The initial depoyment of SegWit will not enable Schnorr signatures, will it? Won't they require a hard fork anyway?

Even with Schnorr signatures, the miners would still have to accept old-style multisigs produced by old clients, right?  Then an attacker could still generate those hard-to-validate blocks, no?

As a temporary fix, a soft fork can be deployed limiting the max number of signatures.  Even a low limit like 100 is no restriction, only a small annoyance for the few users who would want to use more   It woudl be a good use of an "arbitrary numerical limit", like the 1 MB limit was when it was introduced.  

But there is no logical reason why signature validation should take quadratic time.  That is a bug in the protocol, that should be fixed by changing the algorithm -- with a hard fork if need be.

(By the way,  [for a couple of hours today](https://statoshi.info/dashboard/db/transactions?from=1458258715516&to=1458259562505) there was an apparent "stress test" where each transaction was 10 kB long (rather than the usual 0.5 kB).  Was the "tester" trying to generate such troll blocks?)

Linear scaling of sighash operations

A major problem with simple approaches to increasing the Bitcoin blocksize is that for certain transactions, signature-hashing scales quadratically rather than linearly.

Linear versus quadratic

In essence, doubling the size of a transaction increases can double both the number of signature operations, and the amount of data that has to be hashed for each of those signatures to be verified. This has been seen in the wild, where an individual block required 25 seconds to validate, and maliciously designed transactions could take over 3 minutes.

Segwit resolves this by changing the calculation of the transaction hash for signatures so that each byte of a transaction only needs to be hashed at most twice. This provides the same functionality more efficiently, so that large transactions can still be generated without running into problems due to signature hashing, even if they are generated maliciously or much larger blocks (and therefore larger transactions) are supported.
Who benefits?

Removing the quadratic scaling of hashed data for verifying signatures makes increasing the block size safer. Doing that without also limiting transaction sizes allows Bitcoin to continue to support payments that go to or come from large groups, such as payments of mining rewards or crowdfunding services.

The modified hash only applies to signature operations initiated from witness data, so signature operations from the base block will continue to require lower limits.