Let $(N,e)$ be an RSA public key, where $N=pq$ is the product of equal bitsize primes $p,q$. Let $d_p, d_q$ be the corresponding secret CRT-RSA exponents.

Using a Coppersmith-type attack, Takayasu, Lu and Peng (TLP) recently showed that one obtains the factorization of $N$ in polynomial time, provided that $d_p, d_q leq N^{0.122}$. Building on the TLP attack, we show the first Partial Key Exposure attack on short secret exponent CRT-RSA. Namely, let $N^{0.122} leq d_p, d_q leq N^{0.5}$. Then we show that a constant known fraction of the least significant bits (LSBs) of both $d_p, d_q$ suffices to factor $N$ in polynomial time.

Naturally, the larger $d_p,d_q$, the more LSBs are required.
E.g. if $d_p, d_q$ are of size $N^{0.13}$, then we have to know roughly a $frac 1 5$-fraction of their LSBs, whereas for $d_p, d_q$ of size $N^{0.2}$ we require already knowledge of a $frac 2 3$-LSB fraction. Eventually, if $d_p, d_q$ are of full size $N^{0.5}$, we have to know all of their bits.
Notice that as a side-product of our result we obtain a heuristic deterministic polynomial time factorization algorithm on input $(N,e,d_p,d_q)$.

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