(38G) Hill's Encryption System

[Gerald H]

The following four programmes implement Hill's Cypher system for the HP 38G.

HILLSET stores the parameters, encyphering & decyphering matrices & additional cypher vector, in M9, M0 & M8.
The programme asks for an encyphering modulus, for English perhaps 26, & size of cyphering matrices & vector, conveniently 4 to fit on the screen.

ENCY encyphers the conformable matrix M1 & stores the result in M1.

DECY decyphers the conformable matrix M1 & stores the result in M1.

M1ADDV8 adds/subtracts the comformable vector M8 to the rows of M1.

For info on Hill's system see:

https://en.wikipedia.org/wiki/Hill_cipher

HILLSET

Code:


INPUT C;"Hill Cryptosystem"; "Modulus";" Cypher Modulus ► C";26:
INPUT S;"Hill Cryptosystem"; "Size";" Size of Cypher Matrix ► S";4:
IDENMAT(S)►M0:
FOR I=1 TO S STEP 1;
FOR J=1 TO S STEP 1;
IF I==J
THEN
IF RANDOM>.5
THEN
-1►M0(I,I):
END:
S►J:
ELSE
INT(C*(RANDOM))►M0(I,J):
END:
END:
END: 
M0:
Ans*TRN(Ans):
MAKEMAT(Ans(I,J)MOD C,S,S
)►M9:
M0^-1:
MAKEMAT(
ROUND(Ans(I,J),0),S,S):
TRN(Ans)*Ans:
MAKEMAT(Ans(I,J)MOD C,S,S
)►M0:
MAKEMAT(INT(C*RANDOM),1,S)►M8:

ENCY

Code:


SIZE(M1):
Ans(1)►T:
SIZE(M9):
Ans(1)►S:
M1*M9:
MAKEMAT(Ans(I,J)MOD C,T,S
)►M1:
1:
RUN M1ADDV8:

DECY

Code:


-1:
RUN M1ADDV8:
SIZE(M1):
Ans(1)►T:
SIZE(M0):
Ans(1)►S:
M1*M0:
MAKEMAT(Ans(I,J)MOD C,T,S
)►M1:

M1ADDV8

Code:


Ans►V:
SIZE(M1):
MAKEMAT((M1(I,J)+V*M8(1,J))MOD C,Ans(1),S)►M1:

[Gerald H]

Sorry, the programme HILLSET did not set up M0 efficiently, here is a more efficient version, the difference being in the line with the command "BREAK":

Code:


 INPUT C;"Hill Cryptosystem"; "Modulus";" Cypher Modulus ► C";26:
 INPUT S;"Hill Cryptosystem"; "Size";" Size of Cypher Matrix ► S";4:
 IDENMAT(S)►M0:
 FOR I=1 TO S STEP 1;
 FOR J=1 TO S STEP 1;
 IF I==J
 THEN
 IF RANDOM>.5
 THEN
-1►M0(I,I):
 END:
 BREAK:
 ELSE
 INT(C*(RANDOM))►M0(I,J):
 END:
 END:
 END: 
 M0:
 Ans*TRN(Ans):
 MAKEMAT(Ans(I,J)MOD C,S,S
 )►M9:
 M0^-1:
 MAKEMAT(
 ROUND(Ans(I,J),0),S,S):
 TRN(Ans)*Ans:
 MAKEMAT(Ans(I,J)MOD C,S,S
 )►M0:
 MAKEMAT(INT(C*RANDOM),1,S)►M8: