VanitySearch

(Link to Jean-Luc PONS GitHub https://github.com/JeanLucPons)

VanitySearch is a bitcoin address prefix finder. If you want to generate safe private keys, use the -s option to enter your passphrase which will be used for generating a base key as for BIP38 standard (VanitySearch.exe -s “My PassPhrase” 1MyPrefix). You can also use VanitySearch.exe -ps “My PassPhrase” which will add a crypto secure seed to your passphrase.

• Fixed size arithmetic
• Fast Modular Inversion (Delayed Right Shift 62 bits)
• SecpK1 Fast modular multiplication (2 steps folding 512bits to 256bits using 64 bits digits)
• Use some properties of elliptic curve to generate more keys
• SSE Secure Hash Algorithm SHA256 and RIPEMD160 (CPU)
• Multi-GPU support
• CUDA optimisation via inline PTX assembly
• Seed protected by pbkdf2_hmac_sha512 (BIP38)
• Support P2PKH, P2SH and BECH32 addresses
• Support split-key vanity address

VanitySearch [-check] [-v] [-u] [-b] [-c] [-gpu] [-stop] [-i inputfile]
             [-gpuId gpuId1[,gpuId2,...]] [-g g1x,g1y,[,g2x,g2y,...]]
             [-o outputfile] [-m maxFound] [-ps seed] [-s seed] [-t nbThread]
             [-nosse] [-r rekey] [-check] [-kp] [-sp startPubKey]
             [-rp privkey partialkeyfile] [prefix]

 prefix: prefix to search (Can contains wildcard '?' or '*')
 -v: Print version
 -u: Search uncompressed addresses
 -b: Search both uncompressed or compressed addresses
 -c: Case unsensitive search
 -gpu: Enable gpu calculation
 -stop: Stop when all prefixes are found
 -i inputfile: Get list of prefixes to search from specified file
 -o outputfile: Output results to the specified file
 -gpu gpuId1,gpuId2,...: List of GPU(s) to use, default is 0
 -g g1x,g1y,g2x,g2y, ...: Specify GPU(s) kernel gridsize, default is 8*(MP number),128
 -m: Specify maximun number of prefixes found by each kernel call
 -s seed: Specify a seed for the base key, default is random
 -ps seed: Specify a seed concatened with a crypto secure random seed
 -t threadNumber: Specify number of CPU thread, default is number of core
 -nosse: Disable SSE hash function
 -l: List cuda enabled devices
 -check: Check CPU and GPU kernel vs CPU
 -cp privKey: Compute public key (privKey in hex hormat)
 -kp: Generate key pair
 -rp privkey partialkeyfile: Reconstruct final private key(s) from partial key(s) info.
 -sp startPubKey: Start the search with a pubKey (for private key splitting)
 -r rekey: Rekey interval in MegaKey, default is disabled

The bitcoin address (P2PKH) consists of a hash160 (displayed in Base58 format) which means that there are 2¹⁶⁰ possible addresses. A secure hash function can be seen as a pseudo number generator, it transforms a given message in a random number. In this case, a number (uniformaly distributed) in the range [0,2¹⁶⁰]. So, the probability to hit a particular number after n tries is 1-(1-1/2¹⁶⁰)ⁿ. We perform n Bernoulli trials statistically independent.
If we have a list of m distinct addresses (m<=2¹⁶⁰), the search space is then reduced to 2¹⁶⁰/m, the probability to find a collision after 1 try becomes m/2¹⁶⁰ and the probability to find a collision after n tries becomes 1-(1-m/2¹⁶⁰)ⁿ.
An example:
We have a hardware capable of generating 1GKey/s and we have an input list of 10⁶ addresses, the following table shows the probability of finding a collision after a certain amount of time:

Calculation has been done using this online high precision calculator