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Silver Member Username: Koko_wawaPost Number: 184 Registered: Aug-07 | Analysis of the Nagravision Video Scrambling Method Markus G. Kuhn 23 August 1998 Abstract The Kudelski Nagravision pay-TV conditional access system can be practically broken by image processing algorithms that rearrange the lines of a eld based on statistical properties of typical TV images. With some knowledge about the limitations of the scrambling hard- ware one can reconstruct the scrambled TV image in real-time without knowledge of the cryptographic secret stored in the subscriber smart- card. Draft Technical Report $Id: nagra.tex,v 1.11 2000-10-11 11:40:53+01 mgk25 Exp $ 1 Introduction Pay-TV broadcasters employ conditional access systems to ensure that only TV viewers who have payed a subscription fee and who have in return received a decoder box can watch the TV channel. The Nagravision [1] conditional access system for PAL television developed by Kudelski SA, Cheseaux, Switzerland, is used for instance by the pay-TV broadcasters Premiere (Germany), Teleclub (Switzerland), Canal+ (France, Spain), and Cinemania (Spain). Like with other hybrid video scrambling systems such as EuroCrypt [2, 3] or VideoCrypt [4], Nagravision sends a digitally encrypted control word over the radio interface to the decoder in order to control the descrambling of an analog TV signal. The control word is decrypted in a University of Cambridge, Computer Laboratory, Pembroke Street, Cambridge CB2 3QG, United Kingdom. Email: mkuhn@acm.org M. Kuhn: Analysis of the Nagravision Video Scrambling Method 2 smartcard and converted into the seed value for a random number generator. This random number generator then controls the image descrambling process for the next few seconds. Nagravision scrambles the video signal by permuting the lines within a eld. It also inverts the audio spectrum by mixing it with a 12.8 kHz sine wave carrier to make it unrecognizable. The audio signal can trivially be descrambled by just inverting its spectrum a second time; it is not protected by any cryptographic mechanisms. Like with all hybrid scrambling systems, which digitally control the scrambling of a video signal that is transmitted in analog form, there are two di erent classes of techniques for descrambling the video signal without using a regular decoder or smartcard: Microelectronics testing equipment can be used to extract the decryption algorithm and secret key data from the smartcard and with this knowledge compatible pirate smartcards and decoders can be manufactured [5]. Properties of typical TV signals can be used to reconstruct the original image or the random number seed value that controls the descrambler which is then used to descramble the entire image in high quality [6, 7]. This technique makes it unnecessary to break the digital cryptography or smartcard security aspects of the system and it can be implemented without using any genuine decoder hardware. The rst type of attack can also be used on fully digital systems such as DVB, which encrypt an MPEG compressed TV signal. The second type of attack, on which we focus here, is not any more possible with digital conditional access systems. 2 Video Scrambling The B,G/PAL TV standard [8, 9], which is used for instance in Germany, displays 25 frames per second. Each frame is displayed as a sequence of two interlaced elds so that the screen image is updated with a rate of 50 elds per second. With B,G/PAL 15625 lines are displayed per second, which leaves 64 s per line. Around 52 s of this line interval contain active line content; the remaining time is the horizontal blanking interval, which consists of a 1.55 s front porch, a 4.7 s sync pulse and a 5.8 s back porch. Of the 15625=25 = 625 nominal lines that are transmitted per frame in 1/25 s, M. Kuhn: Analysis of the Nagravision Video Scrambling Method 3 the frame line number intervals 23{310 and 336{623 each contain the 288 = 28 +25 visible lines of one eld. In the following, we will only talk about the lines within a single visible eld and we will use eld line numbers ranging from 0 to 287 to refer to these lines. The remaining 625 − 2 288 = 49 lines of a frame do not contain a visible image signal and form the vertical blanking intervals. These are used for the vertical sync pulse and for digitally transmitted data such as videotext and control signals for conditional access systems. Nagravision scrambles the image by permuting lines within a eld. In addition, the boundaries between elds are shifted by 32 lines between the scrambled and descrambled image as Fig. 1 shows. Line 287 of any eld is not a ected by Nagravision. The last 32 lines ( eld lines 255{286) of one scrambled eld and the rst 255 lines ( eld lines 0{254) of the following eld together form a group of 287 lines that are permuted and then used together to form a single eld in the descrambled signal. The decoder sends out the rst line of the descrambled eld while the 33rd line of the scrambled eld is being received. This line scrambling can be described by a permutation function p : f0; : : : ; 286g ! f−32; : : : ; 254g which says that eld line i from the clear image appears as eld line p(i) in the scrambled signal. A negative eld line number p(i) refers to eld line number 287 + p(i) in the previous eld. The descrambling permutation p−1 : f−32; : : : ; 254g ! f0; : : : ; 286g is just the inverse function of p such that line −32 j 254 in the scrambled eld can be found as line p−1(j) in the descrambled signal. The 4.43 MHz PAL color burst signal in the back porch is not permuted. However, in the SECAM variant of Nagravision, the unmodulated 4.406 or 4.250 MHz chroma subcarrier in the back porch is permuted together with the rest of the line. Nagravision permutes the 287 lines that will form a eld in the descrambled signal by bu ering 32 lines in RAM and by writing and reading lines into and out of this bu er in a pseudo-random order. We shall refer to these 32 bu er lines as B0; : : :; B31. While eld line number i is being received, the content of bu er Bv(i) is sent out as the descrambled signal, and then bu er Bv(i) will be immediately overwritten with the signal of the incoming line. The bu er selection function v has the form v(i) = ( S(u(i)); for 0 i 254 i − 255; for 255 i 286 : Using v, we can write the descrambling permutation function as p(i) =maxfj j−32 j < i ^ v(j mod 287) = v(i)g M. Kuhn: Analysis of the Nagravision Video Scrambling Method 4 Figure 1: Example of a Nagravision scrambled image eld. or equivalently p−1(i) = minfj ji < j < 287 ^ v(j) = v(i mod 287)g: S : f0; : : : ; 255g ! f0; : : : ; 31g is a substitution table stored in non-volatile memory in the descrambler. It is constant over a long time, but it can be updated over the radio interface from time to time. The function u : f0; : : : ; 255g ! f0; : : : ; 255g depends on two parameters r 2 f0; : : : ; 255g and s 2 f0; : : : ; 127g. It has the form u(i) = (r + ti) mod 256 with t = 2s + 1: The 15-bit seed value (r; s) changes for every eld. It is calculated from the decrypted 64-bit control word that the smartcard sends to the decoder every two seconds. Since t = 2s + 1 has no common factor with 256, the function u is for all combinations of r and t a permutation on f0; : : : ; 255g. The odd numbers form a multiplicative subgroup in the set of integers modulo 256. This means that for every i 2 f1; 3; : : : ; 255g there exists exactly one inverse element i−1 2 f1; 3; : : : ; 255g such that i i−1 mod 256 = 1. With 215 = 32768 M. Kuhn: Analysis of the Nagravision Video Scrambling Method 5 possible combinations of r and t, there are 32768 di erent functions u and depending on the structure of S there are up to as many di erent functions v and p possible with a xed substitution table S. To learn more about the relationship between members of the set VS of all functions v for a xed S, we rst have a look at the structure of the set U of all 215 functions u: For any pair of functions u; u0 2 U with u(i) = (r + ti) mod 256 and u0(i) = (r0 + t0i) mod 256 there exists exactly one pair of numbers a and b such that u(a + bi) = u0(i). Proof: The numbers a = (r0 − r)t−1 and b = t0t−1 do the job, because u(a + bi) = (r + t(a + bi)) mod 256 = (r + t((r0 − r)t−1 + t0t−1i)) mod 256 = (r + (r0 − r) + t0i) mod 256 = (r0 + t0i) mod 256 = u0(i). Equivalent transformations are possible in the set VS of functions v. However, there could exist more than one pair of numbers a and b such that v(a+bi) = v0(i) for a given pair of functions v; v0 2 VS. This can happen with certain pathological substitution tables S. For instance, if S(i) = 0 for all i, then any pair (a; b) will result in v(a + bi) = v0(i) for all i. The nature of the scrambling method restricts the permutation p by the condition p(i) <i> i, and by the condition that the sequence p(0); : : : ; p(286) can be split up into 32 monotonically increasing subsequences. Each of these subsequences corresponds to the sequence of lines that were stored in one of the 32 bu ers, that is for any 0 i < j 286 with v(i) = v(j) we have p(i) < p(j). This leaves 32287−32 = 21275 possible permutations p if S is not known, compared to only 215 possible permutations if S is known. 3 Attack techniques The following techniques are based on the observation that in a typical TV image C, the correlation of two pixels drops quickly as the distance between these pixels increases. This means for instance that for two pixel luminosities Cx;y and Cx0;y0 , the average absolute di erence E(jCx;y − Cx0;y0 j) is smaller or alternatively the normalized correlation E(Cx;yCx0;y0)= q E(C2 x;y)E(C2 x0;y0) is larger if the two pixels are direct neighbors than if they are many lines apart. The permuted lines can be sorted back into an arrangement close to their original order just by rearranging them in a way that maximizes the similarity (correlation) between neighbor lines. M. Kuhn: Analysis of the Nagravision Video Scrambling Method 6 3.1 Reconstructing the Permutation Let Cx;y be the luminosity or even the whole three-dimensional color vector of the pixel (x,y) in the scrambled eld, where as before negative line numbers refer to pixels in the preceding eld. Then the matrix K 2 IR288288 shall be the correlation matrix for a eld, de ned as Ki;j = P qP k Ck;i−33Ck;j−33 k jCk;i−33j2 P k jCk;j−33j2 : Ki;j is a measure for the similarity of lines i − 33 and j − 33. Obviously Ki;j = Kj;i and Ki;i = 1, therefore we only have to determine Ki;j for all 1 i < j 288. Exchanging two lines i − 33 and j − 33 in the image C corresponds in K to swapping the contents of the lines i and j, plus swapping the columns i and j. The goal of rearranging the lines of C to form the original image corresponds to permuting lines and columns in K to bring the largest values as close as possible to the diagonal, so that we maximize the value of a pro t function such as G(K) = X287 i=1 Ki;i+1: This corresponds to nding the permutation matrix P that maximizes the value G(PKPT). P relates to the permutation p that we want to reconstruct by Pp(i)+33;i = 1 for all i and all other Pi;j are zero. In an alternative formulation of the same problem, we look at an undirected graph GK with nodes Ni (−32 i 254), of which each corresponds to a eld line i in the scrambled image. The edge connecting Ni and Nj in this graph has the value Ki+33;j+33 for all i and j. We then look for a Hamiltonian path (i.e., a path that visits all nodes exactly once) of the form Np(0); : : :;Np(287), that ful ls the previously stated conditions for p and whose sum of edge labels is maximal. Finding such a path is a variant of the Traveling Salesman Problem [10, 11], which unfortunately is known to be NPcomplete, although there exist a number of useful approximation algorithms. 3.2 Reconstructing the Substitution Table One possible way of determining S is to reverse engineer a Nagravision decoder and read the entire table out of its non-volatile memory. Since this procedure might be illegal in some regions, alternative approaches might be M. Kuhn: Analysis of the Nagravision Video Scrambling Method 7 attempted. A logic analyzer can be used to just observe the sequence of accesses to the line bu ers Bi, which results in a large recorded collection of functions v 2 VS. If we assume that opening the decoder is also not acceptable for legal reasons, we can use a PC video adapter to perform a chosen cipher image attack in which we send to the decoder a test image that contains genuine encrypted control word information in the vertical blank interval and that uses a redundant binary code to mark every line with its eld line number. We record the descrambled test image and by reading the sequence of line number markers in there, we get the permutation p. If no access to a Nagravision decoder at all is allowed or possible, we can also attempt to use one of the Traveling Salesman approximation algorithms to determine samples of p from the correlation matrix of scrambled TV images alone as described in the previous section. In both cases, we have to transform the observed permutations p into bu er access functions v before we can extract S. This can be accomplished with the following simple algorithm, provided that the given p is error-free: We set bi := i − 32 for all 0 i 31. Then for each line 0 j 254 that the decoder outputs, we nd the i for which bi = p(j) and we set both v(j) := i and bi := j. As a nal check, we verify that after these 255 steps we have bi = p(255 + i) for all 0 i 31. In this way, we collect a number of members of VS. Any of these reconstructed functions v(i) = S((r + ti) mod 256) for 0 i 254 shows all values of S except for one, but permuted by unknown parameters r and t. We just pick one v and chose our reconstructed table ~ S such that ~ S(i) := v(i) for all 0 i 254. We then reconstruct another bu er access function v0 and search for parameters a and b such that v0((a + bi) mod 256) = ~ S(i) for 0 i 254 and once we found these (assuming we didn't by bad luck get some with (a + b 255) mod 256 = 255), we have also found the remaining value of ~ S with ~ S(255) = v0((a + b 255) mod 256). We are not concerned about the fact that our ~ S is just a permuted version of S, because if ~ S(i) = S((a+bi) mod 256) for some (a; b) then this means that in the correlation search for the correct parameters (r; t) that follows now, we just nd instead parameters (~r; ~t) that compensate exactly this permutation of ~ S and result in the same v that we would have obtained with the correct table S and parameters (r; t). M. Kuhn: Analysis of the Nagravision Video Scrambling Method 8 3.3 Realtime Determination of the Permutation Based on a Known Substitution Table 3.3.1 Using Pixel Correlations Once we know S either by extracting it from a Nagravision decoder or by determining it as outlined in the previous section, we can reverse the scrambling rather eciently. A simple approach as implemented for instance in [12] is to perform a brute force search over all 215 possible (r; t) tuples. For every possible (r; t) pair, the value of a penalty function is estimated by measuring the di erence jCx;p(y)−Cx;p(y+1)j between a small number of randomly selected selected pixel pairs in the scrambled image that would under the tested (r; t) become neighbor pixels in the descrambled image. This can be implemented very eciently since the permutation has to be performed only for the few test pixels and not for the entire image. We search for the (r; t) pair, for which the penalty function H = Xn i=1 jCxi;p(yi) − Cxi;p(yi+1)j is minimal. The (p(yi); p(yi + 1)) pairs are precalculated for all 215 (r; t) pairs for increased eciency. Once this (r; t) pair has been identi ed, the corresponding permutation function is used to rearrange all lines in realtime. A potentially much more ecient approach could be a binary subdivision search instead of a linear search over all 215 possible (r; t) tuples. To implement this, we need a preparatory phase in which for a given substitution table S we build a binary decision tree. Each node in this decision tree lists a number of test pixel coordinates (xi; yi) and we branch to the left or the right subtree depending on whether H for these test pixels is above or below a threshold. Each leave of this tree is labeled with the (r; t) tuple that shall be used as the most likely candidate. A carefully built decision tree should be roughly balanced such that the maximum depth is not much over 15. 3.3.2 Using the SECAM Color Carrier For Nagravision scrambled SECAM signals, there exists a simple alternative to looking at pixel luminosity correlations. In SECAM, color is encoded on a frequency modulated carrier in form of the two di erence signals R−Y (red minus luminance) and B −Y (blue minus luminance) [8, 9]. The modulated R − Y and B − Y signals are added on alternating lines, where R − Y uses M. Kuhn: Analysis of the Nagravision Video Scrambling Method 9 a 4:406 MHz = 282 15:625 kHz carrier and B −Y uses a 4:250 MHz = 272 15:625 kHz carrier to allow the TV receiver to synchronize its color decoder. The unmodulated color carrier signal is present on the front and back porch in the horizontal blanking interval and since it is permuted together with the active line, it is easy to see whether a scrambled line is in the descrambled eld an odd or even numbered line. The sequence of 4.406 MHz and 4.250 MHz color carrier frequencies in the back porch of a scrambled SECAM signal is characteristic for the (r; t) pair that has been used to scramble this eld. A pirate decoder only has to form a bit string representing the sequence of carrier frequencies found in the back porches of the lines 255{286 and use this bit string as the key in a hash-table lookup to access the (r; t) pair that descrambles this sequence correctly into one with alternating carrier frequencies. This (r; t) pair is then used to descramble the remaining eld correctly. Commercial hardware implementations of this attack became available in France around 1995 [13]. As a counter measure, the broadcaster Canal+ uploaded a new substitution table S that ensures that the sequence of the color carrier frequencies is always alternating and therefore does not leak information about the (r; t) pair. An improved version of the attack looks not only at the frequency but also at the phase of the color carrier in the back porch. The SECAM color carrier is phase shifted by 180 for every third line to suppress visible dot patterns caused by the carrier signal. Again, a bit sequence that indicates which of the rst 32 lines shows this phase shift acts as a hash-table lookup key to nd the appropriate (r; t) pair quickly. Since the PAL color burst is not permuted, the SECAM color carrier attack technique cannot directly be transferred to Nagravision for PAL. However, with the continuing introduction of the EBU Wide Screen Signal (WSS) in frame line 23 [14], the rst line in every second clear eld often has an easily recognizeable known structure. If theWSS line can be located in line w of the scrambled eld, then we know that 0 > p(0) = w and v(0) = w +32 = S®, which reduces the number of possible r values from 256 down to around 8 and speeds up the (r; t) search by a factor of 32. 4 Properties of the Substitution Table The substitution table S used by the broadcasters Premiere, Teleclub and many others until today has the form 10, 11, 12, 13, 16, 17, 18, 19, 13, 14, 15, 16, 0, 1, 2, 3, M. Kuhn: Analysis of the Nagravision Video Scrambling Method 10 21, 22, 23, 24, 18, 19, 20, 21, 23, 24, 25, 26, 26, 27, 28, 29, 19, 20, 21, 22, 11, 12, 13, 14, 28, 29, 30, 31, 4, 5, 6, 7, 22, 23, 24, 25, 5, 6, 7, 8, 31, 0, 1, 2, 27, 28, 29, 30, 3, 4, 5, 6, 8, 9, 10, 11, 14, 15, 16, 17, 25, 26, 27, 28, 15, 16, 17, 18, 7, 8, 9, 10, 17, 18, 19, 20, 29, 30, 31, 0, 24, 25, 26, 27, 20, 21, 22, 23, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 15, 9, 10, 11, 12, 2, 3, 4, 5, 30, 31, 0, 1, 24, 25, 26, 27, 2, 3, 4, 5, 31, 0, 1, 2, 7, 8, 9, 10, 13, 14, 15, 16, 26, 27, 28, 29, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 5, 6, 7, 8, 19, 20, 21, 22, 12, 13, 14, 15, 17, 18, 19, 20, 27, 28, 29, 30, 10, 11, 12, 13, 11, 12, 13, 14, 6, 7, 8, 9, 1, 2, 3, 4, 0, 1, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 8, 9, 10, 11, 15, 16, 17, 18, 23, 24, 25, 26, 29, 30, 31, 0, 25, 26, 27, 28, 9, 10, 11, 12, 21, 22, 23, 24, 20, 21, 22, 23, 30, 31, 0, 1, 16, 17, 18, 19, 28, 29, 30, 31 This particular table has the curious property S(i) = (S(i − i mod 4) + i mod 4) mod 32; but it is not clear what the reason behind this is. The broadcaster Canal+ in France replaced the above table in September 1997 with the following one, as a response to the availability of unauthorized Nagravision for SECAM decoders that reconstructed the (r; t) pair from the sequence of the color carrier frequencies in the scrambled image: 0, 1, 2, 3, 4, 5, 6, 7, 2, 5, 4, 7, 8, 9, 10, 11, 14, 17, 16, 19, 22, 25, 24, 27, 28, 31, 30, 1, 24, 27, 26, 29, 8, 11, 10, 13, 20, 23, 22, 25, 20, 21, 22, 23, 30, 31, 0, 1, 16, 17, 18, 19, 28, 29, 30, 31, 10, 11, 12, 13, 16, 17, 18, 19, 12, 15, 14, 17, 0, 1, 2, 3, 20, 23, 22, 25, 18, 19, 20, 21, 22, 25, 24, 27, 26, 27, 28, 29, 18, 21, 20, 23, 10, 13, 12, 15, 28, 29, 30, 31, 4, 5, 6, 7, 22, 23, 24, 25, 4, 7, 6, 9, 30, 1, 0, 3, 26, 29, 28, 31, 2, 5, 4, 7, 8, 9, 10, 11, 14, 15, 16, 17, 24, 27, 26, 29, 14, 17, 16, 19, 6, 9, 8, 11, 16, 19, 18, 21, 28, 31, 30, 1, 24, 25, 26, 27, 20, 21, 22, 23, 0, 3, 2, 5, 6, 7, 8, 9, 12, 13, 14, 15, 8, 11, 10, 13, 2, 3, 4, 5, 30, 31, 0, 1, 24, 25, 26, 27, 2, 3, 4, 5, 30, 1, 0, 3, 6, 9, 8, 11, 12, 15, 14, 17, 26, 27, 28, 29, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 4, 7, 6, 9, 18, 21, 20, 23, 12, 13, 14, 15, 16, 19, 18, 21, 26, 29, 28, 31, 10, 11, 12, 13, 10, 13, 12, 15, 6, 7, 8, 9, 0, 3, 2, 5 M. Kuhn: Analysis of the Nagravision Video Scrambling Method 11 This new table has the property S(i) i (mod 2). This way, the resulting permutation always alternates between odd and even numbered lines and the sequence of color subcarrier frequencies in a scrambled SECAM image can only reveal the value r mod 2 and not the complete r and t values. If S were selected such that i 6 j (mod 6) =) S(i) 6= S(j); then even the combination of color carrier phase and frequency, which is repeated every six lines in the clear signal, could only reveal r mod 6 and t mod 3. Apparently the Canal+ or Kudelski technicians who designed the above countermeasure table failed to understand the threat of a color carrier phase analysis at that time. 5 Conclusion and Final Remarks Nagravision uses a surprisingly weak scrambling technique that can rather easily be defeated without using any cryptographic secrets that might be stored in the subscriber smartcard. While image processing attacks can only approximate the original signal for cryptographic scrambling systems such as VideoCrypt and EuroCrypt, Nagravision allows the attacker to determine reliably the seed value in such a short time that the clear image can be reconstructed without any quality loss in real time using standard personal computers or decoder designs that cost not much more than the ocial decoder. The color-carrier sensing pirate decoders for the SECAM version of Nagravision can easily be defeated by a more carefully designed substitution table. Whether lasting countermeasures are possible against pixel-correlation based pirate decoders depends on whether the broadcasters can upgrade the elded decoders easily to use a larger set of permutation parameters than 215 and whether v can be replaced by a cryptographically strong cipher function. This paper is work in progress and might still contain errors. I started writing it in order to get a better understanding of the mathematical properties of the Nagravision scrambling method and the algorithms used in the various currently available pirate decoders. These have been designed by individuals who want to stay anonymous because they are afraid that the work on these decoders might be considered illegal in their home country (France). I also wrote this paper to collect and discuss possibly useful ideas and insights towards more advanced attacks and countermeasures. Since the Nagravision system is anyway scheduled to be replaced by a DVB conditional access M. Kuhn: Analysis of the Nagravision Video Scrambling Method 12 system, I do not think that publishing my thoughts on the topic can do any economic harm, but I hope they might be of some educational bene t. Special thanks to Fabian Petitcolas, Roberto Deza Asensio, and \Zorglub" for comments on the paper and to Ralph Metzler for providing frame-grabber images for experiments. Suggestions for improving this text are very welcome. References [1] Andre Kudelski. Method for scrambling and unscrambling a video signal. United States Patent 5375168, 20 December 1994. [2] Access control system for the MAC/packet family: EUROCRYPT. European Standard EN 50094, CENELEC, December 1992. [3] Vincent Lenoir. EUROCRYPT, a successful conditional access system. IEEE Transactions on Consumer Electronics, 37(3):432{436, August 1991. [4] Michael Cohen and Jonathan Hashkes. A system for controlling access to broadcast transmissions. European Patent Application 0 428 252 A2, 22 May 1991. [5] Ross J. Anderson and Markus G. Kuhn. Tamper resistance { a cautionary note. In The Second USENIX Workshop on Electronic Commerce Proceedings, pages 1{11, Oakland, California, 18{21 November 1996. [6] V. Mangulis. Security of a popular scrambling scheme for TV pictures. RCA Review, 41(3):423{432, September 1980. [7] D. Raychaudhuri and L. Schi . Unauthorized descrambling of a random line inversion scrambled TV signal. IEEE Transactions on Communi- cations, 31(6):816{821, June 1983. [8] Television systems. ITU-R Recommendation BT.470, International Telecommunication Union, Geneva. [9] Jim Slater. Modern Television Systems { to HDTV and beyond. Pitman, London, 1991. [10] Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Intro- duction to Algorithms. MIT Press, 1990. M. Kuhn: Analysis of the Nagravision Video Scrambling Method 13 [11] Eugene L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, and D.B. Shmoys. The Traveling Salesman Problem. John Wiley & Sons, 1985. [12] \Gaston". NagraTV 2.0. Internet http://eurosat.com/salp/gaston/, June 1998. Linux open source software in C. [13] \Zorglub". La page technique du Nagravision [The Nagravision technology page]. Internet http://eurosat.com/salp/zorglub/, 1998. (in French). [14] Television systems; 625-line television Wide Screen Signaling (WSS). ETS 300 294, ETSI, Sophia Antipolis, September 1997. [15] John McCormac. European Scrambling Systems 5 { The Black Book. Waterford University Press, 1996. ISBN 1-873556-22-5. [16] V. Zacharopouloulos, Ch. Mantakas, K. Dagakis, and C. Caroubalos. An analogue scrambling scheme for television signals. International Journal of Electronics, 59(4):501{509, October 1985. |
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Silver Member Username: KirankumarKenya Post Number: 538 Registered: Oct-07 | kaka, this is tooooooo much information for me after 6 beers.Happy new year to you |
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Bronze Member Username: Sparky41701Chavies, Ky Usa Post Number: 77 Registered: Jun-06 | what does it mean |
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Bronze Member Username: Leo_herePost Number: 18 Registered: May-06 | And your point is... |
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Silver Member Username: Espn3Post Number: 213 Registered: Aug-06 | karkour kaka, very good writting. Glad to see that the huge majority of people on this forum write only when they have something good related to FTA. CHEERS, 2008 !! |
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Bronze Member Username: BernardmiPost Number: 32 Registered: Dec-07 | It would have been simpler to say: A very good analysis of the Nagravision Video Scrambling Method can be seen here: |
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Silver Member Username: Guanajuatos_bestPost Number: 120 Registered: Jul-07 | me sorry. me not amerikan canot read inglish. tu much wurds |