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Showing posts with label PhD. Show all posts
Showing posts with label PhD. Show all posts

## Tuesday 5 September 2023

### 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.

## Sunday 25 April 2021

### Exploring What a PhD Is Like

Some weeks ago, it was my pleasure, and honour, to be invited to participate as a panellist in the online event Explore What a PhD is Like organised by PhD Social Support Network from Loughborough University. The event aimed to give undergraduate and postgraduate students a summary of Doctoral Researchers’ lives and an idea of what it’s like to do a PhD at Loughborough University.

With so much confusing and contradictory information out there, it becomes a bit difficult to have a good understanding of many things before embarking on doing a PhD. So I decided to write down my answers for those of you who could not attend the event and are interested in doing a PhD. Because we were four panellists, I just answered some questions, but in this post, I share my answers to all questions, which mainly depend on my personal circumstances and experiences at Loughborough University — And I do hope to help clear some things up. In case that you have any other questions, please let me know in the comment section.

HELLO, I'M PERCY REYES! — a book lover, healthy lifestyle lover... I've been working as a senior SQL Server Database Administrator (DBA) for over 20 years; I'm a three-time awarded Microsoft Data Platform MVP. I'm currently doing a PhD in Computer Science (cryptography) at Loughborough University, England — working on cryptographic Boolean functions, algorithmic cryptanalysis, number theory, and other algebraic aspects of cryptography. READ MORE