a calculator for large natural numbers (original) (raw)

bdcalc is a command-line calculator and mini-programming language that works with very large unsigned integers, the natural numbers ℕ = { 0,1,2,…} used to carry out computations in cryptography. The numbers can theoretically be of unlimited size. bdcalc has been built using our free BigDigits library.

bdcalc has built-in functions (see below) to carry out number theoretical computations such as modular exponentiation and modular inversion, as used in the RSA and Diffie-Hellman algorithms. You can generate random prime numbers of a given bit length and test for primality.

bdcalc provides a mini-programming environment with assignments to stored variables, conditional statements (if-then-else) and control loops (for, while, repeat). See the documentation for more details.

You can use bdcalc in interactive mode, typing commands on the console until you type quit to exit. Alternatively you can read input directly from a script file using the -file option; or you can enter your input in one line on the command line, perhaps as part of a batch file.

New update

2026-04-05: Released new version 2.3 - see What's new
Download it now

Example session |Built-in Functions |Example Scripts |Documentation |Download |What's new |Acknowledgements |Contact Us

Example session

bdcalc lets you assign numbers to variables, do arithmetic and call functions in the way you would expect.

a=99 99 b=a*11 1089 ? a+b 1188 println("a =",a,"b =",b) a = 99 b = 1089 p=genprime(128) 187188849449410847765185120249130623559 !p 0x8cd342d39544246b9743c7b68d5da247 bitlen(p) 128 ??isprime(p) true x=1;y=2;z=x+y;?z 3 for i in (1..15) do print(prime(i), " ") done; println("") 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

Built-in Functions

Function Returns Remarks
binomial(n,k)† the value of n choose k n!/k!(n−k)!
bitlen(X) the bit length l of the integer X 2_l_−1 ≤ x < 2_l_
bytelen(X) the length L of integer X in bytes
cbrt(X) the truncated integer cube root of X ⎣3√{x} ⎦
compl(X,n) the bitwise NOT of the rightmost n bits of X
factorial(n)† the value of factorial n n!
fillbytes(n,b) an integer of n bytes each set to b mod 256
gcd(X,Y,Z,...) the greatest common divisor of X,Y,Z,...
genprime(n) a random prime p of length exactly n bits 2n−1 ≤ p < 2n
getbit(X,n) value 0 or 1 of bit n of X =(b_l_−1…bn…b1b0)
getbyte(X,n) value of byte n of X
iif(B,X,Y) X if B is true, otherwise Y [Note 1]
isprime(X) true if X is prime, otherwise false [Note 2]
jacobi(X,M) the Jacobi symbol (X | M) in {0,1,2}, 2 ⇒ −1 [Note 3]
max(X,Y,Z,...) the maximum of X,Y,Z,...
min(X,Y,Z,...) the minimum of X,Y,Z,...
modexp(X,Y,M) X raised to the power Y modulo M xy mod m
modinv(X,M) the inverse of X modulo M x−1 mod m
modmul(X,Y,M) X multiplied by Y modulo M xy mod m
modpowof2(X,n) X with all bits cleared at positions ≥ n x mod 2n
permutations(n,k)† the value of n permute k n!/(n−k)!
pow(X,n) X raised to the power n xn
prime(n) the n-th prime number 1 ≤ n ≤ 104
randbits(n) a random integer r of length at most n bits 0 ≤ r < 2n
random(M) an integer r generated at random from [0, M-1] 0 ≤ r < M
revbytes(X,[n]) X as an n-byte integer with its byte order reversed
setbit(X,n,b) X =(b_l_−1…bn…b1b0) with bit n set to value b b ∈ {0,1}
setbyte(X,n,b) X with byte n set to value b mod 256
sha1(X,n) the SHA-1 hash of the rightmost n bits of X [Note 4]
sha256(X,n) the SHA-256 hash of the rightmost n bits of X [Note 4]
sqrt(X) the truncated integer square root of X ⎣√x ⎦
square(X) the square of X x2

† new in version 2.3

For notes and examples of use, see the manual.

Displaying numbers in decimal and hexadecimal

To enter a number in hexadecimal, prefix it with "0x". It will display automatically in decimal. To display a number in hexadecimal, print with the "!" command.

0xdeadbeefcafebabebeddeddecadedeed 295990755076957304711832595911747231469 ! 295990755076957304711832595911747231469 0xdeadbeefcafebabebeddeddecadedeed

Example scripts

qr_find.bdscr

How to find a quadratic residue by exhaustive search (source)

discretelog.bdscr

Compute discrete logarithm (source)

primes1000.bdscr

Write out the first 1000 primes (source)

rsa_make.bdscr

Make an RSA key pair and test it (source)

rsa_make_exact.bdscr

Make an RSA key pair of exact bit length (source)

rsa_quint.bdscr

Perform RSA calculation with private key in CRT quintuple form (source)

rsacrack.bdscr

Crack RSA if used incorrectly to three recipients (source)

rDSA.bdscr

Example of the rDSA algorithm from ANSI X9.31 (source)

dsa_test.bdscr

Example of DSA from Appendix 5 FIPS PUB 186-2 (source)

dh_gen.bdscr

Generate domain parameters for Diffie-Hellman (source)

dh_keyexch.bdscr

Perform Diffie-Hellman key exchange using parameters generated above (source)

poly1305.bdscr

Poly1305 Example and Test Vector (source)

Documentation

bdcalc manual in PDF

bdcalc manual in HTML

Download

**Windows:**Download the latest bdcalc installation program now. Use either

Unzip the zip file and run the Install.exe program inside it, or download the exe program directly and run it. The latest version is 2.3.0 released 5 April 2026.

Windows binary: bdcalc is a simple stand-alone Windows EXE file just 270 kB in size. If you just want the plain bdcalc.exe file to install yourself, plus the help and sample scripts, download bdcalc-files.zip (575 kB).

Linux x86_64 binary: bdcalc-linux.x86.zip (634 kB) [sha1=3c0c99fd8b5a30d37b50cf6f631317e04951ca4f]

See the included README file for installation instructions.

The executable bdcalc has been compiled using gcc on an x86_64 platform. It has worked for us just by copying onto three separate Linux platforms (Debian 12, Redhat, and Ubuntu 24 on WSL2).

Please note it is a breach of copyright to put a copy of these installation files on another server or to distribute them in any manner except by providing a link to this page.

bdcalc is free software. Please read the licence conditions.

What's new?

What's new? Version 2.3 released 5 April 2026.

Older:
Version 2.2 (17 June 2016) This fixes up a few annoyances we had with print and help and adds a couple of new functions.

dir file
BDCALC ERROR: syntax error at symbol 'file'
dir file
BDCALC ERROR: syntax error at symbol 'file'

WTF why isn't the dir command working?

? b # ... OH NO! ...

Acknowledgements

Contact

Any comments, feedback, questions: please send us a message.

This page first published 12 May 2013. Last updated 8 April 2026.