Revision $Id: md5-analysis-prehash.base,v 1.5 2006/09/09 18:54:25 klm Exp $ Purpose The purpose of this analysis was to examine the advantages, if any, of prehashing the leading portion of a data stream when that portion is found to be fixed or relatively fixed. More specifically, this analysis focused on data streams that can be broken into two consecutive sub-streams where the first sub-stream is fixed or relatively fixed (i.e., easily inferred/guessed) and the second sub-stream is unpredictable (random) or hard to guess/infer (pseudo-random). While the observations and findings of this study were limited to the MD5 algorithm, it is likely that they would apply to all hashing techniques in general. Motivation The driving force behind this analysis was the desire to find faster ways to compute MD5 hashes for data streams that meet the prehashing criteria described above. Background Session IDs are popular components of web applications. Often, these IDs appear to be random at first glance, but closer inspection often reveals that they fall short of that mark. In many cases these IDs can be partially or completely predicted. One technique used to create a session ID is to compute the message digest (or hash) of a given stream of data. Typically, a number of variables such as username, realm, IP address, requested resource, time, shared secrets, nonces, etc. are concatenated together, and the resulting data stream is hashed using an algorithm such as MD5. The hash is then passed back to the browser as a cookie or hidden value. Any future requests from the same browser that include this session ID can easily be validated by the server. The belief being that because session IDs are computationally hard to guess (i.e., brute force attacks would not, in general, be practical), only an authenticated browser would be able to supply the real session ID within the window of time (usually minutes to hours) deemed to be valid. Analysis To characterize the behavior of the MD5 algorithm under various scenarios, a test program was created (see Appendix 1). This program was designed to record the amount of time it takes to compute a specified number of hashes over a given data stream. This program computes hashes using two different techniques: normal (or straight) and prehash (or shortcut). In normal mode, the hash is computed over the entire data stream N times. In prehash mode, a partial hash is computed over the first substream (the prefix); the MD5 context of that operation is saved and subsequently used to seed the MD5 context of the second substream (the suffix); finally, the second substream is hashed N times. In both cases the message, prefix length, and N are specified at run time. The test program was used to answer the following question: How does the time required to compute one million hashes of a 1024-byte data stream consisting of all A's behave as a function of the prefix length [0-1024] with and without prehashing enabled? All testing was conducted on a FreeBSD 6.0 system with an AMD Athlon XP 3000+ (2162.74-MHz) CPU. The test procedure used is described here: 1. Compile the test program. The source code for this program is provided in analysis.tgz.uu, which is located in Appendix 1. gcc -o md5-analysis-prehash md5-analysis-prehash.c -lmd -O2 2. Compute one million hashes with prehashing disabled over a fixed 1024 by message stream using a sliding prefix that ranges from 0 to 1024. for i in `perl -e 'foreach $i (0..1024) { print "$i\n"; }'` ; do ./md5-analysis-prehash -n 1000000 -o ${i} -s `perl -e 'print "A"x1024;'` >> md5-analysis-prehash-1024-As-straight.data ; done 3. Repeat Step 2 with prehashing enabled. for i in `perl -e 'foreach $i (0..1024) { print "$i\n"; }'` ; do ./md5-analysis-prehash -n 1000000 -o ${i} -s `perl -e 'print "A"x1024;'` -p >> md5-analysis-prehash-1024-As-shortcut.data ; done Once the testing was complete, the results were processed with the following commands: awk -F \| '{print $6"\t"$7}' md5-analysis-prehash-1024-As-straight.data > md5-analysis-prehash-1024-As-straight.plot awk -F \| '{print $6"\t"$7}' md5-analysis-prehash-1024-As-shortcut.data > md5-analysis-prehash-1024-As-shortcut.plot Then, a graph was constructed using the following gnuplot script: gnuplot << EOF set terminal png set output 'md5-analysis-prehash-1024-As.png' set key on top right box set title "MD5 Computation Comparisons - MD5(FixedPrefix+VariableSuffix)" set grid set yrange [0:6] set xlabel "Fixed Prefix Length (bytes)" set ylabel "Time to compute 1,000,000 hashes (seconds)" set xtics 64 set ytics 0.5 set style data steps plot 'md5-analysis-prehash-1024-As-straight.plot' using 1:2 title 'straight method', 'md5-analysis-prehash-1024-As-shortcut.plot' using 1:2 title 'shortcut method' quit EOF The .data, .plot, and .png files generated by the author are provided in analysis.tgz.uu, which is located in Appendix 1. Note: You can compute your own results by executing the commands provided in Steps 2-3 above, or you can run the following wrapper command, which has been provided in analysis.tgz.uu: md5-analysis-wrapper Observations Computation times for the straight method appear to remain constant as a function of the prefix length. This result was expected since the straight method hashes the entire message each time through its internal loop. Computation times for the shortcut method appear to decrease linearly with steps at 64-byte intervals as a function of the prefix length. This result was not surprising since the shortcut method only hashes the suffix each time through its internal loop -- the prefix is only hashed once. Conclusions 1. The results depicted in the graph clearly show that prehashing can significantly reduce the time required to compute one million hashes when the prefix length exceeds 64 bytes. When the prefix reaches 1020 bytes, the performance gain is roughly 6:1. 2. There is no apparent benefit to the shortcut method until the prefix length exceeds 64 bytes. 3. Based on the results, the approximate time required for one machine to compute all possible hashes of a 1020-byte fixed prefix plus a 4-byte random suffix would be 3,841 and 23,345 seconds for the shortcut and straight methods, respectively. The calculations that produced those numbers are shown here: shortcut: From the data we know that 1,000,000 computations for offset 1020 took 0.894215 seconds. Therefore, the amount of time (in seconds) required to try 2^32 suffixes is: (2 ^ 32 ) / ( 1000000 / 0.894215 ) = 3840.624181 straight: From the data we know that 1,000,000 computations for offset 1020 took 5.435432 seconds. Therefore, the amount of time (in seconds) required to try 2^32 suffixes is: (2 ^ 32 ) / ( 1000000 / 5.435432 ) = 23345.002680 Therefore, a session ID (of this kind) could be cracked by 5 machines in less than 15 minutes using the shortcut method. This does not account for the time required to try each session ID. 4. Placing the random/variable part of the message at or near the beginning of the data stream would neutralize the shortcut method described in this document. 5. Increasing the length of the fixed portion of the data stream would not neutralize the shortcut method if the extra information was easily inferred/guessed and part of the prefix. Credits This analysis was conducted by Klayton Monroe. References None Appendix 1 Extract the attached uuencoded, gzip'd tarball with: $ sed -e '1,/^--- analysis.tgz.uu ---$/d; /^--- analysis.tgz.uu ---$/,$d' md5-analysis-prehash.txt > analysis.tgz.uu $ uudecode analysis.tgz.uu $ tar -zxf analysis.tgz If you don't have uudecode on your system, try the following: $ perl -ne 'next if (/^begin/); last if (/^end/); chomp; print unpack("u",$_);' < analysis.tgz.uu > analysis.tgz --- analysis.tgz.uu --- begin 644 analysis.tgz M'XL(`/U?`T4``^R]Z\YL.7(=V'_S>XIZ@2KS$A?RIQ^EK!:F!;=DH:LU@(%^ M^%EQV:FQYI3LSRL]@#%S@.XZ/)D9.S897(S@(B-^_:=?__Q??_N'W_[PO_#/ M&,-5?XK_3I'_YK_/GY_FT#%,W5U_&G.M;7_X2?]7*O7\^9??_OKK7Z#*?_[S M/_Z[W_OO?=[O\?[O_R9_?NWQ_P__^$?]^6G\_,]_^?L__?K;GWZ>8\G/__&W MGW_[TW_YRU__[E_^^LL??_WKK]]^!OK#_LVX_^OXKZ5NAO%?/MW6P-_'FK[F M'WX:_PO>]__QY__CX_]'\?\TE_^GOUM__/OU1SO^QS_^W5E__/7OMLK?R=2_ M_=.O?_V'__/O__98P-]FO>#?PC3^-OZFO\C!<-XO3M`,02;[;E+0"D%WV3)2 MT`Y!+CJ5%"0IZ`[ZU30[6X\?4I!59Z_#"O(4I$8/_\E7.\N$%'13HVL^68,, MT]Y7@4^LI+#M;;8VV]TSC'OK&8NUR;GS[:;/P4H*\]Z^==+]%/:]S]Y.2[+4 M"?9$]Y/GV(ELUC#GR;=3%;K';[Z=G,7.NC7*GG0[*REM_&*RL&.WTL9MGT&O M!&GC;KYH267C5VC+7&GCY@`H5E+9^(5KQ4I*&S_#:1M?:>-VSV#GW;H]=LJ. 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