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ffa_ch6_simplest_...    1 ------------------------------------------------------------------------------
ffa_ch6_simplest_...    2 ------------------------------------------------------------------------------
ffa_ch6_simplest_...    3 -- This file is part of 'Finite Field Arithmetic', aka 'FFA'.               --
ffa_ch6_simplest_...    4 --                                                                          --
ffa_ch6_simplest_...    5 -- (C) 2017 Stanislav Datskovskiy ( www.loper-os.org )                      --
ffa_ch6_simplest_...    6 -- http://wot.deedbot.org/17215D118B7239507FAFED98B98228A001ABFFC7.html     --
ffa_ch6_simplest_...    7 --                                                                          --
ffa_ch6_simplest_...    8 -- You do not have, nor can you ever acquire the right to use, copy or      --
ffa_ch6_simplest_...    9 -- distribute this software ; Should you use this software for any purpose, --
ffa_ch6_simplest_...   10 -- or copy and distribute it to anyone or in any manner, you are breaking   --
ffa_ch6_simplest_...   11 -- the laws of whatever soi-disant jurisdiction, and you promise to         --
ffa_ch6_simplest_...   12 -- continue doing so for the indefinite future. In any case, please         --
ffa_ch6_simplest_...   13 -- always : read and understand any software ; verify any PGP signatures    --
ffa_ch6_simplest_...   14 -- that you use - for any purpose.                                          --
ffa_ch6_simplest_...   15 --                                                                          --
ffa_ch6_simplest_...   16 -- See also http://trilema.com/2015/a-new-software-licensing-paradigm .     --
ffa_ch6_simplest_...   17 ------------------------------------------------------------------------------
ffa_ch6_simplest_...   18 ------------------------------------------------------------------------------
ffa_ch6_simplest_...   19 
ffa_ch6_simplest_...   20 with FZ_Basic; use FZ_Basic;
ffa_ch6_simplest_...   21 with FZ_Pred;  use FZ_Pred;
ffa_ch6_simplest_...   22 with FZ_Shift; use FZ_Shift;
ffa_ch6_simplest_...   23 with FZ_Mul;   use FZ_Mul;
ffa_ch12_karatsub...   24 with FZ_Sqr;   use FZ_Sqr;
ffa_ch6_simplest_...   25 with FZ_Divis; use FZ_Divis;
ffa_ch6_simplest_...   26 
ffa_ch6_simplest_...   27 
ffa_ch6_simplest_...   28 package body FZ_ModEx is
ffa_ch6_simplest_...   29    
ffa_ch6_simplest_...   30    -- Modular Multiply: Product := X*Y mod Modulus
ffa_ch6_simplest_...   31    procedure FZ_Mod_Mul(X        : in  FZ;
ffa_ch6_simplest_...   32                         Y        : in  FZ;
ffa_ch6_simplest_...   33                         Modulus  : in  FZ;
ffa_ch6_simplest_...   34                         Product  : out FZ) is
ffa_ch6_simplest_...   35       
ffa_ch6_simplest_...   36       -- The wordness of all three operands is equal:
ffa_ch6_simplest_...   37       L     : constant Indices := X'Length;
ffa_ch6_simplest_...   38       
ffa_ch6_simplest_...   39       -- Double-width register for multiplication and modulus operations
ffa_ch6_simplest_...   40       XY    : FZ(1 .. L * 2);
ffa_ch6_simplest_...   41       
ffa_ch6_simplest_...   42       -- To refer to the lower and upper halves of the working register:
ffa_ch6_simplest_...   43       XY_Lo : FZ renames XY(1     .. L);
ffa_ch6_simplest_...   44       XY_Hi : FZ renames XY(L + 1 .. XY'Last);
ffa_ch6_simplest_...   45       
ffa_ch6_simplest_...   46    begin
ffa_ch6_simplest_...   47       
ffa_ch6_simplest_...   48       -- XY_Lo:XY_Hi := X * Y
ffa_ch11_tuning_a...   49       FZ_Multiply_Buffered(X, Y, XY_Lo, XY_Hi);
ffa_ch6_simplest_...   50       
ffa_ch7_turbo_egy...   51       -- Product := XY mod M
ffa_ch7_turbo_egy...   52       FZ_Mod(XY, Modulus, Product);
ffa_ch6_simplest_...   53       
ffa_ch6_simplest_...   54    end FZ_Mod_Mul;
ffa_ch6_simplest_...   55    
ffa_ch6_simplest_...   56    
ffa_ch12_karatsub...   57    -- Modular Squaring: Product := X*X mod Modulus
ffa_ch12_karatsub...   58    procedure FZ_Mod_Sqr(X        : in  FZ;
ffa_ch12_karatsub...   59                         Modulus  : in  FZ;
ffa_ch12_karatsub...   60                         Product  : out FZ) is
ffa_ch12_karatsub...   61       
ffa_ch12_karatsub...   62       -- The wordness of both operands is equal:
ffa_ch12_karatsub...   63       L     : constant Indices := X'Length;
ffa_ch12_karatsub...   64       
ffa_ch12_karatsub...   65       -- Double-width register for squaring and modulus operations
ffa_ch12_karatsub...   66       XX    : FZ(1 .. L * 2);
ffa_ch12_karatsub...   67       
ffa_ch12_karatsub...   68       -- To refer to the lower and upper halves of the working register:
ffa_ch12_karatsub...   69       XX_Lo : FZ renames XX(1     .. L);
ffa_ch12_karatsub...   70       XX_Hi : FZ renames XX(L + 1 .. XX'Last);
ffa_ch12_karatsub...   71    
ffa_ch12_karatsub...   72    begin
ffa_ch12_karatsub...   73       
ffa_ch12_karatsub...   74       -- XX_Lo:XX_Hi := X^2
ffa_ch12_karatsub...   75       FZ_Square_Buffered(X, XX_Lo, XX_Hi);
ffa_ch12_karatsub...   76       
ffa_ch12_karatsub...   77       -- Product := XX mod M
ffa_ch12_karatsub...   78       FZ_Mod(XX, Modulus, Product);
ffa_ch12_karatsub...   79       
ffa_ch12_karatsub...   80    end FZ_Mod_Sqr;
ffa_ch12_karatsub...   81    
ffa_ch12_karatsub...   82    
ffa_ch6_simplest_...   83    -- Modular Exponent: Result := Base^Exponent mod Modulus
ffa_ch6_simplest_...   84    procedure FZ_Mod_Exp(Base     : in  FZ;
ffa_ch6_simplest_...   85                         Exponent : in  FZ;
ffa_ch6_simplest_...   86                         Modulus  : in  FZ;
ffa_ch6_simplest_...   87                         Result   : out FZ) is
ffa_ch6_simplest_...   88       
ffa_ch8_randomism.kv   89       -- Working register for the squaring; initially is copy of Base
ffa_ch6_simplest_...   90       B : FZ(Base'Range)     := Base;
ffa_ch6_simplest_...   91       
ffa_ch8_randomism.kv   92       -- Copy of Exponent, for cycling through its bits
ffa_ch6_simplest_...   93       E : FZ(Exponent'Range) := Exponent;
ffa_ch6_simplest_...   94       
ffa_ch6_simplest_...   95       -- Register for the Mux operation
ffa_ch6_simplest_...   96       T : FZ(Result'Range);
ffa_ch6_simplest_...   97       
ffa_ch8_randomism.kv   98       -- Buffer register for the Result
ffa_ch8_randomism.kv   99       R : FZ(Result'Range);
ffa_ch8_randomism.kv  100       
ffa_ch6_simplest_...  101    begin
ffa_ch6_simplest_...  102       -- Result := 1
ffa_ch8_randomism.kv  103       WBool_To_FZ(1, R);
ffa_ch6_simplest_...  104       
ffa_ch8_randomism.kv  105       -- For each bit of R width:
ffa_ch8_randomism.kv  106       for i in 1 .. FZ_Bitness(R) loop
ffa_ch6_simplest_...  107          
ffa_ch6_simplest_...  108          -- T := Result * B mod Modulus
ffa_ch8_randomism.kv  109          FZ_Mod_Mul(X => R, Y => B, Modulus => Modulus, Product => T);
ffa_ch6_simplest_...  110          
ffa_ch6_simplest_...  111          -- Sel is the current low bit of E;
ffa_ch6_simplest_...  112          --    When Sel=0 -> Result := Result;
ffa_ch6_simplest_...  113          --    When Sel=1 -> Result := T
ffa_ch8_randomism.kv  114          FZ_Mux(X => R, Y => T, Result => R, Sel => FZ_OddP(E));
ffa_ch6_simplest_...  115          
ffa_ch6_simplest_...  116          -- Advance to the next bit of E
ffa_ch6_simplest_...  117          FZ_ShiftRight(E, E, 1);
ffa_ch6_simplest_...  118          
ffa_ch12_karatsub...  119          -- B := B^2 mod Modulus
ffa_ch12_karatsub...  120          FZ_Mod_Sqr(X => B, Modulus => Modulus, Product => B);
ffa_ch6_simplest_...  121          
ffa_ch6_simplest_...  122       end loop;
ffa_ch6_simplest_...  123       
ffa_ch8_randomism.kv  124       -- Output the Result:
ffa_ch8_randomism.kv  125       Result := R;
ffa_ch8_randomism.kv  126       
ffa_ch6_simplest_...  127    end FZ_Mod_Exp;
ffa_ch6_simplest_...  128    
ffa_ch6_simplest_...  129 end FZ_ModEx;