Mayelana nokuqina kwe-IBAN04
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Njengoba kwaziwa, i-IBAN yaseJalimane iqukethe ikhodi yezwe (DE), idijithi yesheke enezinombolo ezimbili (ngokwe- ISO 7064 ), ikhodi yasebhange (amadijithi angu-8) kanye nenombolo ye-akhawunti (kuhlanganise nenombolo ye-akhawunti encane, 10). -idijithi, amadijithi alahlekile agcwaliswa ngoziro abaholayo) ngakho-ke inamadijithi angama-22. Ukuze ubale idijithi yesheke, lokho okubizwa nge-BBAN (ikhodi yasebhange nenombolo ye-akhawunti) kanye nekhodi yezwe yezinombolo \(1314\) yaseJalimane kanye nedijithi yesheke \(00\) ) kwakhiwa.

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Isibonelo, ikhodi yasebhange engu-21050170 kanye nenombolo ye-akhawunti ethi 12345678 ibuyisela i-BBAN 210501700012345678, inwetshwe ngekhodi yezwe kanye nedijithi yesheke engu-00 bese \(x = 210501700012345678131400\) idijithi ethi 9 \(98 - (x \mod 97)\) inombolo engu-9) manje: 8 ikuphi: \(98 - (x \mod 97)\) . Akuqondakali ukuthi lokhu kuhlukaniswe ngokuthi \(97\) . Njengenombolo enkulu yamadijithi amabili eyinhloko, ibona okufakiwe okungalungile njengamadijithi aguquliwe okungenzeka kakhulu. Manje sibonisa izitatimende ezilandelayo:

1. Ukushintsha idijithi eyodwa ye-IBAN evumelekile kuzoholela ku-IBAN engavumelekile.
2. Ukushintsha amadijithi amabili ahlukene e-IBAN evumelekile kungaholela ku-IBAN evumelekile.
3. Uma izikhundla ezimbili ezihlukene ze-IBAN evumelekile zishintshwa, kwakhiwa i-IBAN engavumelekile.
4. Uma ushintshanisa kabili izikhundla ezimbili ezihlukene ze-IBAN evumelekile, kungaba ne-IBAN evumelekile.

Vumela $$A = DE P_1 P_2 N_1 N_2 N_3 N_4 N_5 N_6 N_7 N_8 N_9 N_{10} N_{11} N_{12} N_{13} N_{14} N_{15} N_{16} N_{17} N_{18}$$ i-IBAN evumelekile.

Bese kuthi $$A_B = N_1 N_2 N_3 N_4 N_5 N_6 N_7 N_8 N_9 N_{10} N_{11} N_{12} N_{13} N_{14} N_{15} N_{16} N_{17} N_{18} 131400$$ i-BBAN ehlobene (inwetshiwe ngekhodi yezwe enekhodi DE kanye nedijithi yesheke \(00\) ).

1. Shintsha manje \(N_k\), kuyinto \(A_B^* = A_B + l \cdot 10^{24-k}\) nge \(1 \leq k \leq 18\) futhi \((-1) \cdot N_k \leq l \leq 9-N_k \wedge l \neq 0\). Nge \( P = 98 - (A_B \mod 97) \) kodwa \(P^* = 98 - \left((A_B + l \cdot 10^{24-k}) \mod 97\right) \). Ngokuvamile kusebenza ku \( a \equiv a' \mod m, b \equiv b' \mod m \): \(a + b \equiv a' + b' \mod m\). Nge \(A_B \equiv R_1 \mod 97\) futhi \(l \cdot 10^{24-k} \equiv R_2 \mod 97\) kuyinto \( (A_B + l \cdot 10^{24-k}) \equiv R_1 + R_2 \mod 97 \). Kodwa manje sekunjalo \( 0 < R_2 < 97 \) futhi kanjalo \( P^* = 98 - (R_1+R_2) \neq 98 - R_1 = P \) futhi ngalokho \( P_1 \neq P_1^* \vee P_2 \neq P_2^* \). Lokhu kushiya ushintsho olulodwa kuphela lwedijithi ukusuka \( P \) ku \( P^* \neq P \). Lapha kodwa \( N_k \) ihlala ingashintshiwe, i-checksum iyakhiwa \( P \neq P^* \).
2. Lawa ma-IBAN amabili alandelayo avumelekile:
   $$\begin{align} A_1 = DE89207300\boldsymbol{\color{red}01}0012345674 \\ A_2 = DE89207300\boldsymbol{\color{red}98}0012345674 \end{align}$$ , ukuthi sikhulise amadijithi amabili ancikene kokuthi \(A_1\) ngokuthi \(97\) . Ngaphezu kwalokho, i-IBAN ayisebenzi ngokusemthethweni kuphela, kodwa amakhodi asebhange ayisisekelo athi 20730001 kanye no-20730098 akhona ngempela.
3. Sizama kuqala, \( N_{k_1} \) futhi \( N_{k_2} \) ukushintshanisa. Okokuqala ngu \( P = 98 - (A_B \mod 97) \) njengoba \(P^* = 98 - \left((A_B + l \cdot 10^{24-k_1} - l \cdot 10^{24-k_2}) \mod 97\right) \) nge \(l = N_{k_2} - N_{k_1}\) futhi \(1 \leq k_1, k_2 \leq 18\). Manje kungenxa
   
   $$\begin{array} {|c|c|} \hline k & R = 10^{24-k} \mod 97 \\ \hline 1 & 56 \\ \hline 2 & 25 \\ \hline 3 & 51 \\ \hline 4 & 73 \\ \hline 5 & 17 \\ \hline 6 & 89 \\ \hline 7 & 38 \\ \hline 8 & 62 \\ \hline 9 & 45 \\ \hline 10 & 53 \\ \hline 11 & 15 \\ \hline 12 & 50 \\ \hline 13 & 5 \\ \hline 14 & 49 \\ \hline 15 & 34 \\ \hline 16 & 81 \\ \hline 17 & 76 \\ \hline 18 & 27 \\ \hline \end{array}$$
   \( \forall k_1 \neq k_2 \in \left\{ 1, \ldots, 18 \right\} : R_{k_1} \neq R_{k_2}\). Kanjalo \( P \neq P^* \). Ngakho kusamele kubhekwe lokho \(P_n\) futhi \(N_k\) nge \( 1 \leq n \leq 2 \) futhi \( 1 \leq k \leq 18 \) uhwebo. Kungenzeka \(P = 98 - (A_B \mod 97)), (R_1 = (A_B \mod 97)\), \(P^* = 98 - (A_B + (l \cdot 10^{24-k}) \mod 97)\), \(R_2 = (A_B + (l \cdot 10^{24-k}) \mod 97)\). Kusukela thina \(A_B\) nxazonke \(l \cdot 10^{24-k}\) kufanele sishintshe \(P_1\) noma \(P_2\) nxazonke \(-l\), ngakho \(P\) nxazonke \(-10^m l\) nge \(m \in \{0,1\}\) ushintsho: Khona-ke \(P^* = 98 - R_2\) kodwa futhi \(P^* = P - 10^m l = 98 - R_1 - 10^m l\), ngenxa yalokho \(R_2 = R_1 + 10^m l,\) futhi kanjalo
   $$((A_B \mod 97) + (l \cdot 10^{24-k} \mod 97)) \mod 97 = (A_B \mod 97) + 10^m l$$ Nokho, lesi sibalo asifezeki, njengoba umbhalo olandelayo ubonisa:
   
   

   See the Pen IBAN FORMULA CHECK by David Vielhuber (@vielhuber) on CodePen.

   Lokhu kushiya kuphela ukushintshana okungenzeka kwe \(P_1\) futhi \(P_2\). Lapha kodwa \( N_k \) ihlala ingashintshiwe, i-checksum iyakhiwa \( P \neq P^* \).
4. Lawa ma-IBAN amabili alandelayo avumelekile:
   $$\begin{align*}A_1 = DE\boldsymbol{\color{red}8}\boldsymbol{\color{green}3}20220800\boldsymbol{\color{red}1}000000\boldsymbol{\color{green}0}00 \\ A_2 = DE\boldsymbol{\color{red}1}\boldsymbol{\color{green}0}20220800\boldsymbol{\color{red}8}000000\boldsymbol{\color{green}3}00\end{align*}$$ Nalapha, i-BIC 20220800 ikhona ngempela.