Identity amortization lets Sybil attackers cut cost per identity up to 4.3×

The five-minute version

Identity amortization-shared use of resources like phone numbers or IP addresses-can dramatically lower the cost of Sybil attacks. The authors show that per-account cost estimates for phone-verification services overstate an attacker’s provisioning cost by a factor of 1.6-4.3, and that raising Tor’s relay-per-address limit from 2 to 8 reduces the modeled cost of reaching a quarter of hidden-service directories by 8%-72% depending on price ratios. The evidence is based on analytical models and measurements of public price catalogues and the Tor network size, not on observed attacks.

What they found 2

• Phone-verification cost estimates overstate attacker provisioning cost by 1.6-4.3×

  “On published phone-verification prices, a peraccount estimate overstated the adversary’s provisioning cost by a factor between 1.6 and 4.3, and the cheapest reported market price was below the least cost of verifying each account with its own number; the first strict reduction occurred where predicted, raising the price of the honest participant’s resource left the adversary’s cost unchanged, and a limit of three accounts per number removed the reduction.”

• Increasing Tor’s relay-per-address limit from 2 to 8 lowers modeled attack cost by up to 72%

  “Raising the limit from 2 to 8 lowers the cost of reaching the threshold by 24.9%, 53.5%, and 68.0% at r = 1, 5, and 20, and by between 8.3% and 72.0% over the whole range considered.”

What undercuts it the paper’s own results

• These are model-based costs on measured inputs, not measurements of an attack, and they do not establish that the limit was exploited.
• The analysis gives conditional results within an explicit provisioning model; it does not measure how often identity amortization occurs in deployed systems.

Stated limits 4

• These are model-based costs on measured inputs, not measurements of an attack, and they do not establish that the limit was exploited.
• The analysis gives conditional results within an explicit provisioning model; it does not measure how often identity amortization occurs in deployed systems.
• The catalogue results assume linear instance prices, whereas the general model admits bulk discounts, and the intervention comparison considers an honest participant with one identity.
• The phone catalogue uses prices from 2013-2014; Section 7.4 varies the capacity and the identity-specific cost on those prices and replaces only the code price with a current, platform-averaged value.

What’s new here 4

• Formal definition of identity amortization as a failure of per-identity cost guarantees.
• A decision procedure that determines exactly when sharing reduces provisioning cost and by how much.
• Analysis of defensive interventions (raising identity-specific costs, resource prices, or capping sharing) with provable optimality conditions.
• Quantitative evaluation on real-world phone-verification price data and on the Tor relay-per-address limit.

Artifacts & methods 5

• capacity model of resource sharingtheory
• decision-procedure test for identity amortizationprimitive
• phone-verification price cataloguedataset
• Tor network measurement (N=2814 relays)dataset
• model of attack-cost reduction under varying relay limitsevaluation

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