Math

Bitcoin transaction nonce reuse vulnerability

published on
This post aims to analyse an attack against the Bitcoin, in this attack were Found 123 vulnerable transactions and 416 private keys were recovered summing up 26.85729198 btcs (2685729198 satoshis) could have been compromised, which at this exact moment worth 166,219.51 dollars. Cryptographic concept of the attack When the nonce is reused it become vulnerable and result in a trivial equation to be solved. $$ Key=((r \times (s_1 - s_2))^{p - 2} \mod{p}) \times ((m_1 \times s_2) - (m_2 \times s_1)) \mod{p} $$ Read More...

Linear Programming

published on
Linear programming is a mathematical method to achieve the best result for a given problem. This problem is expressed through a mathematical model which represents the real world problem. Also called linear optimization because of it’s essence to optimize a linear objective function. In other words, linear programming aim to find the optimal input value for the function, value which will also be the optimal solution for the problem. Usually linear optimization is a good method to solve assignment problems which are a fundamental kind of combinatorial optimization problems. Read More...