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"DELAYED CODE" technology (version 1.1)

Z0mbie
Top Device Online [10]
October 2000

2
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Introduction

Let we wrote a virus. Avers will create antiviral code to detect it, and after some time period all infected computers will be cured. This article describes another technology of prolonging this time period.

Idea

We may write code which will change initial virus bytes (or any other virus characteristics) after two months, for example. If the virus will initially contain such modificating-code, antivirus will just contain not one, but two or more checksums, or checksum calculated at other, constant code range.

There are only one way to prohibit analysis of the modificating-code: to hide it from avers. And there are the following ways to implement this action:

  1. At required time, download code from the Internet, or encrypt code and wait for decryption-key.
  2. Encrypt code with such method, that decryption will take exactly required time. ("delayed code")

As you can see, last variant allows us to write completely automated virus with hidden "delayed" features.

Theory (sux)

Lets encrypt some random buffer A[] with some hashing algorithm so many times N, so it will take us time period T. After these calculations done, we have another random buffer B[] which is used to encrypt/decrypt our "delayed" code.

There is no way to perform required N iterations using more than one computer ('coz each time current buffer is encrypted), so minimal decryption time is limited with maximal CPU speed.

If you will use computer which is fast enough, and use some time to encrypt fucking random buffer, then you may be sure that the same operation may not be done in a less time period.

So, each time the virus is active, it iterates N encryption cycles until buffer A[] will be converted into B[]. After time T will be spent to decryption, virus will got buffer B[] and use it to decrypt "delayed code".

Theory (rulez)

Main trouble is that we dont want to wait for some months to encrypt fucking data, 'coz in example showed above, encryption and decryption both takes the same time period T.

This means that we will use RSA algorithm. In the RSA algorithm, encryption and decryption keys are different.

So, to encrypt "delayed code" we will take random buffer A[], encrypt it N times and got buffer B[].

But, in contrast to previously described hashing algorithm, our virus will iterate not the same operation. Our virus will decrypt buffer B[] back into A[].

In the encryption operation will be used small (low-bit) exponent, and in the decryption operation we will use big exponent.

This means that encryption will take much less time than decryption. We will encrypt our "delayed code" for some minutes/hours, but active virus copies (as well as avers ;-) will decrypt it for some months.

Encryption/decryption time interdependence

Now our task is to answere, how many times should we encrypt our "delayed code" so it will be decrypted for some months.

As you know, RSA encryption means the following:

    encryption: encr = (text ^ e) % m
    decryption: text = (encr ^ d) % m

where {e,m} and {d,m} pairs are public and secret keys. ('^' sign means raising to a power, '%' means modulus, remainder after division)

As a rule, e is a small number (with a low # of bits), such as 3, 17, 50003 and so on. And d is a big number, consisting of 1023 bits for example.

In our scheme there is no public/secret meaning at all. Here is our scheme:

Encryption (encrypting "delayed code", at home ;-)Decryption (decrypting "delayed code", on infected or on avers' PC)
  • A[] <-- random buffer/any data
  • encrypt "delayed code" with A[]
  • x = A[]
    N times: x = (x ^ e) % m
    B[] = x
  • store B[] in virus
  • x = B[]
    N times: x = (x ^ d) % m
    A[] = x
  • decrypt "delayed code" with A[]

Now lets consider our main 'modexp' subroutine.

    // modexp:  subroutine, raising to a power and returning modulus
    // returns: x = (a ^ e) % m

    void modexp(bignumber& x,   // output
                bignumber a,    // input
                bignumber e,    // exponent
                bignumber m,    // modulus
    {
        x = 1;
        bignumber t = a;
        for (int i = 0; i <= MaxBit(e); i++)
        {
            if (e.GetBit[i] == 1)
              x = (x * t) % m;        // modmult()
            t = (t * t) % m;          // modmult()
        }
    }

As you can see, modexp() subroutine calls modmult() subroutine (e.#bit + e.#bit1 - 1) times. (-1 here means that last t*t multiplication is skipped; i just simplified the code showed above) This number of modmult() calls is a main difference between encryption and decryption.

  Decr.time = Encr.time * (D.#bit+D.#bit1 - 1) / (E.#bit1+E.#bit1 - 1) * K

where:

    #bit  == total number of bits
    #bit1 == number of 1s
    #bit + #bit1 - 1 == number of modmult() calls

    K = 0.9+-10% -- Appeared because of variable modmult() time usage.
                    As it seems, when N-->oo, K-->1

Example

Lets calculate, how many times (N) should we encrypt the message, so it will be decrypted for 10 minutes. Note, that all these tests were performed on a slow pc, so not the numbers, but their proportionality has a meaning.

At first, we must create RSA key. Let it be 1024-bit key with low exponent e = 3. Executing: 'KEYGEN.EXE KEY\DPGN 1024 3 3' Key parameters are: 1024-bit N, E==3, D=1023-bit/519*'1'

Theoretical time ratio: (1023+519-1)/(2+2-1)*0.9 = 462+-10%

But we want higher ratio precision, so lets find real time ratio, kinda "calibrate" a key.

    Executing: 'DGPGN.EXE e 100'
    result: 100 iterations done, encryption time = 815 ms
    Executing: 'DGPGN.EXE d 100'
    result: 100 iterations done, decryption time = 360228 ms

    'Real' ratio: 360228/815 = 441

Now we may calculate N for 10-min decryption.

If 100 decryption iterations used 360228 ms, and N iterations will use 10*60*1000 ms (10 minutes), then N = 60*10*1000 * 100 / 360228 = 167

If 167 decryption iterations will use 60*10*1000 ms, then encryption time is 60*10*1000 / 441 = 1360 ms.

So, about one second of encryption will result in 10 mins of decryption.

    Executing: 'DPGN.EXE e 167'
    encryption time: 1268 ms

    Executing: 'DPGN.EXE d 167'
    decryption time: 600477 ms = 10 minutes + 0.5 seconds

Lets show here some other calculation results:

DecryptionEncryptionN (1024-bit key)
K5-100Celeron-500
10 min 1.3 sec 167 950
1 hour 7.8 sec 1000 5700
1 day 3 min 24000 136800
1 week 21 min 168000 957600
1 month 1.5 hour 672000 3830400
1 year 18 hours 8064000 45964800
16 months 1 day    
10 years 1 week    
40 years 1 month    

8-( )

Increasing speed of calculations

Decryption algorithm 'text = (encr ^ d) % m' may be also represented as follows:

      a = ((encr % p) ^ dp) % p            // dp = d % (p-1)
      b = ((encr % q) ^ dq) % q            // dq = d % (q-1)
      if (b < a) b += q
      text = a + p * (((b - a) * u) % q)       // u: (u * p) % q = 1

In such algorithm, decryption time should be faster by some times. But, i dont know if it is possible to find p and q knowing d,e and m.

Slowing down speed of calculations

Because of d is not unique key, and d variants may be calculated using formula:

   d' = d + (p-1)*(q-1) * t, t=0,1,2,...,

then d length may be increased as we want, that will slow down calculations by many times.

But, if p and q will be found (knowing d'), then original d can also be found, and then somebody will be able to perform DPGN calculations many times faster, that is bad.

Other bad stuff

  1. In a real life, there is no need to publish N number (# of iterations), just any good CRC will be enough. So, nobody will know what is IT and when IT will be decrypted and executed. |-> Also, it is good to add some random part to N number and do not make resulting time T day- or hour- aligned.
  2. I'm not sure, but - maybe - {N times: x = (x ^ d) % m} operation may be changed to something more fast (using some perverted math). To avoid such shit, you may do some additional encryption between 'modexp' calls, for example as following:
    N times:
    {
      x = (x ^ d) % m;
      x = x xor <some-big-number>;
    }
    
    DPGN.EXE just xors some dwords within the x number on each iteration.

"Delayed code" usage (which code to encrypt?)

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