Leaderboard

Literally the definition of Karatsuba, to split in half and perform on half length thus reducing the complexity of time needed not the complexity of the implementation, in case of 64bit then only two half is needed with no recursion, Wikipedia page explain it, but there is simpler resources on the Internet to explain it. Fun fact : There is also an algorithm named Toom-Cook https://en.wikipedia.org/wiki/Toom–Cook_multiplication reduce the multiplication further but increase the complexity of implementation more, both algorithm shift the operation into smaller part reducing the need for multiplication carry but increase the addition operation with its carry. Just common knowledge to whom may be interested. Yes it is simple, but if you want the most beautiful mathematically algorithm (i see it like that), is El-Gamal (sometimes written (ElGamal), and once you built your RSA you will find implementing ElGamal is relatively close and not any more a complex task, as you will need the little different or adjusted arithmetic, i mean you will have primality test along with GCD (GCD might be needed but that depend on your approach or method), ElGamal has a feature which can be used with Elliptic Curve and their finite fields hence decreasing the length of the keys substantially, so it might interest you and your friends ! https://en.wikipedia.org/wiki/ElGamal_encryption https://en.wikipedia.org/wiki/ElGamal_signature_scheme A little more detailed resources https://www.geeksforgeeks.org/elgamal-encryption-algorithm/ https://compare-encryption-algorithms.mojoauth.com/rsa-4096-vs-elgamal-variable-key-size/ Yup, nothing beats Miller–Rabin test in speed, it looks nice book. Focus on RSA !, ElGamal will need different beast https://en.wikipedia.org/wiki/Modular_exponentiation but after RSA you will find it easy as it is pretty straight forward as listed in Wikipedia. Again good luck.

It apparently is: It does not happen on my laptop with a single HD screen. Nor on my desktop when I turn off the 4K monitor or alternatively the HD monitor. And after starting Delphi once with only the HD monitor connected, it no longer happens with both monitors. Sounds like an easily reproducible problem, doesn't it?

I have never made my own classes before and I have just started to learn. There is one field FName in the class below. What if I have 50 different Fxxxxx? Do I have to write Setter and Getter for every field? Can I declare a record inside the class? Type TEmployee = class private FName : string; //FSalary : Currency; Function GetName : string; Procedure SetName(Const Value : string); public Property Name : string read GetName write SetName; end; implementation {$R *.dfm} Function TEmployee.GetName: string; begin Result:=FName; end; Procedure TEmployee.SetName(const Value: string); begin if value='' then raise Exception.Create('Name must have a value'); FName:=value; end;

I don't have any of the mentioned above IDEs, but i see a problem or two .. well more than that a lot, but will talk about your exact problem first 1) The directives are wrong and mixed, and here how they should look like function TRandom.Next(Bits: Integer): UInt32; begin {$IFOPT R+} {$DEFINE HasRangeChecks} {$ENDIF} {$IFOPT Q+} {$DEFINE HasOverflowChecks} {$ENDIF} {$RANGECHECKS OFF} {$OVERFLOWCHECKS OFF} FSeed := (FSeed * CMultiplier + CIncrement); Result := UInt32(FSeed shr (64 - Bits)); // Use the highest bits; Lower bits have lower period. {$IFDEF HasRangeChecks} {$RANGECHECKS ON} {$ENDIF} {$IFDEF HasOverflowChecks} {$OVERFLOWCHECKS ON} {$ENDIF} end; Because we have two overflow check can be triggered here, not one !, Integer overflow range overflow come from multiplication and form truncation while mixing signed and unsigned, both need to be disabled, also the R+ for the range while wrongly was Q. 2) I tried this small test procedure RunTest; var Rand: IRandom; A, B, C: BigInteger; begin Rand := TRandom.Create($FF00FE01FD02FC03); // sooner ! Trigger overflow check at TRandomBase.NextBytes //Rand := TRandom.Create($FF00FF01FF02FF03); // Trigger overflow check at TRandom.Next A.Create(1024, Rand); B.Create(1024, Rand); C := A * C; Writeln('A = ' + A.ToHexString); Writeln('B = ' + B.ToHexString); Writeln('C = ' + C.ToHexString); end; And we have another place that has an overflow, but the fix is easy (again sign bit!!) procedure TRandomBase.NextBytes(var Bytes: array of Byte); var Head, Tail: Integer; N, {Rnd,} I: Integer; Rnd : UInt32; // <--- fix overflow begin Didn't go through more tests or any deeper in digging into the source. Now to the other problems 3) This pseudorandom number generator is not cryptographically secure , it has very small duration and depend on single modular operation which is 2^(64-Bits)= 2^k, this can't be considered secure it is as predictable as it can be by design, but choosing 2^k make brute force algorithm for it way much faster ! 4) I don't understand from where the assumption of only 48 bits are only used, this is strange and out of the context or this family of PRNG, may be i missed something with Bits, but will not dig deeper in it. 5) the core problem is depending on Int64, this is signed and by using signed we lose a bit and confuse the compiler and math, while gains nothing in return, this family of PRNG which call LCG https://en.wikipedia.org/wiki/Linear_congruential_generator doesn't handle signed numbers, and doesn't need as it is by definition, so using Int64 should be replaced with UInt64 for the constants, and the algorithm too. 6) tried to figure out this code You are going with Karatsuba https://en.wikipedia.org/wiki/Karatsuba_algorithm , nice it is the right way when you are in the corner, also much cleaner for limbs, yet the last masking is again wrong assuming (you are following the original code) it can or should be signed operation, this should be changed to unsigned, and return the sign bit to the fold, as it is by design is using the highest 32 bit, by losing the sign, where entropy is lost, we left with 31 bit randomness. About learning and implementing RSA, yes do it and you will learn much, and i wish you good luck, also a suggestion : why not read more about CSPRNG and implement one ,a cryptographically secure (CS) one, there is one i liked very much due it speed and portability, it is based on CHAHCA with reduced rounds called ChaCha8, it use the same permutation as ChaCha20 but with 8 rounds, it is secure and small as it can be, and used in Go Lang applications extensively, anyway it is not so important and most important thing is understanding is that security is like a chain and the chain is weak as its weakest link, randomness is always the most crucial link that when break (insecure) it will render everything built on it insecure, and last suggestion if you are going to use you own implementation of RSA in production for clients then test it then test it and test it again and think a lot before using your own implementation, it is not recommended by anyone ( as i think you read again and again, things like don't implement your own...), but you should learn it inside out, so go with it.

You can reserve a video against embedding, so that might be a factor?

It works very well for multithreading. You just have to change the sampling mode.

You are using the version of FormatDateTime() that relies on global variables initialized with your PC's locale settings. For instance, the '/' specifier is not a literal slash character, it is a placeholder that uses the global DateSeparator variable in the SysUtils unit. This is documented behavior. You can update those globals to customize things like the date/time separators, but this affects the whole app, and is not thread-safe. When you need custom formatting that is locale-agnostic, you should use the version of FormatDateTime() that takes a TFormatSettings parameter, eg: procedure TForm1.Button1Click(Sender: TObject); var lDate: TDateTime; lFmt: TFormatSettings; begin lFmt := TFormatSettings.Create; lFmt.DateSeparator := '/'; lDate := EncodeDate(2025, 3, 26); Edit1.Text := FormatDateTime('dd/mm/yyyy', lDate, lFmt); end; The alternative is to wrap desired literal text with quotes in your format string, eg: procedure TForm1.Button1Click(Sender: TObject); var lDate: TDateTime; begin lDate := EncodeDate(2025, 3, 26); Edit1.Text := FormatDateTime('dd"/"mm"/"yyyy', lDate); end;

That is pretty trivial to implement, eg: procedure TMainForm.GoBtnClick(Sender: TObject); var url: string; idx: integer; begin { change this https://www.youtube.com/watch?v=ZJhJILyS388 to this https://www.youtube.com/embed/ZJhJILyS388 } url := StringReplace(addresscb.Text, 'watch?v=', 'embed/', [rfIgnoreCase]); addressCb.Text := url; WVBrowser1.Navigate(url); idx := ComboBox1.Items.IndexOf(url); if idx = -1 then ComboBox1.Items.Add(url); end;