L2 · OPERATIONMEASURED

Encrypted Modular Multiplication

encrypted-mulmod · spec v0.1.0 · 0 implementations · 6 runners

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DESCRIPTION

Computes (a · b) mod m with all three operands encrypted.

The same shape as encrypted modular addition and materially harder: the intermediate product is twice the width of the operands, so a realization either carries that width or finds a reduction that never forms it.

INTERFACE

encrypted_mulmod(
  in  ct     : Ciphertext  // the encrypted first operand
  in  ct_b   : Ciphertext  // the encrypted second factor, with the modulus alongside
  out ct     : Ciphertext  // the encrypted result of the opcode
  ...               // anything else the realization needs — keys, context, encoding — is its own concern
)

PARAMETER SCHEMA

NAMETYPERANGE

word_maxinteger255 – 2^32

target_precisionnumber0.5 – 1

The schema belongs to the kernel. Each implementation declares which part of it it supports.

CORRECTNESS

01The result equals the product reduced modulo m, computed as though the intermediate product had unbounded width.

02A modulus of zero returns zero, as the EVM defines.

03The result matches the EVM definition of the opcode exactly, including its behaviour at the boundaries.

An opcode is exact by definition. Where the scheme is approximate, the precision threshold is what stands in for exactness, and it has to hold at every integer in range.

SECURITY PROPERTIES

Operands and result stay encrypted throughout. Nothing about the values may be observable through timing or control flow, which rules out any realization that branches on a decrypted intermediate.

ASSUMPTIONS

Operands are integers held exactly at the point of encryption.

REFERENCES

repoFHERMA participation guide