On the web, you can find a lot of controversy regarding the hacking of Bitcoin Wallets. The result of the discussion is the selection of two main ways: by gaining access to the PC of cryptocurrency owners and through the selection of private keys (с помощью личных данных пользователя). Bitcoin and other cryptocurrencies traditionally attract increased attention хакеров of various calibers,…

In this article, we implement an efficient Frey-Rück Attack algorithm for signing ECDSAa transaction on the Bitcoin blockchain. In our earlier posts, we touched on the topic of signature vulnerability several times ECDSA. With a critical vulnerability in the Bitcoin blockchain transaction, we can solve the rather difficult discrete logarithm problem to extract the ECDSA secret key"K" (NONCE) from the vulnerable signature in order to ultimately…

There are many forms to create a Bitcoin wallet. One of the first methods to create a Bitcoin wallet was known as  BrainWallet .BrainWallet convenient in the sense that it allows you to store in memory or in a notebook  " passphrase " . The passphrase is hashed using an algorithm  SHA-256, and is used as the seed to generate the  private key . Due to their popularity and…

Over the years, a whole cult has formed in the crypto community to create beautiful addresses for crypto wallets. Everyone can generate a "beautiful" address for themselves, which will not only be unique, but will also contain a certain combination of letters and numbers. This is a very exciting and interesting process, but the risk associated with involving a…

In pursuit of qubits,  Baidu Inc  , as the leader among Chinese search engines, does not lag behind its Western competitor  Alphabet Inc. In August 2022, Chinese search engine giant Baidu Inc developed its own quantum computer, soon dubbed "Qianshi". All super-powerful computers use quantum physics to solve complex problems that traditional devices cannot, using qubits, an evolution of the classic…

We all know the phrase:  "Everything that gets on the Internet, remains in it forever and becomes publicly available." Down to hidden content. The  2021 году pandemic brought back popularity  QR-кодов. For  the first time QR-коды they were used in production in  1994 году a subsidiary  Toyota in Japan and introduced them at an assembly plant to control produced cars and parts for them. Unlike a barcode,  QR-код it contains more…

We all know that the disclosure of the secret key in the ECDSA signature can lead to the complete recovery of the Bitcoin Wallet. In our earlier articles, we looked at weaknesses and vulnerabilities in blockchain transactions, but there are also ECDSA short signatures that also lead to the full recovery of a Bitcoin Wallet. Why are these ECDSA signatures…

In this article, we will try to show how you can reduce the private key knowing only the leak from the "BLOCKCHAIN ​​FOLBIT LEAKS" list and the public key from "UTXO" . In the experimental part, we will use the 08ReducePrivateKey scripts and restore the Bitcoin Wallet. Elliptic curve scalar multiplication is the operation of adding a pointPto the curvektimes. Q=kP=P+P+P, k times Pis a…

In this article, we will look  secp256k1 at the endomorphism acceleration function that helps in optimizing the validation  ECDSA for the Bitcoin cryptocurrency, but first, a little history. 12 января 2009 года Satoshi Nakamoto sent Hal Finney   in the earliest bitcoin transactions  10 BTC. That Satoshi Nakamoto chose Hal as the first recipient of Bitcoins is not surprising. Satoshi had great respect for Hal, who established…

In this article, we will look at the fastest algorithm for ECDLP from the field of computational number theory, Pollard's kangaroo is also called Pollard's lambda algorithm. Pollard's kangaroo method computes  discrete logarithms  in arbitrary cyclic groups. It is applied if the discrete logarithm is known to lie in a certain range, say  [ a , b ], and then has…