RSA算法和RSA数字签名算法的实现

1、邢唷? ?68?5欹?餜?,0bjbj? ?.8俲俲 l?ZZZZf?.333?$?l?Q?33333?3?J3333?33?3?3?rEP莃律8Z3?0?J3J?3?J?6?R S A梴 誰孴 R S A peWT 梴誰剉瀃皊Xd 亯:R S A梴誰/f N 蛓 lQ芠x 梴誰.瀃皊 R S A梴誰 S 靊 u bR S A芠, (uR S A 燫芠膲 R 孴銐芠膲 R Y tpenc. R S A peWT 梴誰)R(uR S A 梴誰瀃皊 peWT. ,g 噀 鎷 饛 哊 R S A梴 誰 剉 鶺 ,g 烻 t,R S A燫 芠 梴 誰 剉 瀃 皊 錘 蔛 俌UO)R(uR S A 瀃皊

2、 peWT.sQ.昗:R S A 梴誰,peWT,lQ _芠,羪篘芠,燫芠,銐芠N _?彇wQ軂b/g 剉迾愌 SU,酧 o塠 hQ騗 b:N 烴卂銐砆剉顣槝. lQ芠xSO6R-N, 銐芠孴燫芠芠NT, 銐芠孴燫芠颯 R 粂, 愥 O 蘏筫鄀構 NHQbc 芠1颯鷁藌 w 嵼 O 芠 愥 O,儚Y0W銐砆哊 O 邁芠xSO6R(WQ軂 愥 O-N 鶴皊剉顣槝. 鍿 Y, 彇w5uPFU剉裇 U, Q軂ND嵮憚v5uPbc 錯蕍憳A, 俌UO2朾k酧 o剉*O 悓T:k 棜_N b:N?蛻亯剉顣槝. peWT 颯錘 w?R 珟齆翄, 8h 芉 penc 孾 te剉O(u. 顅 MRsQ 嶯 p

3、eWT 剉 xvz;N 亯茤-N 鶺嶯 lQ芠xSO6R 剉 peWT.lQ芠xSO6R 剉 yr 筽 /f: :N 蟢 *N(u7bu N 鵞 芠( P K孴S K ) ; P K lQ _, S K軴芠;蜰 P K鶴 S K /f 坃餠緰剉; A , B 蘏筫 愥 O鰁, A 惽忹 NUO 悇_諷梍 B 剉 lQ, (uB 剉 lQ燫芠酧 o. 燫芠T 剉酧 o颯 惽忹 NUON 塠 hQ 酧 S 愌 S? B 6e0R 芠噀酧 oT, (u 陙馷羪銐芠 bY 鶴f 噀.lQ芠xSO6R 騗 b:Nnx 軴酧 o剉塠 hQ剉 sQ.晙 b/g. R S A lQ芠xSO6R0R顅 MR:N

4、bk 貜/f N 蛓颯:N 塠 hQ 剉 SO6R. ,g 噀鎷饛哊 R S A梴誰孴(uR S A梴誰瀃皊peWT 剉 t 簨, 錘蔛僛霳(W 瀃 E 枖(u-N 剉瀃皊.孨 R S A 梴誰孴 R S A peWT 梴誰剉 t 簨蟘饛1R S A 梴誰R S A 梴誰剉 t 簨鶺x/f N 蛓 yr 妅剉颯 ?jB袕梴.緥 n /f$N*NNTGY pep 孴 q 剉飝, sS: n = p q ,( n ) = ( p - 1 ) ( q - 1 ) .歔 IN 芠zz 魰k = ( n , p , q , d , e ) | n = p q , p孴q /f pe, d e 1m o

5、d( n ) , e :N 彇:gtepe ,鵞蟢 N*Nk = ( n , p , q , d , e ) ,歔 IN 燫芠豐 bc:NE k ( x ) = x bm o dn , x Z n ;銐芠豐 bc:ND k ( x ) = y am o dn , y Z n , Z n :Ntepe 茤T.lQ _n 孴 b , 軴芠 p , q 孴 a .:N 翄f 燫芠豐 bcE k 孴銐芠豐 bcD k 醤硩 D k ( E k ( x ) ) = x , 購虘N 燫翄f 剉 _(uNb?N*N 歔 t:歔 t1 ( E u l e r ) 鵞鸑a剉a ( Z n * ,ga ( ( n

6、 ) ( 1m o dn , vQ-NZ n * = x ( Z n | g c d (x , n ) = 1 , ( ( ? ) h?yE u l e r 齉 pe.歔 t2緥 p 孴 q /f$N*NNT 剉 pe, n = p q ,( ( n ) = ( p - 1 ) ( q - 1 ) , 鵞鸑a 剉 x ( Z n 蔛鸑a 剉?峵 epek ,gx k ( ( n ) + 1 ( xm o dn .皊(Weg 翄fR S A 梴誰剉燫芠豐 bc 孴銐芠豐 bc 剉 cknx.翄f:鵞嶯燫芠豐 bcE k孴銐芠豐 bcD k .郪:Na b 1m o d( n ) , b 錘颯緥

7、a b = t ( n ) + 1 , t /ftepe Nt 1 . 鵞嶯鸑a剉x Z n ,gD k ( E k ( x ) ) D k ( x b )( x b ) a x t ( n ) + 1 xm o dn . 郪 dk 銐芠菑z/fcknx 剉.2R S A peWT 梴誰R S A peWT 梴誰剉菑z:N: A 鵞f噀m (u銐芠豐bcO:sD k( m ) = m dm o dn , vQ-Nd , n :NA剉羪篘芠, 闟gA Mb 鍂 S 悆; B 6e0RA 剉TT, (uA 剉 lQ孴燫芠豐 bc 梍 0Rf噀,郪:E k ( s ) =E k ( D k( m )

8、 ) =( m d ) em o dn ,萐d e 1m o d( n ) sSd e = l ( n ) + 1 , 9hnck 蒪 歔 tm ( n ) = 1m o dn , b錘E k ( s ) = m l ( n ) + 1 = m ( n ) e m = mm o dn . 鍌f 噀 m 孴TsNw?愘(u7bB , B 颯錘 nx 酧酧 onx 瀃/fA 裇悇 v.T 鰁 A _NN 齹&T愘購*N 酧 o, 郪:Nd 枂 NA ,g 篘 Y, vQ 諲鸑 UO 篘龕鄀誰 1uf 噀 mus . 郪 dkR S A peWT 筫 Hh/f 颯 L 垊 v.FO/fR S

9、 A peWT 梴誰 X(Ww 郪梴筫誰,g 珟T 刧 ?bT f 珗*O 悓 T梴鰁魰晞 v1_筽, 郪 dk 瀃 E 桖噀鯪TMR,梺夰坢 oZPM D 5 豐 bc.M D 5 齉 pe/f N 蛓 US Tce R 齉 pe, 僛 鸑a暒剉坢 o婼) b1 2 8 MO 剉坢 oXd 亯. 擽(uM D 5 剉 US T( sS 賬歔 ce RP,梴坢 o坃緰)孴梑皒瀌( sS 賬歔坢 oM ,亯b0R 鍿N 坢 oM v醤硩$N剉ce RP 坃緰) , 颯錘瀃皊酧 o剉孾 te纇寶. 鍿 Y 鍕齉 pe 剉緥N 鶺嶯鸑 UOGP 緥孴芠xSO6R魐刧 ? gbL 垊 v 惁隷, /f

10、 N 蛓珗踠颯剉 US Tce R 梴誰.NR S A 梴誰剉瀃皊R S A 梴誰剉瀃皊 R:N: u b 芠, 燫芠, 銐芠.1penc 觺刧R S A 芠x 鹼邁剉塠 hQ漁 V 崕 NYpe R 銐剉緰,N,傶畫(u7b愰 b 剉 pep 孴q髞 :N1 0 0 MO, Rn = p q /f 髞 :N2 0 0 MO 剉 AS 蹚 6Rpe.郪 dk 瀃皊R S A 梴誰g 臺亯歔 INYpe 剉 penc 觺刧.t y p e d e fs t r u c tu n s i g n e dl o n gi n tb n M A X _ L E N G T H ;u n s i g n

11、 e di n tKm0R 燫芠 WW-N 剉f 噀. 郪:N(W梴:gNN 颯齹uwck 剉彇:gpe, 瀃 E 柷?uhTgY 嶯 2 2 5 6 MO 剉*O 彇:g 廭 R 裇 uhV.瀃皊菑z:N:( 1 )皨 U_鴙粣$N!kre 鸔.曍 v 剉鰁魰魰敄, 魐 0RN 峇 梺墢?g 婲鯪.( 2 )ZPM D 5梴, 魐 0RN 峇 梺?O 彇:gpe.2 . 2 . 2pe 剉u鵞彇:gpeO 纇Km, 鍌 惽?R:N pe; &T R瀀燫 N*Nek?T峇ZP 纇Km,魐 0Rb 鶴 pe.纇 Km 菓(uF e r m a t Km 諎.購*N 梴誰剉 t 簨漁 nc

12、/f9?l?歔 t: 俌済 m /f N*N pe, NaN/fm 剉Ppe,HN9hnc9?l?歔 tg: am - 1 = 1(m o dm ) .瀃 E枖(u鰁: am - 1=1(m o dm )am=a(mo dm )a =am(m o dm ) ,郪 dk 鵞嶯 tepem ,闟棥嫍am(m o dm ) , 峇 觺済Na 詋儚, 俌済$N鴙T, Rm :N pe.愔 Sa = 2 , RaN 歔N O/f 鸑 UO pe 剉Ppe.3燫芠菑z燫芠膲 R:N: E k ( x ) = x bm o dn , x Z n燫芠菑z 剉搹 eQ:N:f 噀 pencD , !jpen ,

13、燫芠cpee ( lQ燫芠) b 銐芠cped ( 羪燫芠) . 搹鶴:N 芠噀. D 剉暒N 厤菑 l o g 2 n - 1 1 , 錘 nx 軴 l 廱 c:NP K C S h_鰁, kXEQ2N 剉 pe 顅N:N0 .h_ Sf 噀.菓(uP K C S h_:E B=0 0| |B T| |P S| |0 0| |DvQ-NB T h?yWW 剉|媁, P S :NkXEQ2N, D :Nf 噀 penc._4Y:N0 nx 軴 E B 暒Y 嶯 k .鵞 lQ燫芠 B T = 0 2 ,鵞羪銐芠B T = 0 1 . S_B T = 0 2鰁, P S :N?彇:gpe; S_

14、B T = 0 1 , P S P:NF F .f 噀 1uW&媁 pencl 廱 c bte 媁 penc.R S A梴.:Ntepe燫芠WWx O!jB袕梴 : y=x cm o dn , 0 =y:N 芠 噀 , lQ燫 芠鰁, c :NlQ燫芠cpee ; 羪燫芠鰁, c :N 羪燫芠cped .芠噀 1ute 媁 pencl 廱 c bW&媁 penc.4銐芠菑z銐芠膲 R:ND k ( x ) = y cm o dn , y Z n , Z n :Ntepe 茤T, x :N 芠噀.銐芠菑z 剉搹 eQ:N: 芠噀 E D ; !jpen ; 燫芠cpee ( lQ

15、銐芠) b 銐芠cped ( 羪銐芠) , 觺済:Nf 噀.( 1 )芠噀 te 媁 S.( 2 )R S A梴.鵞芠噀ZP!jB袕梴: x=y cm o dn ,0 =xn. , vQ-Nx:Nf 噀.( 3 )dk 鰁f 噀:Nte 媁 penc, l 廱 c:NA S C I I 媁 penc, 梍 0RP K C S h_剉f 噀.( 4 )蜰 P K C S h_f 噀-N R 粂鶴烻f 噀.蜰 P K C S y,0梴:g 芠xf0, 1 9 9 8疩v 齎, 魣歔 N, 褃 f鶴 Hry,0 芠xf黐 _0, 1 9 9 9$&bd?(0,0? ?眭 $U n k n o w nG ? 噝T i m e sN e wR o m a n5 ? S y m b o l3&? 噝A r i a l; ?褳 SOS i m H e i; ?媅 SOS i m S u n?hWFWF16&!Z & ! ) , .: ; ? ? ? ?& 60 0 000000 0 0 0=?( ?