L2 · OPERATIONMEASURED

Encrypted Shift Right

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

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DESCRIPTION

Computes x >> n, the logical right shift, where both operands are encrypted.

Harder than its mirror image: shifting left is multiplication, shifting right is division with truncation, and truncation is a rounding step that encrypted arithmetic does not offer. A realization has to reconstruct the floor without ever seeing the remainder it throws away.

INTERFACE

encrypted_shr(
  in  ct     : Ciphertext  // the encrypted first operand
  in  ct_n   : Ciphertext  // the encrypted shift amount
  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

max_shiftinteger1 – 256

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

CORRECTNESS

01The result equals the floor of x divided by two to the power n.

02Bits shifted out are discarded, not rounded back in.

03Shifting by zero returns the input unchanged.

04The 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