Minerva: Lattice attacks strike again
> This page describes our discovery of a group of side-channel vulnerabilities in implementations of ECDSA/EdDSA in programmable smart cards and cryptographic software libraries. Our attack allows for practical recovery of the long-term private key. We have found implementations which leak the bit-length of the scalar during scalar multiplication on an elliptic curve. This leakage might seem minuscule as the bit-length presents a very small amount of information present in the scalar. However, in the case of ECDSA/EdDSA signature generation, the leaked bit-length of the random nonce is enough for full recovery of the private key used after observing a few hundreds to a few thousands of signatures on known messages, due to the application of lattice techniques.