Probabilistic Estimation of the Algebraic Degree of Boolean Functions

Recently, our cryptography paper on "Probabilistic estimation of the algebraic degree of Boolean functions" was published in Springer Journal as a result of about 3 years of research: https://lnkd.in/eyEw5pce

𝐀𝐛𝐬𝐭𝐫𝐚𝐜𝐭: 𝘛𝘩𝘦 𝘢𝘭𝘨𝘦𝘣𝘳𝘢𝘪𝘤 𝘥𝘦𝘨𝘳𝘦𝘦 𝘪𝘴 𝘢𝘯 𝘪𝘮𝘱𝘰𝘳𝘵𝘢𝘯𝘵 𝘱𝘢𝘳𝘢𝘮𝘦𝘵𝘦𝘳 𝘰𝘧 𝘉𝘰𝘰𝘭𝘦𝘢𝘯 𝘧𝘶𝘯𝘤𝘵𝘪𝘰𝘯𝘴 𝘶𝘴𝘦𝘥 𝘪𝘯 𝘤𝘳𝘺𝘱𝘵𝘰𝘨𝘳𝘢𝘱𝘩𝘺. 𝘞𝘩𝘦𝘯 𝘢 𝘧𝘶𝘯𝘤𝘵𝘪𝘰𝘯 𝘪𝘯 𝘢 𝘭𝘢𝘳𝘨𝘦 𝘯𝘶𝘮𝘣𝘦𝘳 𝘰𝘧 𝘷𝘢𝘳𝘪𝘢𝘣𝘭𝘦𝘴 𝘪𝘴 𝘯𝘰𝘵 𝘨𝘪𝘷𝘦𝘯 𝘦𝘹𝘱𝘭𝘪𝘤𝘪𝘵𝘭𝘺 𝘪𝘯 𝘢𝘭𝘨𝘦𝘣𝘳𝘢𝘪𝘤 𝘯𝘰𝘳𝘮𝘢𝘭 𝘧𝘰𝘳𝘮, 𝘪𝘵 𝘪𝘴 𝘶𝘴𝘶𝘢𝘭𝘭𝘺 𝘯𝘰𝘵 𝘧𝘦𝘢𝘴𝘪𝘣𝘭𝘦 𝘵𝘰 𝘤𝘰𝘮𝘱𝘶𝘵𝘦 𝘪𝘵𝘴 𝘥𝘦𝘨𝘳𝘦𝘦, 𝘴𝘰 𝘸𝘦 𝘯𝘦𝘦𝘥 𝘵𝘰 𝘦𝘴𝘵𝘪𝘮𝘢𝘵𝘦 𝘪𝘵. 𝘞𝘦 𝘱𝘳𝘰𝘱𝘰𝘴𝘦 𝘢 𝘱𝘳𝘰𝘣𝘢𝘣𝘪𝘭𝘪𝘴𝘵𝘪𝘤 𝘵𝘦𝘴𝘵 𝘧𝘰𝘳 𝘥𝘦𝘤𝘪𝘥𝘪𝘯𝘨 𝘸𝘩𝘦𝘵𝘩𝘦𝘳 𝘵𝘩𝘦 𝘢𝘭𝘨𝘦𝘣𝘳𝘢𝘪𝘤 𝘥𝘦𝘨𝘳𝘦𝘦 𝘰𝘧 𝘢 𝘉𝘰𝘰𝘭𝘦𝘢𝘯 𝘧𝘶𝘯𝘤𝘵𝘪𝘰𝘯 𝘧 𝘪𝘴 𝘣𝘦𝘭𝘰𝘸 𝘢 𝘤𝘦𝘳𝘵𝘢𝘪𝘯 𝘷𝘢𝘭𝘶𝘦 𝘬. 𝘐𝘧 𝘵𝘩𝘦 𝘥𝘦𝘨𝘳𝘦𝘦 𝘪𝘴 𝘪𝘯𝘥𝘦𝘦𝘥 𝘣𝘦𝘭𝘰𝘸 𝘬, 𝘵𝘩𝘦𝘯 𝘧 𝘸𝘪𝘭𝘭 𝘢𝘭𝘸𝘢𝘺𝘴 𝘱𝘢𝘴𝘴 𝘵𝘩𝘦 𝘵𝘦𝘴𝘵, 𝘰𝘵𝘩𝘦𝘳𝘸𝘪𝘴𝘦 𝘧 𝘸𝘪𝘭𝘭 𝘧𝘢𝘪𝘭 𝘦𝘢𝘤𝘩 𝘪𝘯𝘴𝘵𝘢𝘯𝘤𝘦 𝘰𝘧 𝘵𝘩𝘦 𝘵𝘦𝘴𝘵 𝘸𝘪𝘵𝘩 𝘢 𝘱𝘳𝘰𝘣𝘢𝘣𝘪𝘭𝘪𝘵𝘺 𝘥𝘵_𝘬(𝘧), 𝘸𝘩𝘪𝘤𝘩 𝘪𝘴 𝘤𝘭𝘰𝘴𝘦𝘭𝘺 𝘳𝘦𝘭𝘢𝘵𝘦𝘥 𝘵𝘰 𝘵𝘩𝘦 𝘢𝘷𝘦𝘳𝘢𝘨𝘦 𝘯𝘶𝘮𝘣𝘦𝘳 𝘰𝘧 𝘮𝘰𝘯𝘰𝘮𝘪𝘢𝘭𝘴 𝘰𝘧 𝘥𝘦𝘨𝘳𝘦𝘦 𝘬 𝘰𝘧 𝘵𝘩𝘦 𝘱𝘰𝘭𝘺𝘯𝘰𝘮𝘪𝘢𝘭𝘴 𝘸𝘩𝘪𝘤𝘩 𝘢𝘳𝘦 𝘢𝘧𝘧𝘪𝘯𝘦 𝘦𝘲𝘶𝘪𝘷𝘢𝘭𝘦𝘯𝘵 𝘵𝘰 𝘧. 𝘛𝘩𝘦 𝘵𝘦𝘴𝘵 𝘩𝘢𝘴 𝘢 𝘨𝘰𝘰𝘥 𝘢𝘤𝘤𝘶𝘳𝘢𝘤𝘺 𝘰𝘯𝘭𝘺 𝘪𝘧 𝘵𝘩𝘪𝘴 𝘱𝘳𝘰𝘣𝘢𝘣𝘪𝘭𝘪𝘵𝘺 𝘥𝘵_𝘬(𝘧) 𝘰𝘧 𝘧𝘢𝘪𝘭𝘪𝘯𝘨 𝘵𝘩𝘦 𝘵𝘦𝘴𝘵 𝘪𝘴 𝘯𝘰𝘵 𝘵𝘰𝘰 𝘴𝘮𝘢𝘭𝘭. 𝘞𝘦 𝘪𝘯𝘪𝘵𝘪𝘢𝘵𝘦 𝘵𝘩𝘦 𝘴𝘵𝘶𝘥𝘺 𝘰𝘧 𝘥𝘵_𝘬(𝘧) 𝘣𝘺 𝘴𝘩𝘰𝘸𝘪𝘯𝘨 𝘵𝘩𝘢𝘵 𝘪𝘯 𝘵𝘩𝘦 𝘱𝘢𝘳𝘵𝘪𝘤𝘶𝘭𝘢𝘳 𝘤𝘢𝘴𝘦 𝘸𝘩𝘦𝘯 𝘵𝘩𝘦 𝘥𝘦𝘨𝘳𝘦𝘦 𝘰𝘧 𝘧 𝘪𝘴 𝘢𝘤𝘵𝘶𝘢𝘭𝘭𝘺 𝘦𝘲𝘶𝘢𝘭 𝘵𝘰 𝘬, 𝘵𝘩𝘦 𝘱𝘳𝘰𝘣𝘢𝘣𝘪𝘭𝘪𝘵𝘺 𝘸𝘪𝘭𝘭 𝘣𝘦 𝘪𝘯 𝘵𝘩𝘦 𝘪𝘯𝘵𝘦𝘳𝘷𝘢𝘭 (0.288788, 0.5], 𝘢𝘯𝘥 𝘵𝘩𝘦𝘳𝘦𝘧𝘰𝘳𝘦 𝘢 𝘴𝘮𝘢𝘭𝘭 𝘯𝘶𝘮𝘣𝘦𝘳 𝘰𝘧 𝘳𝘶𝘯𝘴 𝘰𝘧 𝘵𝘩𝘦 𝘵𝘦𝘴𝘵 𝘸𝘪𝘭𝘭 𝘣𝘦 𝘴𝘶𝘧𝘧𝘪𝘤𝘪𝘦𝘯𝘵 𝘵𝘰 𝘨𝘪𝘷𝘦, 𝘸𝘪𝘵𝘩 𝘷𝘦𝘳𝘺 𝘩𝘪𝘨𝘩 𝘱𝘳𝘰𝘣𝘢𝘣𝘪𝘭𝘪𝘵𝘺, 𝘵𝘩𝘦 𝘤𝘰𝘳𝘳𝘦𝘤𝘵 𝘢𝘯𝘴𝘸𝘦𝘳. 𝘌𝘹𝘢𝘤𝘵 𝘷𝘢𝘭𝘶𝘦𝘴 𝘰𝘧 𝘥𝘵_𝘬(𝘧) 𝘧𝘰𝘳 𝘢𝘭𝘭 𝘵𝘩𝘦 𝘱𝘰𝘭𝘺𝘯𝘰𝘮𝘪𝘢𝘭𝘴 𝘪𝘯 8 𝘷𝘢𝘳𝘪𝘢𝘣𝘭𝘦𝘴 𝘸𝘦𝘳𝘦 𝘤𝘰𝘮𝘱𝘶𝘵𝘦𝘥 𝘶𝘴𝘪𝘯𝘨 𝘵𝘩𝘦 𝘳𝘦𝘱𝘳𝘦𝘴𝘦𝘯𝘵𝘢𝘵𝘪𝘷𝘦𝘴 𝘭𝘪𝘴𝘵𝘦𝘥 𝘣𝘺 𝘏𝘰𝘶 𝘢𝘯𝘥 𝘣𝘺 𝘓𝘢𝘯𝘨𝘦𝘷𝘪𝘯 𝘢𝘯𝘥 𝘓𝘦𝘢𝘯𝘥𝘦𝘳.

Do You Want to Be a Cryptographer?

Alan Turing

I've always been interested in information security since 2003, but it wasn't until I enrolled on the cryptography module — while studying for a Master in Advanced Computer Science in England in 2018— that I started getting more keen on the mathematical side of cryptography; perhaps it was in part because I cherish mathematics and had the right cryptography teacher. What's more, I admire Alan Turing since he strove to do good work in difficult conditions during World War II; his work saved millions of lives. All of these things together inspired me to immerse myself in the world of cryptography.