Differential Power Analysis

[Paul Kocher <paul@cryptography.com>]

Information is now available online about three related attacks we 
have developed at Cryptography Research: Simple Power Analysis, 
Differential Power Analysis, and High-Order Differential Power 
Analysis. 

The basic idea of the attacks is that the power consumption of a 
device (such as a smartcard) is statistically correlated to the 
operations it performs.  By monitoring the power usage (or 
electromagnetic radiation, etc.) during cryptographic operations, it 
is possible to obtain information correlated to the keys.  The 
collected data is then analyzed to actually find the keys.  The three 
attacks use increasingly sophisticated analysis methods. 

We have implemented the attack against a large number of smartcards, 
and have found all to be vulnerable.  At this point, we do not 
believe that any smartcards on the market are immune to these 
analysis techniques. 

There is now an initial summary on Differential Power Analysis on our 
web page at http://www.cryptography.com/dpa, and more information 
will be put on the website as it becomes available.  A condensed text 
version is attached below.  At this point, it's fine to talk about 
this with anyone and to forward this message.  

Anything you can do to keep discussion of this technically accurate 
would be much appreciated. 

Regards,
Paul Kocher


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Introduction: Power Variation

Integrated circuits are built out of individual transistors, which 
act as voltage-controlled switches. Current flows across the 
transistor substrate when charge is applied to (or removed from) the 
gate. This current then delivers charge to the gates of other 
transistors, interconnect wires, and other circuit loads. The motion 
of electric charge consumes power and produces electromagnetic 
radiation, both of which are externally detectable. 

Therefore, individual transistors produce externally observable 
electrical behavior. Because microprocessor logic units exhibit 
regular transistor switching patterns, it is possible to easily 
identify macro-characteristics (such as microprocessor activity) by 
the simple monitoring of power consumption. DPA type attacks perform 
more sophisticated interpretations of this data. 



Simple Power Analysis (SPA)

In SPA attacks, an attacker directly observes a system's power 
consumption. The amount of power consumed varies depending on the 
microprocessor instruction performed. Large features such as DES 
rounds, RSA operations, etc. may be identified, since the operations 
performed by the microprocessor vary significantly during different 
parts of these operations. At higher magnification, individual 
instructions can be differentiated. SPA analysis can, for example, be 
used to break RSA implementations by revealing differences between 
multiplication and squaring operations. Similarly, many DES 
implementations have visible differences within permutations and 
shifts (e.g., the PC1 permutation or rotates of the C and D 

registers), and can thus be broken using SPA. While Cryptography 

Research found many smartcards to be vulnerable to SPA analysis, it 
is not particularly difficult to build SPA-resistant devices. 

The figure above [see web site] shows SPA monitoring from a single 
DES operation performed by a typical smartcard. The upper trace shows 
the entire encryption operation, including the initial permutation, 
the 16 DES rounds, and the final permutation. The lower trace is a 
detailed view of the second and third rounds. 



Differential Power Analysis (DPA)

DPA is a much more powerful attack than SPA, and is much more 
difficult to prevent. While SPA attacks use primarily visual 
inspection to identify relevant power fluctuations, DPA attacks use 
statistical analysis and error correction techniques to extract 
information correlated to secret keys. 

Implementation of a DPA attack involves two phases: Data collection 
and data analysis. Data collection for DPA may be performed as 
described previously by sampling a device's power consumption during 
cryptographic operations as a function of time. For DPA, a number of 
cryptographic operations using the target key are observed. 

The following steps provide an example of a DPA attack process for 
technical readers. (More detailed information will follow in the near 
future.) The following explanation presumes a detailed knowledge of 
the DES algorithm. 

  1.  Make power consumption measurements of the last few rounds of 
      1000 DES operations. Each sample set consists of 100000 data 
      points. The data collected can be represented as a two-
      dimensional array S[0...999][0...99999], where the first index 
      is the operation number and the second index is the sample. For 
      this example, the attacker is also assumed to have the 
      encrypted ciphertexts, C[0...999]. 

  2.  The attacker next chooses a key-dependent selection function D. 
      In this case, the selection function would have the form 
      D(Ki,C), where Ki is some key information and C is a 
      ciphertext. For the example, the attacker's goal will be to 
      find the 6 bits of the DES key that are provided as the input 
      to the DES S box 4, so Ki is a 6-bit input. The result of 
      D(Ki,C) would be obtained by performing the DES initial 
      permutation (IP) on C to obtain R and L, performing the E 
      expansion on R, extracting the 6-bit input to S4, XORing with 
      Ki, and using the XOR result as the input to the standard DES 
      S4 lookup operation. A target bit (for example, the most 
      significant bit) of the S result is selected. The P permutation 
      is applied to the bit. The result of the D(Ki,C) function is 
      set to 0 if the single-bit P permutation result and the 
      corresponding bit in L are equal, and otherwise D(Ki,C) yields 
      1. 

  3.  A differential average trace T[0...63][0...99999] is 
      constructed from the data set S using the results of the 
      function D. In particular:  [See web site for formula] 

  4.  The attacker knows that there is one correct value for Ki; 
      other values are incorrect. The attack goal is to identify the 

      correct value. In the trace T[i][0...99999] where i=Ki, 

      D(i,C[k]) for any k will equal the value of the target bit in L 
      of the DES operation before the DES F function result was 
      XORed. When the target device performed the DES operations, 
      this bit value was stored in registers, manipulated in logic 
      units, etc. -- yielding detectable power consumption 
      differences. Thus, for the portions of the trace T[i=Ki] where 
      that bit was present and/or manipulated, the sample set T[i] 
      will show power consumption biases. However, for samples T[i != 
      Ki], the value of D(i,C[k]) will not correspond to any 
      operation actually computed by the target device. As a result, 
      the trace T[i] will not be correlated to anything actually 
      performed, and will average to zero. (Actually, T[i != Ki] will 
      show small fluctuations due to noise and error that is not 
      statistically filtered out, and due to biases resulting from 
      statistical properties of the S tables. However, the largest 
      biases will correspond to the correct value of Ki.) 

  5.  The steps above are then repeated for the remaining S boxes to 
      find the 48 key bits for the last round. The attack can then be 
      repeated to find the previous round's subkey (or the remaining 
      8 bits can be found using a quick search.) 

While the effects of a single transistor switching would be normally 
be impossible to identify from direct observations of a device's 
power consumption, the statistical operations used in DPA are able to 
reliably identify extraordinarily small differences in power 
consumption. 

The figure below [see web site] is a DPA trace from a typical 
smartcard, showing the power consumption differences from selecting 
one input bit to a DES encryption function used as a random number 
generator. (The function of D was chosen to equal the value of 
plaintext bit 5.) The input initial permutation places this bit as 
part of the R register, affecting the first-round F function 
computation and results. Round 2 effects (due to the use of counter 
mode) are also strong. The trace was produced using 1000 
measurements, although the signals would be discernable with far 
fewer. 



High-Order Differential Power Analysis (HO-DPA)

While the DPA techniques described above analyze information across a 
single event between samples, high-order DPA may be used to correlate 
information between multiple cryptographic suboperations. Naive 
attempts to address DPA attacks can introduce or miss vulnerabilities 
to HO-DPA attacks. 

In a high-order DPA attack, signals collected from multiple sources, 
signals collected using different measuring techniques, and signals 
with different temporal offsets are combined during application of 
DPA techniques. Additionally, more general differential functions (D) 
may be applied. More advanced signal processing functions may also be 
applied. The basic HO-DPA processing function is thus a more general 
form of the of the standard DPA function, for example:   [see web 
site for formula]


Today HO-DPA are primarily of interest to system implementers and 
researchers, since no actual systems are known that are vulnerable to 

HO-DPA that are not also vulnerable to DPA. However, DPA 
countermeasures must also address HO-DPA attacks to be effective. 



Solving the Problems 

Cryptography Research has undertaken a substantial development effort 
to understand hardware security issues and their countermeasures. 
Cryptography Research has pending patents directed to the 
technologies and techniques below. 

DPA and related attacks span the traditional engineering levels of 
abstraction. While many previously-known cryptanalytic attacks (such 
as brute force) can be analyzed by studying cryptographic algorithms, 
DPA vulnerabilities result from transistor and circuit electrical 
behaviors which propagate to expose logic gates, microprocessor 
operation, and software implementations. This ultimately compromises 
the cryptography. 

Techniques for addressing DPA and related attacks can be incorporated 
at a variety of levels: 

Transistor: No feasible alternatives to semiconductors are available 
today, but alternate computation technologies (such as pure optical 
computing) may exist in the future. Cryptography Research has 
developed gate-level logic designs that leak substantially less 
information. 

Circuit, Logic, Microprocessor, and Software: In physically large 
systems, well-filtered power supplies and physical shielding can make 
attacks infeasible. For systems with physical or cost constraints, 
Cryptography Research has developed hardware and software techniques 
that include ways of reducing the amount of information leaked, 
introducing noise into measurements, decorrelating internal variables 
from secret parameters, and temporally decorrelating cryptographic 
operations. In applications where attackers do not have physical 
possession of the device performing cryptographic operations, such 
techniques can be effective. However, because externally-monitorable 
characteristics remain fundamentally correlated to cryptographic 
operations, we do not recommend these approaches as a complete 
solution for applications where attackers might gain physical 
possession of devices. 

Software and Algorithms: The most effective solution is to design and 
implementing cryptosystems with the assumption that information will 
leak. Cryptography Research has developed approaches for securing 
existing cryptographic algorithms (including RSA, DES, DSA, Diffie-
Hellman, ElGamal, and Elliptic Curve systems) to make systems remain 
secure even though the underlying circuits may leak information. In 
cases where the physical hardware leaks excessively, the leak 
reduction and masking techniques are also required.



_____________________________________________________________________
Paul Kocher                          President, Cryptography Research
Tel: 415-397-0123 (FAX: -0127)             870 Market St., Suite 1088
E-mail: paul@cryptography.com                 San Francisco, CA 94102


_____________________________________________________________________
Paul Kocher                          President, Cryptography Research
Tel: 415-397-0123 (FAX: -0127)             870 Market St., Suite 1088
E-mail: paul@cryptography.com                 San Francisco, CA 94102