Challenge & Response

[retepsnikrep]

Seasons Greetings to all.

If you get bored with relatives and feasting today perhaps you might cast your eye over the below.

I have an electronic gadget that has a challenge response going on.

It sends me two bytes.
I have to respond with two bytes somehow derived from the ones it sent me.

I have a few examples below of correct challenges and responses.
Any ideas on how it is working and generating the response?

Challenge $E3 $C5
Response $82 $CB

Challenge $79 $71
Response $04 $35

Challenge $84 $15
Response $ED $85

Challenge $9B $B6
Response $6F $C9

Challenge $C7 $B0
Response $1A $DD

Challenge $AB $19
Response $9A $69

Many thanks and best wishes for the new year.

[retepsnikrep]

I found a C++ solution to this calculation but I need to translate it into PbPro.

The actual seed/key is 3 byte not two as I first thought.

Happy to pay for some help to do this as I know nothing about C++ and don't have Visual Studio etc.

Text file attached..

[mpgmike]

It appears to be a random number generator based on the "Seed". At the top is a function for InitializeComponent(); which isn't anywhere in the body of code. I don't understand fully what it's supposed to do, but can give you some translation ideas. Let's break some of it down. All of the "Using"s listed at the top bring in macros and such from external files that are part of VS. Again, without actually looking each of them up, it's hard to tell what they contribute. The rest of the document is a Collection; more specifically it's called "namespace Calculation"; the rules which are probably spelled out in "System.Collections.Generic;".

"int Func3(int paramInt1, int paramInt2, int paramInt3)" is a subroutine. In PBP we'd use "Func3:", but first we'd have to already declare:

paramInt1 VAR SIGNED WORD
paramInt2 VAR SIGNED WORD
paramInt3 VAR SIGNED WORD

Then prior to GOSUB Func3 we have to assign values to them:

paramInt1 = 1234
paramInt2 = -567
paramInt3 = 890

Next:

int Func3(int paramInt1, int paramInt2, int paramInt3)
        {
            int i = paramInt1 << 8 | paramInt2;
            int j;
            int k; int m; int n; int i1; switch (paramInt3)
            {
                case 65:
                case 66:

"switch (paramInt3)" would be the same as "SELECT CASE paramInt3:" Also, " int i = paramInt1 << 8 | paramInt2;" is the same as
i.HIGHBYTE = paramInt1
i.LOWBYTE = paramInt2
At the bottom of the switch routine is "return Func2(i, j, k, m, n, i1);" In PBP we would have already placed the resultant values in each of these variables with

case 111:
                    j = 16360;
                    k = 6010;
                    m = 0;
                    n = 1;
                    i1 = -2;

"int getKey(int i)" manipulates the input ("i") with masks. I forget the hierarchy as to which gets precedence; ">>" or "&", and without parentheses, I would have to look it up to know for sure which operation is executed first.

I know this isn't everything, but hopefully it will help you to work through much of it. Do what you can then report back where you're having challenges.

[retepsnikrep]

Thanks for the response.

[retepsnikrep]

I've have this so far, but it's not right yet.
Gives same incorrect answer with different seeds.
Any obvious gaffes?

PIC18F2680

'Long Variables for signed Key Calculation

int VAR LONG
key VAR LONG
seed VAR LONG
top_j VAR LONG
top_k VAR LONG
top_l  VAR LONG

F3_i VAR LONG
F3_j VAR LONG
F3_k VAR LONG
F3_m VAR LONG
F3_n VAR LONG
F3_i1 VAR LONG

F2_i VAR LONG
F2_j VAR LONG
F2_k VAR LONG
F2_m VAR LONG
F2_n VAR LONG
F2_i1 VAR LONG


'*******************************************************************************

Start:

Seed.Byte0 = $6B
Seed.Byte1 = $E3
Seed.byte2 = $C5

'Answer should be $82 $CB $6B

lcdout hex2 Seed.byte2," $",hex2 Seed.byte1," $",hex2 seed.byte0

gosub CalcKey          

lcdout hex2 key.byte2," $",hex2 key.byte1," $",hex2 key.byte0

'Try Again

Seed.Byte0 = $6B
Seed.Byte1 = $71
Seed.byte2 = $79

'Answer should be $04 $35 $6B

lcdout hex2 Seed.byte2," $",hex2 Seed.byte1," $",hex2 seed.byte0

gosub CalcKey          

lcdout hex2 key.byte2," $",hex2 key.byte1," $",hex2 key.byte0

Stop


'*******************************************************************************


CalcKey:

top_j = seed >> $10
top_j = top_j & $ff
top_k = seed >> 8
top_k = top_k & $ff
top_l = seed & $ff

F3_i = top_j << 8
F3_i = F3_i | top_k

SELECT CASE top_l
    
                case 1 
                    F3_j = 20483;
                    F3_k = 37495;
                    F3_m = 19380;
                    F3_n = 2;
                    F3_i1 = -1;
                    
                case 2 
                    F3_j = 48737;
                    F3_k = 29064;
                    F3_m = 0;
                    F3_n = -2;
                    F3_i1 = 1;
                     
                case 3 
                    F3_j = 38851;
                    F3_k = 17007;
                    F3_m = 57213;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 4 
                    F3_j = 38191;
                    F3_k = 42963;
                    F3_m = 45416;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 5 
                    F3_j = 31893;
                    F3_k = 60216;
                    F3_m = 0;
                    F3_n = 1;
                    F3_i1 = -2;
                     
                case 6 
                    F3_j = 26458;
                    F3_k = 15181;
                    F3_m = 11362;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 7 
                    F3_j = 10773;
                    F3_k = 36766;
                    F3_m = 28592;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 8 
                    F3_j = 13376;
                    F3_k = 4967;
                    F3_m = 62941;
                    F3_n = 2;
                    F3_i1 = -3;
                     
                case 9 
                    F3_j = 2197;
                    F3_k = 24862;
                    F3_m = 65475;
                    F3_n = -2;
                    F3_i1 = 3;
                     
                case 10 
                    F3_j = 31199;
                    F3_k = 59852;
                    F3_m = 0;
                    F3_n = 1;
                    F3_i1 = -3;
                     
                case 11 
                    F3_j = 45383;
                    F3_k = 9690;
                    F3_m = 0;
                    F3_n = 3;
                    F3_i1 = -2;
                     
                case 12 
                    F3_j = 34146;
                    F3_k = 59163;
                    F3_m = 0;
                    F3_n = -1;
                    F3_i1 = 2;
                     
                case 13 
                    F3_j = 62765;
                    F3_k = 33340;
                    F3_m = 5749;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 14 
                    F3_j = 45458;
                    F3_k = 44092;
                    F3_m = 0;
                    F3_n = -1;
                    F3_i1 = 3;
                     
                case 15 
                    F3_j = 37357;
                    F3_k = 39321;
                    F3_m = 0;
                    F3_n = -2;
                    F3_i1 = 1;
                     
                case 16 
                    F3_j = 8713;
                    F3_k = 454;
                    F3_m = 23575;
                    F3_n = 1;
                    F3_i1 = -2;
                     
                case 17 
                    F3_j = 9988;
                    F3_k = 56677;
                    F3_m = 29637;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 18 
                    F3_j = 57758;
                    F3_k = 34088;
                    F3_m = 11152;
                    F3_n = 1;
                    F3_i1 = -3;
                     
                case 19 
                    F3_j = 33800;
                    F3_k = 14769;
                    F3_m = 0;
                    F3_n = -2;
                    F3_i1 = 1;
                     
                case 20 
                    F3_j = 4069;
                    F3_k = 4013;
                    F3_m = 24616;
                    F3_n = -1;
                    F3_i1 = 2;
                     
                case 21 
                    F3_j = 17056;
                    F3_k = 12969;
                    F3_m = 11927;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 22 
                    F3_j = 31370;
                    F3_k = 60592;
                    F3_m = 0;
                    F3_n = -1;
                    F3_i1 = 3;
                     
                case 23 
                    F3_j = 24184;
                    F3_k = 58486;
                    F3_m = 0;
                    F3_n = -1;
                    F3_i1 = 3;
                     
                case 24 
                    F3_j = 56838;
                    F3_k = 5012;
                    F3_m = 35563;
                    F3_n = 2;
                    F3_i1 = -3;
                     
                case 25 
                    F3_j = 49473;
                    F3_k = 5452;
                    F3_m = 33161;
                    F3_n = 3;
                    F3_i1 = -2;
                     
                case 26 
                    F3_j = 64459;
                    F3_k = 44104;
                    F3_m = 0;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 27 
                    F3_j = 6123;
                    F3_k = 30247;
                    F3_m = 0;
                    F3_n = -1;
                    F3_i1 = 3;
                     
                case 28 
                    F3_j = 62885;
                    F3_k = 57915;
                    F3_m = 28211;
                    F3_n = -2;
                    F3_i1 = 3;
                     
                case 29 
                    F3_j = 56790;
                    F3_k = 34537;
                    F3_m = 0;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 30 
                    F3_j = 34655;
                    F3_k = 4726;
                    F3_m = 0;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 31 
                    F3_j = 45667;
                    F3_k = 2227;
                    F3_m = 0;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 32 
                    F3_j = 64118;
                    F3_k = 22124;
                    F3_m = 0;
                    F3_n = 1;
                    F3_i1 = -3;
                     
                case 33 
                    F3_j = 20483;
                    F3_k = 37495;
                    F3_m = 19380;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 34 
                    F3_j = 18934;
                    F3_k = 33007;
                    F3_m = 45671;
                    F3_n = -1;
                    F3_i1 = 2;
                     
                case 35 
                    F3_j = 53898;
                    F3_k = 43937;
                    F3_m = 8992;
                    F3_n = 3;
                    F3_i1 = -2;
                     
                case 36 
                    F3_j = 26472;
                    F3_k = 30849;
                    F3_m = 15462;
                    F3_n = -2;
                    F3_i1 = 3;
                     
                case 37 
                    F3_j = 18864;
                    F3_k = 16973;
                    F3_m = 0;
                    F3_n = -2;
                    F3_i1 = 2;
                     
                case 38 
                    F3_j = 10153;
                    F3_k = 24758;
                    F3_m = 0;
                    F3_n = -2;
                    F3_i1 = 2;
                     
                case 39 
                    F3_j = 28031;
                    F3_k = 31768;
                    F3_m = 65233;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 40 
                    F3_j = 9577;
                    F3_k = 32816;
                    F3_m = 0;
                    F3_n = -3;
                    F3_i1 = 3;
                     
                case 41 
                    F3_j = 33294;
                    F3_k = 41833;
                    F3_m = 63823;
                    F3_n = 2;
                    F3_i1 = -2;
                     
                case 42 
                    F3_j = 46258;
                    F3_k = 33763;
                    F3_m = 47869;
                    F3_n = 2;
                    F3_i1 = -2;
                     
                case 43 
                    F3_j = 303;
                    F3_k = 15452;
                    F3_m = 49261;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 44 
                    F3_j = 14480;
                    F3_k = 52729;
                    F3_m = 0;
                    F3_n = 2;
                    F3_i1 = -2;
                     
                case 45 
                    F3_j = 26181;
                    F3_k = 30558;
                    F3_m = 11669;
                    F3_n = -1;
                    F3_i1 = 1;
                     
                case 46 
                    F3_j = 57729;
                    F3_k = 31412;
                    F3_m = 0;
                    F3_n = 3;
                    F3_i1 = -3;
                     
                case 47 
                    F3_j = 38273;
                    F3_k = 42785;
                    F3_m = 57170;
                    F3_n = 2;
                    F3_i1 = -3;
                     
                case 48 
                    F3_j = 65304;
                    F3_k = 24702;
                    F3_m = 12077;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 49 
                    F3_j = 25997;
                    F3_k = 16247;
                    F3_m = 11573;
                    F3_n = -2;
                    F3_i1 = 3;
                     
                case 50 
                    F3_j = 47122;
                    F3_k = 17812;
                    F3_m = 0;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 51 
                    F3_j = 62790;
                    F3_k = 184;
                    F3_m = 43056;
                    F3_n = -2;
                    F3_i1 = 1;
                     
                case 52 
                    F3_j = 27811;
                    F3_k = 36172;
                    F3_m = 10312;
                    F3_n = -1;
                    F3_i1 = 2;
                     
                case 53 
                    F3_j = 33495;
                    F3_k = 4706;
                    F3_m = 23772;
                    F3_n = 1;
                    F3_i1 = -3;
                     
                case 54 
                    F3_j = 11806;
                    F3_k = 6016;
                    F3_m = 0;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 55 
                    F3_j = 23022;
                    F3_k = 61027;
                    F3_m = 0;
                    F3_n = 1;
                    F3_i1 = -3;
                     
                case 56 
                    F3_j = 14502;
                    F3_k = 52925;
                    F3_m = 45502;
                    F3_n = -3;
                    F3_i1 = 2;
                     
                case 57 
                    F3_j = 19654;
                    F3_k = 47349;
                    F3_m = 29195;
                    F3_n = 3;
                    F3_i1 = -2;
                     
                case 58 
                    F3_j = 4043;
                    F3_k = 49055;
                    F3_m = 0;
                    F3_n = 1;
                    F3_i1 = -2;
                     
                case 59 
                    F3_j = 238;
                    F3_k = 61025;
                    F3_m = 46052;
                    F3_n = -2;
                    F3_i1 = 3;
                     
                case 60 
                    F3_j = 26525;
                    F3_k = 16314;
                    F3_m = 0;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 61 
                    F3_j = 27577;
                    F3_k = 18161;
                    F3_m = 3841;
                    F3_n = -3;
                    F3_i1 = 1;
                     
                case 62 
                    F3_j = 11820;
                    F3_k = 48834;
                    F3_m = 24936;
                    F3_n = -3;
                    F3_i1 = 2;
                     
                case 63 
                    F3_j = 926;
                    F3_k = 34536;
                    F3_m = 62639;
                    F3_n = -1;
                    F3_i1 = 1;
                     
                case 64 
                    F3_j = 34242;
                    F3_k = 21476;
                    F3_m = 0;
                    F3_n = 2;
                    F3_i1 = -3;
                     
                case 97 
                    F3_j = 11937;
                    F3_k = 0;
                    F3_m = 54278;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 98 
                    F3_j = 11129;
                    F3_k = 0;
                    F3_m = 41060;
                    F3_n = 1;
                    F3_i1 = -3;
                     
                case 99 
                    F3_j = 16232;
                    F3_k = 0;
                    F3_m = 37025;
                    F3_n = 3;
                    F3_i1 = -2;
                     
                case 100 
                    F3_j = 62287;
                    F3_k = 21359;
                    F3_m = 0;
                    F3_n = -1;
                    F3_i1 = 1;
                     
                case 101 
                    F3_j = 19345;
                    F3_k = 63583;
                    F3_m = 20313;
                    F3_n = -2;
                    F3_i1 = 2;
                     
                case 102 
                    F3_j = 50636;
                    F3_k = 34432;
                    F3_m = 58878;
                    F3_n = -2;
                    F3_i1 = 2;
                     
                case 103 
                    F3_j = 8636;
                    F3_k = 42038;
                    F3_m = 0;
                    F3_n = 3;
                    F3_i1 = -1;
                     
                case 104 
                    F3_j = 49296;
                    F3_k = 0;
                    F3_m = 23727;
                    F3_n = -2;
                    F3_i1 = 2;
                     
                case 105 
                    F3_j = 62603;
                    F3_k = 0;
                    F3_m = 7632;
                    F3_n = 2;
                    F3_i1 = -1;
                     
                case 106 
                    F3_j = 54947;
                    F3_k = 13952;
                    F3_m = 0;
                    F3_n = -3;
                    F3_i1 = 2;
                     
                case 107 
                    F3_j = 46336;
                    F3_k = 0;
                    F3_m = 32973;
                    F3_n = -1;
                    F3_i1 = 3;
                     
                case 108 
                    F3_j = 31276;
                    F3_k = 0;
                    F3_m = 41988;
                    F3_n = -2;
                    F3_i1 = 2;
                     
                case 109 
                    F3_j = 24959;
                    F3_k = 31354;
                    F3_m = 55064;
                    F3_n = 1;
                    F3_i1 = -1;
                     
                case 110 
                    F3_j = 39963;
                    F3_k = 29660;
                    F3_m = 0;
                    F3_n = 2;
                    F3_i1 = -3;
                     
                case 111 
                    F3_j = 16360;
                    F3_k = 6010;
                    F3_m = 0;
                    F3_n = 1;
                    F3_i1 = -2;
                     
                case 112 
                    F3_j = 50050;
                    F3_k = 36355;
                    F3_m = 34628;
                    F3_n = 3;
                    F3_i1 = -3;
                    
                end select         
    
    

F2_i = F3_i + F3_j 
F2_i = F2_i & $FFFF

IF (F3_n > 0) then
    F2_j = $FFFF & (F3_i << F3_n | F3_i >> 16 - F3_n)
ELSE
    F2_j = $FFFF & (F3_i >> -F3_n | F3_i << 16 + F3_n)
    
endif    

F2_k = F3_i + F3_k 
F2_k = F2_k & $FFFF

IF (F3_i1 > 0) then
    F2_m = $FFFF & (F2_k << F3_i1 | F2_k >> 16 - F3_i1);
ELSE
    F2_m = $FFFF & (F2_k >> -F3_i1 | F2_k << 16 + F3_i1);
    
endif    

F2_n = F2_j * F2_m

F2_i1 = F2_n + F3_m

key = F2_i1 & $FFFF

key = key << 8
key = key + top_l  

return

[richard]

not sure that pbp correctly left or right shifts negative numbers , see henriks treatise on the bme280 for correct method to deal with signed ints

http://www.picbasic.co.uk/forum/showthread.php?t=24134


ps , i did notice that some cases may lead to doing a left or right shift of a negative number of bits, eg [var << -3 ] i'm not sure how gcc would resolve that

[retepsnikrep]

I agree that does look like a problem, thanks for the heads up.

[retepsnikrep]

I think I have this cracked now thanks to generous help on this and other forums.

In the end I did not need the large lookup table as it was always using the same table entry.

So my code ended up being tiny and did not require LONGS etc. .

W0 VAR WORD
W1 VAR WORD
W2 VAR WORD

SEED1 VAR BYTE 
SEED2 VAR BYTE 
SEED3 VAR BYTE  

'KEY1 = 46336;
'KEY3 = 32973;
'SHIFT1 = 1;   (-1)
'SHIFT2 = 3;       
    
' Calculates and stores the results of two cryptographic operations 
' on the first two seed bytes in W1 and W2
' 
' The operation being carried out consists of adding two 16-bit values
' and performing a bitwise rotation on the result.
' 
' The two results are calculated from adding the 2 seed bytes to both
' KEY1 and KEY2, with a rotation of SHIFT1 and SHIFT2 respectively. 

SEED1 = $C7
SEED2 = $B0
SEED3 = $6B      

'Answer should be $82 $CB $6B


W1.BYTE0 = SEED2
W1.BYTE1 = SEED1

W0 = W1 + 46336 'Key1            

' Does a cyclic bitwise rotation of B0-bits on W0

W0 = (W0 >> 1 | W0 << ($10 - 1))   'Note this is a negative shift

W2 = W0
W0 = W1     

' Does a cyclic bitwise rotation of B0-bits on W0

W0 = (W0 << 3 | W0 >> ($10 - 3))   'Note this is a positive shift

W1 = W0

' Multiplies the contents of W1 and W2 and adds KEY3, stores in W0
' Impicitly calculates 16-bit overflow only

W0 = W1 * W2
W0 = W0 + 32973   'KEY3      

SEED1 = W0.BYTE1
SEED2 = W0.BYTE0

[retepsnikrep]

Are there any optimisations I have missed in the final code in my prev post?