arXiv:1908.05127cs.CR
Breaking the encryption scheme of the Moscow Internet voting system
Abstract
In September 2019, voters for the election at the Parliament of the city of Moscow were allowed to use an Internet voting system. The source code of it had been made available for public testing. In this paper we show two successful attacks on the encryption scheme implemented in the voting system. Both attacks were sent to the developers of the system, and both issues had been fixed after that.The encryption used in this system is a variant of ElGamal over finite fields. In the first attack we show that the used key sizes are too small. We explain how to retrieve the private keys from the public keys in a matter of minutes with easily available resources.When this issue had been fixed and the new system had become available for testing, we discovered that the new implementation was not semantically secure. We demonstrate how this newly found security vulnerability can be used for counting the number of votes cast for a candidate.
The article doesn't mention this, but if you look at the paper[1] it turns out they aren't using ElGamal with elliptic curve fields -- instead they're using prime fields. In that case, you'd want similar key sizes to RSA. (The "less than 256 bit" part is a red herring, the…
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The paper[1] makes it much clearer. They aren't using elliptic curves, they're using prime fields with ElGamal (with a weird construction using three separate keys for some reason). The security is similar to RSA-256 (in other words, "awful") -- it makes sense that they could…
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The paper notes another, distinct, attack possibility: > Before going to this, we mention quickly another mistake in the design that could in itself have led to devastating attacks. The generators that are given in public- key.json are generators of the whole multiplicative…
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