We describe a parallel algorithm for modular exponentiation y ≡ xk mod n. Then we discuss timing attacks against an implementation of the proposed parallel algorithm for modular exponentiation. When we have two processors, which perform modular exponentiation, an exponent k is scattered into two partial exponents k(0) and k(1), where k(0) and k(1) are derived by bitwise AND operation from k such that k(0) = k ∧ (0101⋯01)2 and k(1) = k ∧(1010 ⋯10)2. Two partial modular exponentiations y0 ≡ xk(0) mod n and y1 ≡ xk(1) mod n are performed in parallel using two processors. Then we can obtain y by computing y ≡ y0y1 mod n. In general, the hamming weight of k(0) and k(1) are smaller than that of k. Thus fast computation of modular exponentiation y ≡ xk mod n can be achieved. Moreover we show a timing attack against an implementation of this algorithm. We perform a software simulation of the attack and analyze security of the parallel implementation.
|Number of pages||12|
|Journal||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Publication status||Published - 2003|
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)