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I suggest bcrypt. It is not a cryptographic hash function per se, but it could replace SHA-256 and add some memory constraints that would make its implementation harder on GPUs.

Bcrypt uses blowfish to encrypt a string with a key derived from a password chosen by the user. So given a string and a target, finding a password that encrypts the string below the target works exactly like the Bitcoin lottery.
As for the memory constraints, it is possible to implement bcrypt on a GPU, but it is much harder (probably impossible) to get the same kind of performance improvements we see with SHA. Here is an excerpt from a post on crypto stackexchangecrypto stackexchange about implementing bcrypt with cuda:

Now bcrypt is a variant of the Blowfish key scheduling, which is defined over a table (a few kilobytes) which is constantly accessed and modified throughout the algorithm. Due to the size of the table, each core will have to store it in the GPU main RAM, and they will compete for usage of the memory bus. So bcrypt will run -- but not with full parallelism. At any time, most cores will be stalled, waiting for the memory bus to become free.

I suggest bcrypt. It is not a cryptographic hash function per se, but it could replace SHA-256 and add some memory constraints that would make its implementation harder on GPUs.

Bcrypt uses blowfish to encrypt a string with a key derived from a password chosen by the user. So given a string and a target, finding a password that encrypts the string below the target works exactly like the Bitcoin lottery.
As for the memory constraints, it is possible to implement bcrypt on a GPU, but it is much harder (probably impossible) to get the same kind of performance improvements we see with SHA. Here is an excerpt from a post on crypto stackexchange about implementing bcrypt with cuda:

Now bcrypt is a variant of the Blowfish key scheduling, which is defined over a table (a few kilobytes) which is constantly accessed and modified throughout the algorithm. Due to the size of the table, each core will have to store it in the GPU main RAM, and they will compete for usage of the memory bus. So bcrypt will run -- but not with full parallelism. At any time, most cores will be stalled, waiting for the memory bus to become free.

I suggest bcrypt. It is not a cryptographic hash function per se, but it could replace SHA-256 and add some memory constraints that would make its implementation harder on GPUs.

Bcrypt uses blowfish to encrypt a string with a key derived from a password chosen by the user. So given a string and a target, finding a password that encrypts the string below the target works exactly like the Bitcoin lottery.
As for the memory constraints, it is possible to implement bcrypt on a GPU, but it is much harder (probably impossible) to get the same kind of performance improvements we see with SHA. Here is an excerpt from a post on crypto stackexchange about implementing bcrypt with cuda:

Now bcrypt is a variant of the Blowfish key scheduling, which is defined over a table (a few kilobytes) which is constantly accessed and modified throughout the algorithm. Due to the size of the table, each core will have to store it in the GPU main RAM, and they will compete for usage of the memory bus. So bcrypt will run -- but not with full parallelism. At any time, most cores will be stalled, waiting for the memory bus to become free.

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nmat
nmat
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I suggest bcrypt. It is not a cryptographic hash function per se, but it could replace SHA-256 and add some memory constraints that would make its implementation harder on GPUs.

Bcrypt uses blowfish to encrypt a string with a key derived from a password chosen by the user. So given a string and a target, finding a password that encrypts the string below the target works exactly like the Bitcoin lottery.
As for the memory constraints, it is possible to implement bcrypt on a GPU, but it is much harder (probably impossible) to get the same kind of performance improvements we see with SHA. Here is an excerpt from a post on crypto stackexchange about implementing bcrypt with cuda:

Now bcrypt is a variant of the Blowfish key scheduling, which is defined over a table (a few kilobytes) which is constantly accessed and modified throughout the algorithm. Due to the size of the table, each core will have to store it in the GPU main RAM, and they will compete for usage of the memory bus. So bcrypt will run -- but not with full parallelism. At any time, most cores will be stalled, waiting for the memory bus to become free.