RSA Speedup with Chinese Remainder Theorem Immune against
- Slides: 17
RSA Speedup with Chinese Remainder Theorem Immune against Hardware Fault Cryptanalysis Author: Sung-Ming Yen, Seugjoo Kim, Seongan Lim and Sang-Jae Moon Source: IEEE Transactions on Computers, Vol. 52, No. 4, pp. 461 -472, April 2003 Data: 10/2/2003 Speaker: Jui-Yi Kuo 1
Outline n n n Motivation Previous Countermeasures CRT-1 Protocol & CRT-2 Protocol Performance Conclusions 2
Motivation n n Sign by Smart IC card Computing in finite resource How to Speedup How to Immune against Hardware Fault Cryptanalysis 3
CRT(Chinese Remainder Theorem) where and 4
RSA notation m : message s : signature for m d : secret key e, n: public key p, q : primes 5
RSA signature m m send m ? Secret d sig S 6
The CRT-Based Cryptanalysis 7
Previous Countermeasures n n Performing calculations twice Applying a verification on the computed result to detect any fault 8
CRT-1 Protocol 9
CRT-1 Protocol (Cont. ) 10
CRT-1 Protocol (Example) 11
CRT-1 Protocol (Example-Cont. ) 12
CRT-2 Protocol 13
CRT-2 Protocol (Example) 14
Performance n n Step 2 of CRT-1 need more time but less resource than Step 2 of CRT-2 Some computation of CRT can be finished earlier 15
Performance(Complexity) CRT-Based CRT-1 when One of sp and sq is error Complexity of that generate p or q O(1) CRT-2 One of sp and sq is error with er be known O(n) 16
Conclusions n n n Two novel protocols can speed up the RSA signature or decryption with RNS(residue number system) Immune against hardware fault cryptanalysis No need to performing calculations twice and Applying a verification on the computed result to detect any fault 17
- Rsa
- The number 311-38 is divisible by prime numbers:
- Chinese remainder theorem
- Chinese remainder theorem 3 equations
- Primary immune response and secondary immune response
- Polynomial remainder theorem
- Define remainder theorem
- Remainder theorem
- Yix speedup
- Factor theorem synthetic division
- Remainder theorem
- How to find euler totient function
- Finding an nth degree polynomial
- How to write remainder in synthetic division
- The remainder estimation theorem
- Factor therom
- Remainder theorem
- Stroke's theorem