SHA-1 went from a theoretical break in 2005 to a real collision in 2017 and a rentable chosen-prefix attack in 2020. Here is what “broken” means, what an attack costs, and where SHA-1 still matters, from Git to NIST’s 2030 deadline.
Category: Science & Mathematics
Is the One-Time Pad Unbreakable? Shannon’s Proof and Venona
Claude Shannon proved that the one-time pad gives perfect secrecy, but only when the key is truly random, as long as the message, kept secret and never reused. Here is what the proof says, where the pad came from, and how reused pad pages exposed Soviet messages in Venona.
Hadamard Matrix of Order 668 Found: What It Means for the Conjecture
On 12 August 2026, a 668×668 Hadamard matrix was announced, settling the smallest open case of the Hadamard conjecture after about 20 years. This article covers how it was checked, why the AI credit is still provisional, and what remains unsolved.
Jacques Hadamard: Prime Numbers, Poincaré’s Seat and the H Gate
Jacques Hadamard (1865–1963) proved the prime number theorem in 1896, succeeded Poincaré at the Académie des Sciences and defined well-posed problems. Here is a carefully sourced account of his life that corrects errors repeated online.
Can Quantum Computers Break SHA-256? What Grover and BHT Really Do
Quantum computers weaken SHA-256 in a predictable, bounded way: about 128 bits of preimage security remain, and real hardware costs are far higher than the query counts suggest. Here is what Grover’s and BHT’s algorithms actually do.