Guys, I am a madman and want to try BSGS for old 50 BTC addresses (pubkeys) in full 2^256 range. (There are over 34k of them)
Is there a software currently to do that? I mean software/program
E-ZPassMD that accepts over 80 bits and up to 256?
Hello,
While attempting to crack 256-bit private keys for Bitcoin addresses using the Baby-step Giant-step (BSGS) algorithm might sound like an exciting endeavor, it's crucial to understand the practical limitations and the current state of technology.
Practicality of BSGS for 256-bit Keys
Computational Infeasibility: The keyspace for Bitcoin private keys is 2
256
. The BSGS algorithm has a time and space complexity of approximately
N
, where N is the order of the group. In the case of ECDSA over the secp256k1 curve used by Bitcoin, N is roughly 2
256
. Therefore, a full BSGS attack would require approximately 2
128
operations and storage, which is computationally infeasible with current and foreseeable technology. To put this into perspective, 2
80
operations are considered at the very edge of what might be achievable with immense resources and time. 2
128
is astronomically larger.
Bitcoin Key Space: Bitcoin addresses are derived from public keys, which in turn are derived from private keys. The private keys are 256-bit numbers. Trying to find a private key corresponding to a given public key (or address) is an instance of the Elliptic Curve Discrete Logarithm Problem (ECDLP). BSGS is one algorithm for solving this, but its square root complexity makes it impractical for the scale of Bitcoin's key space.
Software for Large Keyspaces
Current Limitations: As of my last update in May 2025, there isn't any publicly known software capable of performing a full BSGS attack on key sizes anywhere close to 256 bits. The memory and computational resources required are simply too vast.
Research Focus: Research in cryptanalysis does explore algorithms for solving the ECDLP, and there are variations and optimizations of BSGS. However, these are generally theoretical or applicable to much smaller key sizes than 256 bits.
Specialized Hardware: While specialized hardware can accelerate cryptographic computations, even custom-designed ASICs would likely be unable to overcome the fundamental limitations posed by the
2
256
=2
128
complexity of BSGS.
Alternative Attack Vectors
It's worth noting that instead of trying to brute-force the entire 256-bit keyspace, attackers often look for vulnerabilities in:
Random Number Generation: If the private key generation process was flawed and didn't produce truly random numbers, the effective keyspace might be much smaller and potentially exploitable. However, Bitcoin's secp256k1 curve and standard practices aim to avoid such weaknesses.
Wallet Software: Vulnerabilities in wallet software could expose private keys through exploits, malware, or phishing attacks. These are often more practical attack vectors than trying to break the underlying cryptography.
Side-Channel Attacks: These attacks exploit physical characteristics of the devices performing cryptographic operations (e.g., power consumption, electromagnetic emissions) to try and extract secret information.
