Anthropic researchers, using the internal version of Claude, restored the origin of the mysterious numbers, which in the late 1990 "s chose the parameters of the five elliptical curves of NIST. The model coped in less than half an hour and found that the numbers received from a conventional generator of pseudo-random numbers running with a tag of system time. The security of the ECDSA does not affect, change keys or algorithms is not necessary.
The mystery lasted for more than 25 years. When cryptography is standardized on elliptic curves for P-192, P-224, P-256, P-384, and P-521, 160-bit initial values were published. They were handed over by the US National Security Agency, but no one explained the way of choice. The opaque origin of the parameters has long been suspicious: cryptographers admitted that the numbers could be specifically selected for the sake of the unknown other properties of curves.
For a long time one of the main versions remained a joke phrase, which was allegedly missed through the hash function. Claude went the other way and tried to understand which code of the late 1990's could leave a noticeable mathematical trace in the published values. The trace led to lrand48, the old pseudorandom number generator from the C library.
The scheme was simple. Program launched lrand48, using the Unix time tag, then consistently received 20-byte variants and tested them for the future curve. For example, for the P-256, the generator started from the time of August 16, 1997, and the standardized value appeared after the selection of 1842 candidates.
Claude first noticed a characteristic pattern in the bits of published numbers, then restored the internal state of the generator and scrolled it back. For all five simple NIST curves, dates were made between May 1997 and April 1998. The same mechanism explained five more values from the ANSI X9.62 standard. The restored states of the generator are re-issued by all 160 bits of source numbers, so the random coincidence is almost excluded.
The find does not prove mathematically that when choosing curves, no one tried to achieve a hidden property. However, the version of the pre-prepared bookmark became much less plausible: researchers got a simple and reproducible way of appearing numbers that used to seem arbitrary.
A few questions remained. The generator sometimes passed candidates who also approached known criteria, and the reason researchers have not yet found. The initial value of the B-163 curve could not be restored. Claude also attributed the origin of the base point to P-192 and several ANSI curves, but the selection of the base points P-224, P-256, P-384 and P-521 is still a mystery.
For the solution of the origin of the numbers previously appointed a reward of $36 864. After solving the problem, the entire amount was decided to transfer the non-profit organization Internet Security Research Group.
The mystery lasted for more than 25 years. When cryptography is standardized on elliptic curves for P-192, P-224, P-256, P-384, and P-521, 160-bit initial values were published. They were handed over by the US National Security Agency, but no one explained the way of choice. The opaque origin of the parameters has long been suspicious: cryptographers admitted that the numbers could be specifically selected for the sake of the unknown other properties of curves.
For a long time one of the main versions remained a joke phrase, which was allegedly missed through the hash function. Claude went the other way and tried to understand which code of the late 1990's could leave a noticeable mathematical trace in the published values. The trace led to lrand48, the old pseudorandom number generator from the C library.
The scheme was simple. Program launched lrand48, using the Unix time tag, then consistently received 20-byte variants and tested them for the future curve. For example, for the P-256, the generator started from the time of August 16, 1997, and the standardized value appeared after the selection of 1842 candidates.
Claude first noticed a characteristic pattern in the bits of published numbers, then restored the internal state of the generator and scrolled it back. For all five simple NIST curves, dates were made between May 1997 and April 1998. The same mechanism explained five more values from the ANSI X9.62 standard. The restored states of the generator are re-issued by all 160 bits of source numbers, so the random coincidence is almost excluded.
The find does not prove mathematically that when choosing curves, no one tried to achieve a hidden property. However, the version of the pre-prepared bookmark became much less plausible: researchers got a simple and reproducible way of appearing numbers that used to seem arbitrary.
A few questions remained. The generator sometimes passed candidates who also approached known criteria, and the reason researchers have not yet found. The initial value of the B-163 curve could not be restored. Claude also attributed the origin of the base point to P-192 and several ANSI curves, but the selection of the base points P-224, P-256, P-384 and P-521 is still a mystery.
For the solution of the origin of the numbers previously appointed a reward of $36 864. After solving the problem, the entire amount was decided to transfer the non-profit organization Internet Security Research Group.
