L2 · OPERATIONMEASURED

Encrypted Signed Remainder

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

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DESCRIPTION

Computes the signed remainder a % b with both operands encrypted, where the result takes the sign of the dividend.

The sign rule is what distinguishes this from the unsigned modulo kernel: mathematically the remainder could be given either sign, and the EVM fixes one. A realization that reduces into a non-negative range has computed a different function.

INTERFACE

encrypted_smod(
  in  ct     : Ciphertext  // the encrypted first operand
  in  ct_b   : Ciphertext  // the encrypted divisor
  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 remainder carries the sign of the dividend.

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