The existence of the endomorphism is a roughly 20% speedup in a plain multi-exp due to halving the number of doublings. What it does is gives many algorithms which could be batched across multiple point the efficiency they'd have at twice the number of pubkeys.  It's a pretty big speedup and AFAIK at an equivalent level of optimization it makes secp256k1 the fastest to verify of any widely deployed curve. So the motivation there is pretty clear, I think.

Could you give more info on this because I don't see how to have efficient decomposition k.P= (k1+k2.lambda).P using such lambda.
Thanks

Hello,

I would like to present an interval ECDLP solver based on the Pollard's kangaroo method.
This program is fully open source and available on GitHub: https://github.com/JeanLucPons/Kangaroo
It has GPU support (CUDA Only) and works on both Linux and Windows.
This program is currently under development.

Thanks to test it and to share ideas of improvements here

Hello,

I would like to present a new bitcoin prefix address finder called VanitySearch. It is very similar to Vanitygen.
The main differences with Vanitygen are that VanitySearch is not using the heavy OpenSSL for CPU calculation and that the kernel is written in Cuda in order to take full advantage of inline PTX assembly.
On my Intel Core i7-4770, VanitySearch runs ~4 times faster than vanitygen64. (1.32 Mkey/s -> 5.27  MK/s)
On my  GeForce GTX 645, VanitySearch runs ~1.5 times faster than oclvanitygen. (9.26 Mkey/s -> 14.548 MK/s)
If you want to compare VanitySearch and Vanitygen result, use the -u option for searching uncompressed address.
VanitySearch may not compute a good gridsize for your GPU, so make several tries using -g options in order to find best performances.
Using compressed addresses is roughly 20% faster.

VanitySearch is available from https://github.com/JeanLucPons/VanitySearch

Benchmarks for various hardware (By DaveF):
https://bitcointalk.org/index.php?topic=5112311.msg50823897#msg50823897

There is still lots of improvement to do.
Feel free to test it and to submit issue.

Thanks.
Sorry for my bad English.
Jean-Luc