Math

Linear Regression

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Regression analysis and its relation with Machine Learning Machine learning is the field of study that explores the construction of algorithms that learn from data and can make predictions about it. It is a field of artificial intelligence that uses statistical methods to give those predictions. And it’s name comes from the ability that it gives to computer systems to learn from data, without being explicitly programmed. Machine learning by itself sometimes isn’t the best answer, but it can be combined with specialist agents to expand it’s capabilities and reduce the training time. Read More...

Bitcoin transaction nonce reuse vulnerability

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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

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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...