Crypto Lab 2011: Code Challenge Website - Report (v1.0)

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1 Crypto Lab 2011: Code Challenge Website - Report (v1.0) Marius Hansen and Daniel Quanz {hansen_m,quanz}@rbg.informatik.tu-darmstadt.de 1 Features / Use Cases First we create a list with our features. Using these features we create use cases. 1.1 Features The features below are listed in descending order of importance: Creation of random challenges / binary r n matrices a 1,1 a 1,2 a 1,n H r n a 2,1 a 2,2 a 2,n =......, a i,j = P RNG(seed) {0, 1} a r,1 a r,2 a r,n r - number of rows n - number of columns seed - a random value to initialize the pseudorandom number generator (PRNG) Verification of a solution We want to verify H r n e = 0 t 1.1 GV (n, k, q) q := 2, k := n r, n k H - a given binary r n matrix e - a solution vector F n 2 t - number of errors - weight(e) 1.1 GV (n, k, q) - Gilbert-Varshamov bound + 10% tolerance Definition: (q-ary Gilbert-Varshamov bound). Let C be an (n, k, t) code over F q, and let r := n k. The q-ary GV bound is the smallest integer t 0 such that t 0 ( ) n (q 1) i q r i i=0

2 2 Crypto Lab 2011 For large values of n, the last term dominates the sum, so the condition is often approximated by ( ) n (q 1) t0 q r t 0 If the number of errors that have to be corrected is smaller than the GV bound, then there is at most one solution. Otherwise, there can be several solutions. [2] Algorithm 1 Calculate H e = 0 (column-wise multiplication ([3, p. 6]) Require: H r n {a i,j 1 i r, 1 j n, a i,j {0, 1}} Require: e F n 2 result (0,..., 0) r for j = 1 n do if e j = 1 then for i = 1 r do result i result i a i,j end for end if end for return result Submission of a solution The actor should use a form to submit his solution. He has to input his name, his -address, his solution and a description how he has solved this challenge. Each challenge has its own submission form. Listing of solutions in a Hall of Fame If the actor has submited a solution, he will listed in the Hall of Fame list. It is not possible to submit a duplicate solution. Notification system This feature is needed to inform the website administrator. The admin will be notified if the Hall of Fame is changed. It is possible to notify several people. 1.2 Use Cases Figure 1 shows a short overview of all actions of the code challenge website. 2 Implementation In this lab we decided to use Ruby on Rails (RoR), an open source web application framework for the Ruby programming language. In [1] you find a nice step-by-step tutorial to create RoR projects.

3 Crypto Lab Fig. 1. Code Challenge Website Use Cases 2.1 Basics Each RoR - project is structured as follows: app includes the RoR application app/controllers includes the application controllers (MVC) app/helpers includes application helpers app/mailers includes application mailers app/models includes application models (MVC) app/views includes application views (MVC) config includes the RoR application config files db includes the application databases and migration files doc includes the application documentation log includes application logs for each environment public includes the application public files (CSS, Javascript, images) test includes tests of the RoR application 2.2 Database The user input is stored in a sqlite3 database. For this application we need two different tables. Figure 2 shows the relation of these two tables.

4 4 Crypto Lab 2011 Fig. 2. DB relationship Challenge r n seed bound created at updated at Solution e t name mail description challenge id created at updated at number of rows of a binary matrix H number of columns of a binary matrix H input for a PRNG to create a random binary matrix H value of the GV bound of H Creation date date of the last update solution vector weight of solution vector name of solver address of solver Description, how to solve the solution foreign key to challenge Creation date date of the last update 2.3 Creation of random challenges / matrices To create a new challenge we need a random binary r n matrix H. The user has to input to positve integeres r and n, such that r n. These values will be saved in the Challenge -SQLite3-table. In addition the Gilbert-Varshamov (GV) bound will be computed and the seed will be defined. (Lines: 5-6 in Listing 1.1). In line 62ff you find the implementaion of th GV-bound computing. The binary matrix is not created yet. It will be generated, if the user wants to download it. The file that stores the matrix is created temporarily to save memory.

5 Crypto Lab Download a challenge The challenge downlod is implemented in listing 1.2 (14-36). First we read the needed attributes (r, n, seed) from the database. Then we create a temporary file. In this file we write the generated binary matrix. 2.5 Verification of a solution The feature Verification of a solution is implemented in Listing 1.3. First we validate the user input. The user has to input his name (line 6), his address (line 7) and a valid solution vector. A solution vector must be unique for a challenge (line 8), must be a binary string (line 9), the weight of the solution vector must be lower or equal the GV bound of the challenge matrix (line 10) and finally the multiplication H r n e must be zero. (line 11) 2.6 Pages and links of the website Home This one is the welcome page. There you find the rules and how you can participate. You can also find the TOP 5 of the Hall-of-Fame List. <url-to-website>/home Hall of Fame You can find the whole high score list. <url-to-website>/halloffame Create a Challenge On this page the user is able to create a new challenge. <url-to-website>/generate Available Challenges You can find a list of available challenges to download them. <url-to-website>/challenges Download challenge < CID > You can find a list of available challenges to download them. <url-to-website>/challenges/<cid> Submit a solution for challenge < CID > You can find a list of available challenges to download them. <url-to-website>/challenges/<cid>/solutions/new Show solution < SID > for challenge < CID > You can find a list of available challenges to download them. <url-to-website>/challenges/<cid>/solutions/<sid> 2.7 Configuration You find the configuration file of the webpage in config/config.yml The table below lists the config attributes. Each attribute is stored in the APP CONFIG[] - array.

6 6 Crypto Lab 2011 attribute challenge gvbound tolerance challenge max columns challenge download name prefix challenges per page home highscore number highscore per page notifier mail from notifier mail to notifier mail subject Description GV bound tolerance in percent (here 10) the number of the max n a prefix name for the challenge file number of challenges to be listed per page number of hall of fame entries on the welcome page number of solutions per page in the hall of fame notification from: mail-address notify to: mail-address notifier mail subject References 1. M. Hartl. Ruby on Rails 3 Tutorial Livelessons Bundle: Learn Rails by Example. LiveLessons Series. ADDISON WESLEY (PEAR, Robert Niebuhr, Pierre-Louis Cayrel, Stanislav Bulygin, and Johannes Buchmann. On lower bounds for Information Set Decoding over Fq. informatik.tu-darmstadt.de/~rniebuhr/publications/isd-fq.pdf. 3. Falko Strenzke. How to implement the public key operations in code-based cryptography on how to implement the public key operations in code-based cryptography on memory-constrained devices. eprint.iacr.org/2010/465.pdf, A Implementation listings 1 #/ 2 # Model f o r c h a l l e n g e 3 # 4 Marius Hansen, Daniel Quanz 5 # / 6 7 class Challenge < ActiveRecord : : Base 8 9 has many : s o l u t i o n s v a l i d a t e s n u m e r i c a l i t y o f : r, : a l l o w n i l => false, : g r e a t e r t h a n o r e q u a l t o => 1, : l e s s t h a n o r e q u a l t o => : n, : o n l y i n t e g e r => true 12 v a l i d a t e s n u m e r i c a l i t y o f : n, : a l l o w n i l => false, : g r e a t e r t h a n o r e q u a l t o => 1, : l e s s t h a n o r e q u a l t o => APP CONFIG[ challenge max columns ], : o n l y i n t e g e r => true

7 Crypto Lab b e f o r e s a v e ( : on => : c r e a t e ) do 15 s e l f. seed = Time. now 16 s e l f. bound = getgvt ( s e l f. n, s e l f. n s e l f. r ) 17 end def seed 20 return r e a d a t t r i b u t e ( : seed ) 21 end def r 24 return r e a d a t t r i b u t e ( : r ) 25 end def n 28 return r e a d a t t r i b u t e ( : n ) 29 end def bound 32 return r e a d a t t r i b u t e ( : bound ) 33 end p r i v a t e #/ 38 # simple compution o f f a c t o r i a l 39 # / 40 def f a c t ( n ) 41 return n==0? 1 : ( 1.. n ). i n j e c t ( : ) 42 end #/ 45 # compution o f binomial c o e f f i c i e n t 46 # / 47 def binom (n, k ) 48 return ( n==k k==0)? 1 : f a c t ( n ) / ( f a c t (n k ) f a c t ( k ) ) 49 end #/ 52 # q ary G i l b e r t Varshamov bound // updated to 2 ary 53 # 54 # # Paper : On lower bounds f o r Information Set Decoding over Fq 57 # by : Robert Niebuhr (1), Pierre Louis Cayrel (2), S t a n i s l a v Bulygin (2), and Johannes Buchmann (1, 2 ) 58 # (1) TU Darmstadt Fachbereich I n f o r m a t i k Kryptographie und Computeralgebra

8 8 Crypto Lab # (2) CASED Center f o r Advanced S e c u r i t y Research Darmstadt 60 # 61 # / 62 def getgvt (n, k ) 63 i f ( k==1) 64 return n/2 65 end 66 qr = 2 << ( n k 1) 67 s t e p = 2 << ( ( n /2). t o s ( 2 ). l e n g t h 1) 68 l a s t = 1 69 while s t e p!= 1 do 70 tempd = l a s t 71 while getgvtlargen ( n, tempd ) < qr && tempd<n do 72 l a s t = tempd 73 i f tempd+s t e p <= n 74 tempd+=s t e p 75 else 76 tempd=n 77 end 78 end 79 step >>=1 80 end while getgvtsmalln ( n, tempd ) >= qr do 83 tempd =1 84 end 85 return tempd+1 86 end def getgvtlargen ( n, tempd ) 89 return binom ( n, tempd ) 90 end def getgvtsmalln ( n, tempd ) 93 return ( 0.. tempd ). map{ i binom (n, i ) }. i n j e c t (:+) 94 end 95 end Listing 1.1. Challenge model 1 r e q u i r e t e m p f i l e 2 3 class C h a l l e n g e s C o n t r o l l e r < A p p l i c a t i o n C o n t r o l l e r 4 # GET / c h a l l e n g e s 5 # GET / c h a l l e n g e s. xml 6 def index = Challenge. paginate ( : page => params [ : page ], : per page => APP CONFIG[ c h a l l e n g e s p e r p a g e ], : order => c r e a t e d a t DESC )

9 Crypto Lab r e s p o n d t o do format 10 format. html # index. html. erb 11 end 12 end def show = Challenge. f i n d ( params [ : id ] ) 16 prng = Random. new seed ) f i l e = Tempfile. new ( c h a l l e n g e ) data = #{@challenge. r. t o s }\n#{@challenge. n. t o s }\n\n 21 f i l e. w r i t e ( data ) 22 for i in r 23 data n. times. map{ prng. rand ( ) } 24 f i l e. w r i t e ( #{data. j o i n }\n ) 25 end s e n d f i l e f i l e, : f i l e n a m e => #{APP CONFIG[ c h a l l e n g e d o w n l o a d n a m e p r e f i x ] } ID#{params [ : id ] } r } #{@challenge. n }. t x t f i l e. c l o s e 32 f i l e. u n l ink 33 r e s p o n d t o do format 34 format. html { r e d i r e c t t o ( c h a l l e n g e s p a t h ) } 35 return 36 end 37 end # GET / c h a l l e n g e s /new 40 # GET / c h a l l e n g e s /new. xml 41 def new = Challenge. new r e s p o n d t o do format 45 format. html # new. html. erb 46 end 47 end # POST / c h a l l e n g e s 50 # POST / c h a l l e n g e s. xml 51 def c r e a t e = Challenge. new ( params [ : c h a l l e n g e ] ) r e s p o n d t o do format 55 i save

10 10 Crypto Lab format. html { r e d i r e c t t o ( c h a l l e n g e s p a t h, : n o t i c e => You c r e a t e d a new binary #{@challenge. r } x n} matrix ( ID : #{@challenge. i d }). Download i t #{v i e w c o n t e x t. l i n k t o ( ) }.. h t m l s a f e ) } 58 else 59 format. html { render : a c t i o n => new } 60 end 61 end 62 end # DELETE / c h a l l e n g e s /1 65 # DELETE / c h a l l e n g e s /1. xml 66 def d e s t r o y = Challenge. f i n d ( params [ : id ] ) d e s t r o y r e s p o n d t o do format 71 format. html { r e d i r e c t t o ( c h a l l e n g e s u r l ) } 72 end 73 end 74 end Listing 1.2. Challenge Controller 1 class S o l u t i o n < ActiveRecord : : Base 2 3 b e l o n g s t o : c h a l l e n g e 4 5 ## no d u p l i c a t e s o l u t i o n v e c t o r 6 v a l i d a t e s : name, : p r e s e n c e => true 7 v a l i d a t e s : mail, : p r e s e n c e => true, : format => { : with => / ˆ ( [ ˆ@\ s ]+)@( (? : [ a z0 9]+\.) +[a z ] { 2, } ) $/ i }, : l e n g t h => { : within => } 8 v a l i d a t e s : e, : p r e s e n c e => true, : uniqueness => { : scope => : c h a l l e n g e i d } 9 v a l i d a t e : hasvalidcontent 10 v a l i d a t e : gvboundandesize 11 v a l i d a t e : m u l t i p l y I s Z e r o b e f o r e s a v e ( : on => : c r e a t e ) do 14 s e l f. t = counterrors ( ) 15 end def gvboundandesize 18 bound = c h a l l e n g e. bound 19 b = bound + bound / APP CONFIG[ c h a l l e n g e g v b o u n d t o l e r a n c e ] 20 puts b

11 Crypto Lab puts counterrors ( ) 22 i f e. l e n g t h!= c h a l l e n g e. n 23 e r r o r s. add ( : e, has not the c o r r e c t l e n g t h! The l e n g t h o f e i s #{e. l e n g t h }, but i t must be #{c h a l l e n g e. n} ) 24 return f a l s e 25 end i f! ( 1.. b ). i n c l u d e?( counterrors ( ) ) 28 e r r o r s. add ( : e, i s not a non z e r o v e c t o r or weight ( e ) > 1. 1 GVbound GVbound = #{b }. weight ( e ) = #{ counterrors } ) 29 return f a l s e 30 end 31 end def m u l t i p l y I s Z e r o prng = Random. new ( c h a l l e n g e. seed ) 36 r = Array. new ( c h a l l e n g e. n, 0) data = ( c h a l l e n g e. r ). times. map{( c h a l l e n g e. n ). times. map{ prng. rand ( ) }} 39 matrix = data. t r a n s p o s e 40 vec = c o n v e r t S t r i n g 2 D i g i t A r r a y ( e ) upto ( ( c h a l l e n g e. n ) 1) do i 42 i f vec [ i ] == 1 43 r = matrix [ i ]. z i p ( r ). c o l l e c t { t, k t. t o i ˆ k. t o i } 44 end 45 end i f r. i n j e c t (:+)!= 0 48 e r r o r s. add ( : e, i s not a s o l u t i o n > He!= 0 ) 49 return f a l s e 50 end return true 53 end def hasvalidcontent 56 # check each element i s w i t h i n range ( ) 57 vec = c o n v e r t S t r i n g 2 D i g i t A r r a y ( e ) 58 #i f vec. n i l? vec. l e n g t h <= 0 59 # e r r o r s. add ( : e, i s b l a n k ) 60 #r e t u r n f a l s e 61 #end 62 bool = vec. map{ e l ( ). i n c l u d e?( e l ) }. i n j e c t (:&) 63 i f! bool 64 e r r o r s. add ( : e, i s not a binary s t r i n g ) 65 end 66 return bool

12 12 Crypto Lab end def counterrors 70 # count a l l 1 = c o n v e r t S t r i n g 2 D i g i t A r r a y ( e ) 72 i n j e c t (:+) 73 end def c o n v e r t S t r i n g 2 D i g i t A r r a y ( e ) 76 i f ( e. n i l?) 77 return n i l 78 end 79 # c o n v e r t d i g i t s t r i n g to to a d i g i t array 80 return e. s p l i t ( ). map(&: t o i ) 81 end end Listing 1.3. Solution model B Screenshots

13 Fig. 3. Welcome page Crypto Lab

14 14 Crypto Lab 2011 Fig. 4. List of challenges Fig. 5. New challenge created

15 Fig. 6. Hall of Fame Crypto Lab

16 16 Crypto Lab 2011 Fig. 7. Invalid solution Fig. 8. Valid solution