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...
❚ Several weeks ago , i heard a nice talk from one of my colleagues about the Coppersmith method and it application to factoring integers. It is a very powerful method and can, e.g., be applied if partial information of $p$ or $q$ is known, the factors $p$ and $q$ of $N=pq$ have a small differences or to obtain a deterministic algorithm that returns a factor if a multiple of $\varphi(N)$ is known. The trigger for the talk was a discussion about the risk if the inverse of one factor modulo the other factor of an RSA modulus is leaked. That means knowing the following integer $I$: $$I \equiv p^{-1} \pmod{q},\;p,q \in \mathbb{P},\;N=pq$$ Since the Coppersmith method is very powerful it is actually not surprising that it could be used to accomplish this task, at least partially. ❰Coppersmith's Theorem❱ Let $0 < \beta < 1$ and $c,N \geq 1$ and $f \in \mathbb{Z}[x]$ be a monic polynomial of degree $\delta$. The set of all integer $a \in \mathbb{Z}$ with $$\gcd(f(a),N) \geq N...