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# Petr98

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### Petr98

1. 1. . ., . . (www.dekart.com) ) * , . “ t” - \$ , %& , . (.) .* . The problem of tests of the random numbers, applied in cryptography, is considered in this article. The special attention is paid to the empirical test “the maximum of t” – the authors suggest their own way for solving this problem that appears under discretization of the classical test, elaborated by Professor D. Knuth. The results of the random and pseudo-random figures testing are adduced. * & ( , , ) . H , \$ , , . ( & DSS. * DSA ( DSS) % & .K % 0160- q( % ). P , %& , \$ , (Q*RS), %& ( , - T U .). * . R , 2 [1,2]. * , . % * : (Ys n ps ) 2 2 = (1) 1 s k n ps Ys - , % s; ps - , % s; k - ; n– & .
2. 2. 2 * % =k–1 p- , . . . S n , % ps n ps \$ 5. K , , - , [1,3] &“ ”( ) [1]. * “ t”. ` , %& , % %& :1) t %& ;2) .* % “ t”;3) & % “ t” .a “ t” [1] ) -R . H 2( k) . b i- % t- (Xi1, Xi2, ... , Xit). ) 0 k-1 % . * M x = max X ij , 1 j t a , Mx = z %& . Xij – .R p (M x z ) = p( X ij z ) = ( z + 1) k t , t 0 z k 1 1 j t p (M x = z ) = p (M x z ) p(M x z 1) d , [ p(M x = z ) = ( z + 1) t ] z k, t t 0 z k 1. (2) * %* % , (2) & ( . . t- ) \$ 5. ( z \$ 5. – (1) %& & , , , \$ % , % . a `.e [4] %& \$ . * \$ % . * [0, k-1] ,“ t”, \$ \$ . “ t” % , , 2 , \$ %& .( ,
3. 3. (2), %& : p( z1 Mx z2) = [( z + 1) z ] k , 2 t t 1 t z1 z2 C \$ % [0, k-1], & . U \$ “ t” & % .1. a (2) zmin= 0. R , t pmin = 1 / k n pmin= N / (t kt), N– .* , , , N 5 kt). H (t % , t k N \$ \$ .H , t = 8, k = 256, N 7.38 1020.2. ( t. ( % t, %& % t t k N / 5. (3)3. k ( ), N t / k, \$ (3). d , % , “ & ”, %& t k ( (3)), “ t”. b CHITESTS [5], , . ) % & % 2 .P , . CHITESTS , % [1]. k p 0 – 1 % 99 – 100 %, % .k p 99 95 % 5 1 %, % “ ”; p, % 95 90 % 105 %, “ ” [1]. P Q.U RANDOM CD-ROM [6], : , DIEHARD, 60 10- . H DIEHARD. H & % DIEHARD CHITESTS. T calif.bit % , % & % () ,Re`), & % G.Marsalia RANDOM CD-ROM. a random - , , & % RANDOM.SYS, file1.bin - smart- Payflex 1K. b \$ 10 U .
4. 4. 10000000 characters in file: calif.bits HITESTS . / CHI 3 4 A Frequency Test 1.000000 Test error1 B Serial Test 1.000000 Test error C Gap Test 0.976478 Suspicious D Poker Test 1.000000 Unsatisfactory E Coupon Test 0.968074 Suspicious F Permutations Test 0.999634 Unsatisfactory G Runs Up Test 0.669232 Satisfactory H Maximum-of-8 Test 1.000000 Test error I Lapped M-tuple Test 1.000000 Test error DIEHARD . / p-value 3 4 A. BIRTHDAY SPACING .631736 Satisfactory B. OPERM5 .541571 Satisfactory C. BINARY RANK 1.0000 Unsatisfactory D. SQUEEZE .997847 Unsatisfactory E.1 CRAPS: no. of wins .847283 Satisfactory E.2 CRAPS throws/game .441181 Satisfactory F. MINIMUM DISTANCE .792573 Satisfactory G. 3DSPHERES .001891 Unsatisfactory H. OSUM .409425 Satisfactory I.1 RUNS: Runs up .430718 Satisfactory I.2 RUNS: Runs down .622296 Satisfactory K. CDPARK .406615 Satisfactory10000000 characters in file: random HITESTS . / CHI 3 4 A. Frequency Test 0.109633 Satisfactory B. Serial Test 0.551388 Satisfactory C. Gap Test 0.834301 Satisfactory D. Poker Test 0.402890 Satisfactory E. Coupon Test 0.433876 Satisfactory F. Permutations Test 0.683315 Satisfactory G. Runs Up Test 0.360567 Satisfactory H. Max-of-8 Test 0.237868 Satisfactory I. Lapped M-Tuple Test 0.269342 Satisfactory DIEHARD . / p-value 3 4 A. BIRTHDAY SPACING 0.726657 Satisfactory B. OPERM5 0.719636 Satisfactory C. BINARY RANK 0.854952 Satisfactory D. SQUEEZE 0.524926 Satisfactory E.1 CRAPS: no. of wins 0.280685 Satisfactory E.2 CRAPS throws/game 0.159625 Satisfactory F. MINIMUM DISTANCE 0.889075 Satisfactory1 * % & “Test error”, CHI - 1.
5. 5. G. 3DSPHERES 0.948734 Satisfactory H. OSUM 0.079572 Satisfactory I.1 RUNS: Runs up 0.668908 Satisfactory I.2 RUNS: Runs down 0.860145 Satisfactory K. CDPARK 0.377942 Satisfactory11296592 characters in file: file1.bin HITESTS . / CHI 3 4 A. Frequency Test 0.505161 Satisfactory B. Serial Test 0.187295 Satisfactory C. Gap Test 0.330256 Satisfactory D. Poker Test 0.616983 Satisfactory E. Coupon Test 0.081551 Faintly suspicious F. Permutations Test 0.073267 Faintly suspicious G. Runs Up Test 0.516541 Satisfactory H. Max-of-8 Test 0.626726 Satisfactory I. Lapped M-Tuple Test 0.479882 Satisfactory DIEHARD . / p-value 3 4 A. BIRTHDAY SPACING 0.326970 Satisfactory B. OPERM5 0.959323 Satisfactory C. BINARY RANK 0.795310 Satisfactory D. SQUEEZE 0.531174 Satisfactory E.1 CRAPS: no. of wins 0.623129 Satisfactory E.2 CRAPS: throws/game 0.862083 Satisfactory F. MINIMUM DISTANCE 0.904371 Satisfactory G. 3DSPHERES 0.597925 Satisfactory H. OSUM 0.843655 Satisfactory I.1 RUNS: Runs up 0.926601 Satisfactory I.2 RUNS: Runs down 0.636983 Satisfactory K. CDPARK 0.095702 Satisfactory d - , – random(), Borland C - - Elite 730, 510. ) \$ , “ ” - , & % , - % %( ). R , - , ( , , , - % %& ) \$ .* ) “( ” , R ® Dekart Digital Signature System , U - Dekart Media Pay ®, % smart- Payflex 1K RANDOM.SYS. R - % \$ DIEHARD. ( RANDOM.SYS , % ( CHITESTS), , & % smart- , % “ - ” CHITESTS. R : 1. % & % DIEHARD D * . ) , & %
6. 6. ( . . ). RHITESTS D * . 2. RHITESTS 9 , * 2 ; DIEHARD 18 , \$ % p-value [0.025, 0.975], % (“ - ” “ ”) * ) -R . 3. DIEHARD c - \$ 80 . , RHITESTS - % - n ps \$ 5. . ( \$ & ( , DSS) % , - % “ ” \$ .Q - , %& “ ” % , %& % Q*RS & %& . R , & & % .S \$ \$ \$, . R % ) “Dekart” % - - RHITESTS, DIEHARD.[1] ) (. P KaU/ d.2 * .- U.:U , 1977.- 727 .[2] a a.d., H `.T., H H.T. U \$\$ .- U .: a \$. e ., 1984.- 527 .[3] Wegentkittl S. Empirical testing of pseudorandom number generator/ Master’s thesis,University of Salzburg, Austria, 1995.[4] Shapira A. The Discrete Runs Test and the Discrete Maximum of t Test. Technical ReportCS 96-15. ESCE Department Rensselaer Polytehnic Institute. 1996.[5] *(CHITESTS). b . b . ) “DekartS.R.L.”, 1998. [6] DIEHARD: a battery of tests for random number generators developed by George Marsaglia.` P : http://stat.fsu.edu/~geo/diehard.htmlWeaCheslaw L. Oleinik, Dr. of C.S., Ass.Academician of International Informatization Acad-emy, Member of the Balcanic Union for Fuzzy Systems and Artificial Intelligence.Company “Dekart S.R.L.”, Head of Data Security Section of Smart Card TechnologyDepartment.Born: July 4, 1956Author: more than 40 printed-papers.
7. 7. Olga M. Petrova, Dr. of C.S., Senior Scientific Researcher.Company “Dekart S.R.L.”, Leading Specialist of Data Security Section of Smart CardTechnology Department.Born: February 16, 1966.Author: monograph and 14 published works.