>
<p class=MsoNormal>[s15 s11 s7 s3 s14 s10 s6 s2 s13 s9 s5 s1 s12 s8 s4 s0]</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>This is xored with data from DDR. This method is probably
more secure, provided the 16 entry lookup is feasible.</p>
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<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<h2>Inverting the whole scheme:</h2>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal>The address is inverted by inverting the permutation and the
key xor. The shift register operation is done again to obtain the mask and is
applied to the data.</p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><b>Attack</b>:</p>
<p class=MsoNormal>To attack this system, assuming someone has known plaintext
from an illegal version of the same game, one would have to, after the game
starts running, run the searching algorithm to determine these keys. Then he
can make his DDR masquerade as ours. Since we have three random quantities, the
search space multiplies. But still it should be pretty hard to be able to do
this reliably every time without causing enough delay before the illegal game
can start running.</p>
<p class=MsoNormal>To create a new game, one would have to record the data on
the bus. Then analyse it to obtain the keys and use it with the above system to
plug into our DDR. It is probably not trivial but not impossible
.<span
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Wingdings'><span style='mso-char-type:symbol;mso-symbol-font-family:Wingdings'>J</span></span></p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
<p class=MsoNormal><![if !supportEmptyParas]> <![endif]><o:p></o:p></p>
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