Just a Little Bit More

We extend the FLUSH+RELOAD side-channel attack of Benger et al. to extract a significantly larger number of bits of information per observed signature when using OpenSSL. This means that by observing only 25 signatures, we can recover secret keys of the secp256k1 curve, used in the Bitcoin protocol, with a probability greater than 50 percent. This is an order of magnitude improvement over the previously best known result. The new method of attack exploits two points: Unlike previous partial disclosure attacks we utilize all information obtained and not just that in the least significant or most significant bits, this is enabled by a property of the “standard” curves choice of group order which enables extra bits of information to be extracted. Furthermore, whereas previous works require direct information on ephemeral key bits, our attack utilizes the indirect information from the wNAF double and add chain.