[ { "recipient_type": "channel", "channel": "Day 2: Intro to RSA", "color": "#94C849", "topic": "factorization algorithms", "users": { "Manvir Singh": "static/images/characters/starr.png", "Zoe Davis": "static/images/characters/starr.png", "Maxy Stert": "" }, "messages": [ { "sender": "Manvir Singh", "content": "You could use [Pollard's rho algorithm](#), which factors a number n in time $$O(n^{\\frac{1}{4}})$$, faster than trial division:\n\n```python\ndef pollard_rho(n: int) -> int:\n g = lambda x: (x ** 2 + 1) % n\n x, y, d = 2, 2, 1\n while d == 1:\n x, y = g(x), g(g(y))\n d = math.gcd(x - y, n)\n return d\n```", "reactions": { "+1": ["Zoe Davis"] }, "date": {"year": 2024, "month": 5, "day": 14, "hour": 16, "minute": 59} }, { "sender": "Zoe Davis", "content": "The fastest known algorithm is the general number field sieve, which heuristically runs in time:\n$$\\exp\\left(\\left(\\sqrt[3]{\\frac{64}{9}} + o(1)\\right) + (\\ln n)^{\\frac{1}{3}} (\\ln\\ln n)^{\\frac{2}{3}}\\right)$$\n However, it is much more complicated.", "reactions": { "runner": ["Manvir Singh"], "thinking": ["Maxy Stert", "Iago"] }, "date": {"year": 2024, "month": 5, "day": 14, "hour": 18, "minute": 19} } ], "screenshot": "static/images/landing-page/research/image_1.png" }, { "recipient_type": "channel", "channel": "general", "color": "#9987E1", "topic": "paper posted", "users": { "John Lin": "static/images/characters/starr.png", "Anna Smith": "static/images/characters/starr.png", "Bo Lin": "" }, "messages": [ { "sender": "John Lin", "content": "Hi all! We just posted a pre-publication draft of our paper! Sharing here for feedback, suggestions, etc. [paper.pdf](#)", "reactions": { "tada": ["John Lin", "Iago", "Anna Smith", "Bo Lin"], "eyes": ["Anna Smith", "Iago"] }, "date": {"year": 2024, "month": 5, "day": 13, "hour": 14, "minute": 39} }, { "sender": "Anna Smith", "content": "Just noticed a small typo in Figure 4. The caption says `detales` instead of `details`. :smile:", "reactions": { "check": ["John Lin"] }, "date": {"year": 2024, "month": 5, "day": 13, "hour": 14, "minute": 57} } ], "screenshot": "static/images/landing-page/research/image_2.png" }, { "recipient_type": "channel", "channel": "thesis support group", "color": "#95A5FD", "topic": "chat live", "users": { "Zoe Davis": "static/images/characters/starr.png", "James Williams": "static/images/characters/starr.png", "Bo Lin": "", "Nolan Turner": "" }, "messages": [ { "sender": "Zoe Davis", "content": "Hey! How does sound for doing a video call today? My paper just got rejected.", "reactions": { "+1": ["James Williams", "Iago", "Zoe Davis", "Bo Lin", "Nolan Turner"], "broken_heart": ["James Williams", "Iago", "Zoe Davis", "Nolan Turner"] }, "date": {"year": 2024, "month": 5, "day": 13, "hour": 15, "minute": 15} }, { "sender": "James Williams", "content": "I need to send off a draft of chapter 2 to my advisor. Will try to make it!", "date": {"year": 2024, "month": 5, "day": 13, "hour": 15, "minute": 34} }, { "sender": "Zoe Davis", "content": "@**everyone** Video call is happening now! [Join video call.](#)", "date": {"year": 2024, "month": 5, "day": 13, "hour": 16, "minute": 30} } ], "screenshot": "static/images/landing-page/research/image_3.png" } ]