Add SHA256 Tutorial

[RasoulAM]

A tutorial on implementing SHA256 as part of the bounty program has been added, utilizing concrete operations. The accompanying notebook details all necessary steps and implements required operations such as 32-bit additions, rotations, and shifts. Some assumptions are:

• Data can be of variable length
• The client splits data into small pieces before encryption
• Bitlength of the pieces can be adjusted to get the best performance
• Added support for 32-bit addition, rotation, and shifts
• Test cases available in the code to show the correctness
• Compilation and runtime generally take a long time, but smaller examples with fewer iterations are included in the notebook

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Thank you for your pull request. We require contributors to sign our Contributor License Agreement / Terms and Conditions, and we don't seem to have the users @m-meidani, @RasoulAM on file. In order for us to review and merge your code, please sign:

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[aquint-zama]

@cla-bot check

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The cla-bot has been summoned, and re-checked this pull request!

[umut-sahin]

Could you use chunks terminology instead of slices?

[RasoulAM]

Could you use chunks terminology instead of slices?

Done. 88a0847

[umut-sahin]

Can you replace explicit tables:

extract_one_bit_carry = fhe.LookupTable([x // (2 ** WIDTH) for x in range(2**(WIDTH+1))])
extract_chunk_from_two_operand_sum = fhe.LookupTable([x % (2 ** WIDTH) for x in range(2**(WIDTH+1))])

extract_two_bit_carry = fhe.LookupTable([x // (2 ** WIDTH) for x in range(2**(WIDTH+2))])
extract_chunk_from_four_operand_sum = fhe.LookupTable([x % (2 ** WIDTH) for x in range(2**(WIDTH+2))])

with regular operations

    carries = extract_two_bit_carry[added]
    # to
    carries = added // (2**WIDTH)
    # or even better
    carries = added >> WIDTH  # extract the carry bit

[RasoulAM]

Are those operations implemented? When we were implementing they were not.

[umut-sahin]

Constant ones are implemented a long time ago, only all operands encrypted version was not :)

[RasoulAM]

Done. b8d19a0

[umut-sahin]

Still two remaining:

extract_one_bit_carry = fhe.LookupTable([x // (2 ** WIDTH) for x in range(2**(WIDTH+1))])
extract_chunk_from_two_operand_sum = fhe.LookupTable([x % (2 ** WIDTH) for x in range(2**(WIDTH+1))])

[RasoulAM]

Thanks for pointing those out. Does that mean these can be replaced as well?

# Extracts the [shift] lower bits of a [WIDTH]-bit number and places them at the top
table_extract_low_bits_and_raise = {
    shift : fhe.LookupTable([2**(WIDTH-shift) * (x %2**shift) for x in range(2**WIDTH)])
    for shift in range(WIDTH)
}

# Extracts the [WIDTH-shift] higher bits of a [WIDTH]-bit number
table_extract_high_bits = {
    shift : fhe.LookupTable([x//2**shift  for x in range(2**WIDTH)])
    for shift in range(WIDTH)
}

[umut-sahin]

Yes, they can be replaced, I'd replace the first one with fhe.univariate and second one with a direct division.

[umut-sahin]

Lastly, could you:

• remove get_sha256
• change def sha256(data) to def sha256(data, number_of_rounds=64)
• compile using compiler = fhe.Compiler(lambda data: sha256(data, number_of_rounds), {"data": "encrypted"}) instead of compiler = fhe.Compiler(get_sha256(self.number_of_rounds), {"data": "encrypted"})

Then it's good to go for me :)

[RasoulAM]

We decided not to give number_of_rounds as an argument to the function because it complicates many other parts of the code. For example, the inputset must be adjusted to include the number of rounds as well, mainly when you are less than 64 rounds.

[umut-sahin]

We decided not to give number_of_rounds as an argument to the function because it complicates many other parts of the code. For example, the inputset must be adjusted to include the number of rounds as well, mainly when you are less than 64 rounds.

This is not the case with the changes I've suggested. You can wrap it in a lambda with a single argument :)

[RasoulAM]

Done. Thanks for the suggestion :D
d4a357b

[umut-sahin]

Lovely, could you squash your commits into a single one with the message:

docs(frontend-python): add sha256 tutorial

[m-meidani]

Done. Does that looks good?

[aquint-zama]

close zama-ai/bounty-program#39