A Security Scheme for Dependable Key Insertion in Mobile Embedded Devices

Algorithm 1

GF multiplication of 𝑈⋅𝑉 mod 𝑃 by adding 𝑛 times.

Requires: 𝑈(𝑥)=𝑢_𝑛−1𝑥^𝑛−1+⋯+𝑢₁𝑥+𝑢₀∈GF(2^𝑛),

  𝑉(𝑥)=𝑣_𝑛−1𝑥^𝑛−1+⋯+𝑣₁𝑥+𝑢₀∈GF(2^𝑛),

  𝑃(𝑥)=𝑥^𝑛+𝑝_𝑛−1𝑥^𝑛−1+⋯+𝑝₁𝑥+𝑝₀∈GF(2^𝑛+1)

Ensure: 𝑈(𝑥)𝑉(𝑥)mod𝑃(𝑥)

(1) 𝑇(𝑥)=𝑡_𝑛𝑥^𝑛+⋯+𝑡₁𝑥+0←0

(2) for 𝑖=𝑛−1  to 0 do

(3)    𝑚←𝑢_𝑖⋅𝑉(𝑥)

(4)    𝑟←𝑡_𝑛⋅𝑃(𝑥)

(5)    𝑇(𝑥)←(𝑇(𝑥)+𝑚−𝑟)𝑥

(6)    𝑖←𝑖−1

(7) end for

(8) return  𝑇(𝑥)/𝑥