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@CanalQb no YouTube

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Analisando Entropia em Chaves Públicas Hexadecimais

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Sempre crie uma frase de segurança única para jogos, testnets ou airdrops e evite usar sua carteira principal.

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Análise de Entropia em Chaves Públicas Hexadecimais com Python

Neste artigo, apresentamos um estudo prático sobre entropia em chaves públicas representadas no formato hexadecimal. Utilizando Python, realizamos a conversão dessas chaves para bits e avaliamos a distribuição estatística dos bits através do cálculo de entropia. Este tipo de análise é útil em criptografia e segurança digital para avaliar o grau de aleatoriedade de uma chave, o que está diretamente ligado à sua força contra ataques.

O Que é Entropia?

Na ciência da informação, a entropia mede a imprevisibilidade ou aleatoriedade de um conjunto de dados. Em criptografia, uma chave com alta entropia é geralmente considerada mais segura, pois oferece maior resistência a ataques de força bruta ou previsibilidade estatística.

Objetivo do Script

O objetivo principal deste script é calcular a entropia de uma grande lista de valores hexadecimais que representam possíveis chaves públicas. Esses valores são convertidos para bits, e em seguida aplicamos a fórmula da entropia de Shannon para mensurar a aleatoriedade de cada chave.

Funcionalidades Implementadas

• Conversão de hexadecimal para sequência de bits
• Cálculo de entropia bit a bit
• Comparação entre entropia atual e anterior
• Relatório linha a linha sobre o tamanho da chave, valor e comparação

Exemplo de Saída

Exemplo de Saída

Linha 1 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000001 - Entropia (0.000000 bits) - Tamanho da chave pública (256) bits - Nenhum comparativo anterior
Linha 2 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000002 - Entropia (0.081705 bits) - Tamanho da chave pública (256) bits - Maior
Linha 3 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000003 - Entropia (0.125000 bits) - Tamanho da chave pública (256) bits - Maior
Linha 4 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000004 - Entropia (0.094009 bits) - Tamanho da chave pública (256) bits - Menor
Linha 5 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000008 - Entropia (0.000000 bits) - Tamanho da chave pública (256) bits - Menor
Linha 6 - Chave Pública: 000000000000000000000000000000000000000000000000000000000000000F - Entropia (0.250000 bits) - Tamanho da chave pública (256) bits - Maior
Linha 7 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000010 - Entropia (0.000000 bits) - Tamanho da chave pública (256) bits - Menor
Linha 8 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000020 - Entropia (0.081705 bits) - Tamanho da chave pública (256) bits - Maior
Linha 9 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000040 - Entropia (0.094009 bits) - Tamanho da chave pública (256) bits - Maior
Linha 10 - Chave Pública: 0000000000000000000000000000000000000000000000000000000000000080 - Entropia (0.000000 bits) - Tamanho da chave pública (256) bits - Menor

Código Python Completo

import math

def hex_to_bits(hex_string):
    bin_string = bin(int(hex_string, 16))[2:].zfill(len(hex_string) * 4)
    return bin_string

def calculate_entropy(bits):
    bit_counts = {'0': bits.count('0'), '1': bits.count('1')}
    total_bits = len(bits)
    probabilities = [bit_counts['0'] / total_bits, bit_counts['1'] / total_bits]
    entropy = -sum(p * math.log2(p) for p in probabilities if p > 0)
    return entropy

public_keys = [
"1","1","1",
"2","3","3",
"4","7","7",
"8","8","f",
"10","15","1f",
"20","31","3f",
"40","000000000000000000000000000000000000000000000000000000000000004c","7f",
"80","e0","ff",
"100","00000000000000000000000000000000000000000000000000000000000001d3","1ff",
"200","202","3ff",
"400","483","7ff",
"800","0000000000000000000000000000000000000000000000000000000000000a7b","fff",
"1000","1460","1fff",
"2000","2930","3fff",
"4000","00000000000000000000000000000000000000000000000000000000000068f3","7fff",
"8000","000000000000000000000000000000000000000000000000000000000000c936","ffff",
"10000","000000000000000000000000000000000000000000000000000000000001764f","1ffff",
"20000","000000000000000000000000000000000000000000000000000000000003080d","3ffff",
"40000","000000000000000000000000000000000000000000000000000000000005749f","7ffff",
"80000","00000000000000000000000000000000000000000000000000000000000d2c55","fffff",
"100000","00000000000000000000000000000000000000000000000000000000001ba534","1fffff",
"200000","00000000000000000000000000000000000000000000000000000000002de40f","3fffff",
"400000","556e52","7fffff",
"800000","0000000000000000000000000000000000000000000000000000000000dc2a04","ffffff",
"1000000","0000000000000000000000000000000000000000000000000000000001fa5ee5","1ffffff",
"2000000","000000000000000000000000000000000000000000000000000000000340326e","3ffffff",
"4000000","0000000000000000000000000000000000000000000000000000000006ac3875","7ffffff",
"8000000","000000000000000000000000000000000000000000000000000000000d916ce8","fffffff",
"10000000","0000000000000000000000000000000000000000000000000000000017e2551e","1fffffff",
"20000000","000000000000000000000000000000000000000000000000000000003d94cd64","3fffffff",
"40000000","000000000000000000000000000000000000000000000000000000007d4fe747","7fffffff",
"80000000","00000000000000000000000000000000000000000000000000000000b862a62e","ffffffff",
"100000000","00000000000000000000000000000000000000000000000000000001a96ca8d8","1ffffffff",
"200000000","000000000000000000000000000000000000000000000000000000034a65911d","3ffffffff",
"400000000","00000000000000000000000000000000000000000000000000000004aed21170","7ffffffff",
"800000000","00000000000000000000000000000000000000000000000000000009de820a7c","fffffffff",
"1000000000","0000000000000000000000000000000000000000000000000000001757756a93","1fffffffff",
"2000000000","00000000000000000000000000000000000000000000000000000022382facd0","3fffffffff",
"4000000000","0000000000000000000000000000000000000000000000000000004b5f8303e9","7fffffffff",
"8000000000","000000000000000000000000000000000000000000000000000000e9ae4933d6","ffffffffff",
"10000000000","00000000000000000000000000000000000000000000000000000153869acc5b","1ffffffffff",
"20000000000","000000000000000000000000000000000000000000000000000002a221c58d8f","3ffffffffff",
"40000000000","000000000000000000000000000000000000000000000000000006bd3b27c591","7ffffffffff",
"80000000000","00000000000000000000000000000000000000000000000000000e02b35a358f","fffffffffff",
"100000000000","0000000000000000000000000000000000000000000000000000122fca143c05","1fffffffffff",
"200000000000","00000000000000000000000000000000000000000000000000002ec18388d544","3fffffffffff",
"400000000000","00000000000000000000000000000000000000000000000000006cd610b53cba","7fffffffffff",
"800000000000","0000000000000000000000000000000000000000000000000000ade6d7ce3b9b","ffffffffffff",
"1000000000000","000000000000000000000000000000000000000000000000000174176b015f4d","1ffffffffffff",
"2000000000000","00000000000000000000000000000000000000000000000000022bd43c2e9354","3ffffffffffff",
"4000000000000","00000000000000000000000000000000000000000000000000075070a1a009d4","7ffffffffffff",
"8000000000000","000000000000000000000000000000000000000000000000000efae164cb9e3c","fffffffffffff",
"10000000000000","00000000000000000000000000000000000000000000000000180788e47e326c","1fffffffffffff",
"20000000000000","00000000000000000000000000000000000000000000000000236fb6d5ad1f43","3fffffffffffff",
"40000000000000","000000000000000000000000000000000000000000000000006abe1f9b67e114","7fffffffffffff",
"80000000000000","000000000000000000000000000000000000000000000000009d18b63ac4ffdf","ffffffffffffff",
"100000000000000","00000000000000000000000000000000000000000000000001eb25c90795d61c","1ffffffffffffff",
"200000000000000","00000000000000000000000000000000000000000000000002c675b852189a21","3ffffffffffffff",
"400000000000000","00000000000000000000000000000000000000000000000007496cbb87cab44f","7ffffffffffffff",
"800000000000000","0000000000000000000000000000000000000000000000000fc07a1825367bbe","fffffffffffffff",
"1000000000000000","00000000000000000000000000000000000000000000000013c96a3742f64906","1fffffffffffffff",
"2000000000000000","000000000000000000000000000000000000000000000000363d541eb611abee","3fffffffffffffff",
"4000000000000000","0000000000000000000000000000000000000000000000007cce5efdaccf6808","7fffffffffffffff",
"8000000000000000","000000000000000000000000000000000000000000000000f7051f27b09112d4","ffffffffffffffff",
"10000000000000000","000000000000000000000000000000000000000000000001a838b13505b26867","1ffffffffffffffff",
"20000000000000000","000000000000000000000000000000000000000000000002832ed74f2b5e35ee","3ffffffffffffffff",
"40000000000000000","00000000000000000000000000000000000000000000000730fc235c1942c1ae","7ffffffffffffffff",
"80000000000000000","00000000000000000000000000000000000000000000000bebb3940cd0fc1491","fffffffffffffffff",
"100000000000000000","","1fffffffffffffffff",
"200000000000000000","349b84b6431a6c4ef1","3fffffffffffffffff",
"400","483","7ff",
]

def main():
    pula = 0
    previous_entropy = None
    for i, pub_key_hex in enumerate(public_keys, start=1):
        if pub_key_hex == "0":
            continue
        pub_key_hex = pub_key_hex.zfill(64)
        pub_key_bits = hex_to_bits(pub_key_hex)
        entropy = calculate_entropy(pub_key_bits)
        if pula % 3 == 0:
            print()
        if previous_entropy is not None:
            if entropy > previous_entropy:
                maiormenor = "Maior"
            elif entropy < previous_entropy:
                maiormenor = "Menor"
            else:
                maiormenor = "Igual"
            print(f"Linha {i} - Chave Pública: {pub_key_hex.upper()} - Entropia ({entropy:.6f} bits) - Tamanho da chave pública ({len(pub_key_bits)}) bits - {maiormenor}")
        else:
            print(f"Linha {i} - Chave Pública: {pub_key_hex.upper()} - Entropia ({entropy:.6f} bits) - Tamanho da chave pública ({len(pub_key_bits)}) bits - Nenhum comparativo anterior")
        previous_entropy = entropy
        pula += 1

    print(calculate_entropy(hex_to_bits('400'.zfill(64))))
    print(calculate_entropy(hex_to_bits('483'.zfill(64))))
    print(calculate_entropy(hex_to_bits('7ff'.zfill(64))))
    print()
    print(calculate_entropy(hex_to_bits('400')))
    print(calculate_entropy(hex_to_bits('483')))
    print(calculate_entropy(hex_to_bits('7ff')))

if __name__ == "__main__":
    main()

Considerações Finais

Este tipo de análise é extremamente útil para programadores, pesquisadores de segurança e entusiastas de criptografia que desejam entender melhor o comportamento estatístico de chaves criptográficas. A entropia é uma métrica importante no desenvolvimento de sistemas mais seguros e no estudo de algoritmos criptográficos eficientes.

Referência

Se quiser aprofundar o estudo sobre manipulação de chaves e criptografia em Python, recomendo visitar a documentação oficial do Python: https://docs.python.org/3/