Skip to main content

Featured Post

Backdooring Cryptography - Two characters that break your SSL encryption

In this article, we demonstrate a subtle but devastating backdoor in finite-field Diffie–Hellman. By computing public keys modulo $p^2$ instead of $p$ while restricting the secret exponent to $x \leq p-1$, the discrete logarithm becomes efficiently recoverable using Fermat quotients. We show the full derivation and provide a working Sage implementation. Backdoors are always bad — but they are catastrophic when they are embedded in a fundamental primitive like Diffie–Hellman key exchange. If your browser shows a green lock, you assume your connection is secure. But what if the implementation of Diffie–Hellman contains a tiny change that looks harmless in code review — and yet allows an attacker to recover the private exponent in milliseconds? In this post I’ll show a nasty little backdoor that requires only a tiny modification: using a modulus of $p^2$ instead of $p$, while keeping the secret exponent bounded by $p$ This ...
Post a Comment

Gallery

In this gallery you will find some drawings i did in the past and that are related to some aspects that are covered in this blog. My drawings, so my Copyright only :)

Cryptography
Indistinguishability Obfuscation

Kryptos K4 - Speculations


Mathematics
The Pointcaré Conjecture

P vs. NP

The Yang-Mills Mass Gap



The Riemann-Hypothesis

 
The Birch and Swinnerton-Dyer Conjecture


The Navier-Stokes Equations


Comments

Post a Comment

Popular posts from this blog

Kryptos - The Cipher (Part 4) - Correctly positioned decryption of the word BERLIN

EASTNORTHEAST - This is not exactly the hint Jim Sanborn (JS) gave for K4 on the 29th of January this year. He only gave NORTHEAST - which refers to the positions 26-34 of K4's plaintext.  Beside BERLIN and CLOCK it is the third revealed plaintext word of K4. However, also this hint does not seem to help much.  However, it just so happened, that a member in the yahoo kryptos group had a conversation with Jim Sanborn due to a submitted solution. Sandborn's answer to the question contained again the last clue which surprisingly was EASTNORTHEAST at position 22-34. Jim Sanborns compass rose at CIA There is disagreement if Jim revealed this on purpose or he did it accidentially, but the new extended clue seem to be serious and valid.Interestingly, EASTNORTHEAST is exactly the direction which is illustrated on the compass rose on one of the stones around kryptos, also created by Jim Sanborn. Actually, i dont really kn...
116 comments
Read more

Kryptos - The Cipher (Part 1) - Introduction

Introduction. Since I think that KRYPTOS does not need any introduction, I will only give you a brief description of one of the most famous and only partially solved ciphers known today: KRYPTOS - Von Jim Sanborn - Jim Sanborn, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=8253447 KRYPTOS was constructed in Nov. 1990 on the ground of the CIA Headquarter in Langley, Virginia by Jim Sanborn It contains 4 ciphers (K1,K2,K3,K4) on its left side and some kind of Vigenère-Table on its right side K1, K2 and K3 were solved by James Gillogly in 1999. Afterwards, the CIA and later the NSA claimed that they had a solution to the first three ciphers at an earlier point in time Ed Scheidt, a cryptoanalyst and former director of the CIA, gave Sanborn the input of possible cryptographic techniques to use K1 is a variant of the Vigenère-Cipher (Quagmire 3) with the codewords KRYPTOS and PALIMPSES...
7 comments
Read more

Kryptos - The Cipher (Part 3) - K4 Intentional vs. non-intentional errors

This post is about is more or less a collection of several approaches and facts that has been said as well as some speculations. B-ary integer representation According to [1] during a Question and Answer round, Jim Sanborn was asked again about the hint BERLIN. The question was if N decodes to B, Y decodes to E, etc, etc. and Jim confirmed it does. Emphatically . It is written, that Jim Sanborn rattled through the entire crib: \begin{align}   \texttt{N} &\stackrel{\text{decode}}{\rightarrow} \texttt{B} \\   \texttt{Y} &\stackrel{\text{decode}}{\rightarrow}  \texttt{E} \\   \texttt{P} &\stackrel{\text{decode}}{\rightarrow}  \texttt{R} \\   \texttt{V} &\stackrel{\text{decode}}{\rightarrow}  \texttt{L} \\   \texttt{T} &\stackrel{\text{decode}}{\rightarrow}  \texttt{I} \\   \texttt{T} &\stackrel{\text{decode}}{\rightarrow}  \texttt{N} \end{align} When the same q...
1 comment
Read more