Why RSA2048 sign of Intel accelerate card is fast? Intel accelerate card

This card executes rsa2048 sign 35K ops(operation/second). My fast version is only 100 ops.

I can't find any HSM paper that has same performance level.

I am interested in this problem. I know modexp, montgomery, crt, PE-array and some other circuit skills, but I can't reach such a high performance.

Could someone give me a hand please? Thanks very much.
Specialized hardware is the answer. This machine uses asynchronous computation, very likely using parallel Montgomery multipliers and a local register of 4096 bits (4096 seems to be the largest key size for RSA, so we can conclude that this is the size of the register). Similar hardware can be found in Smart Card CPU's. These don't go as fast, because they are hampered by low power consumption, TDP, a relatively slow - often 8/16 bit - CPU and large transistor sizes. The solution requires OpenSSL 1.1 to utilize the asynchronous API that the Intel QuickAssist hardware offers.

Newer Intel chips have vectoring instructions that also help to speedup the multiplication and squaring required to perform fast modular exponentiation (the base of any RSA calculation). However, they don't offer a Montgomery multiplier of sufficient size to overtake fully specialized hardware (actually, the use of the vectoring constructions may quickly lead to overheating and scaling down of processor frequencies).

It's unlikely you can beat specialized hardware in software; modular exponentiation is not a cheap operation (it's only fast compared to finding large primes required for RSA key pair generation). Furthermore, you may make a very fast implementation that is not protected against side channel attacks, which is a major requirement for keeping your private key secure.

Note that the specialized hardware is not an RSA accelerator (that the software delivered with the hardware does offer). It performs the mathematical operations more quickly. It can also be used to speed up (EC)DH and (EC)DSA, for instance.