Efficient CRT-Based RSA Cryptosystems Immune against the Hardware Fault Attack and

Efficient CRT-Based RSA Cryptosystems Immune against the Hardware Fault Attack and the FPGA Implementations Yonghong Yang Supervisors: Prof. Z. Abid & Prof. W. Wang Department of Electrical and Computer Engineering the University of Western Ontario, Canada

Outline • Introduction • Literature Review • Proposed Efficient Two-Prime RSA Cryptosystem • Proposed Efficient Multi-Prime RSA Cryptosystem • FPGA Implementations and Results • Conclusions

Introduction Network security is needed everywhere:

Introduction • Electronic banking and voting • Electronic commerce, such as online bidding • Email, file exchange/submission • Web browsing, etc. • Wide applications need security

Introduction • Cryptography • The mathematical science to secure the • confidentiality/authentication of data by • replacing them with a transformed version • Two types: secret-key and public-key • Cryptography guarantees the needed security • Privacy or confidentiality • Data integrity • Authentication • Non-repudiation

Introduction • Secret-Key Cryptography • Traditional method of cryptography • Theoretical basis: “communication theory of secrecy systems” • Single key is used to encrypt and decrypt texts • DES, NSA and IDEA etc. • Disadvantages: • Difficult key management • Keys need to be changed frequently • Cannot yield efficient signature mechanisms

Introduction • Public-Key Cryptography • Relatively new field – 1975, initiated by the paper “New directions in cryptography ” • Different keys are used for encryption and decryption • RSA, DSA, DSS etc.

Introduction • Public-Key Cryptography • Advantages: • Easier key management • Key can remain unchanged for longer time • Yields efficient digital signature mechanisms • Disadvantage: • Slower throughputs since keys have larger wordlengths

Introduction • RSA Cryptography One of the most widely used, simplest public- key cryptography so far • Scheme Alice Bob Encrypt using B’s public key Decrypt using by B’s private key Sign with A’s private key Check signature by A’s public key

Literature Review • RSA Cryptosystem • Public quantities: n, e;secret quantities: d, • Encryption/decryption: • Encryption: • Decryption: • Signing/signature verification: • Signing: • Signature verification:

Literature Review • Chinese Remainder Theorem Based RSA • Chinese Remainder Theorem is often used to speedup the operations of RSA • Attacks on the CRT-based RSA • Hardware fault attack • Timing attack • Power attack

Literature Review • Countermeasures to the attack • Padding the message, drawback: collision-free hash function (hard) • Checking the intermediate or final results, drawback: double the operational time and not secure • Revising the signature expression, make sure no secret information is leaked

Proposed Two-Prime RSA • Standard CRT-based two-prime RSA To calculate:

Proposed Two-Prime RSA • Standard CRT-based two-prime RSA • Vulnerable to the hardware fault attack: When available: and factors the system

Proposed Two-Prime RSA • CRT-2 protocol proposed by Yen et al. 1. 2. 3. where

Proposed Two-Prime RSA • Proposed Two-Prime RSA 1. 2. 3. where

Proposed Two-Prime RSA • Block diagram of the proposed two-prime RSA

Proposed Two-Prime RSA • Comparison of the operational speed where ( ) , and

Proposed Two-Prime RSA • Factorization complexity • The complexity of factoring the proposed RSA system: • The complexity of factoring CRT-2: • Similar

Proposed Multi-Prime RSA • Standard CRT-based multi-prime RSA

Proposed Multi-Prime RSA • Immunity of CRT-based multi-prime RSA: • When (j-1) faulty signatures available, calculations according to these (j-1)faulty signatures factors the multi-prime RSA • Still vulnerable to the hardware fault attack

Proposed Multi-Prime RSA • Proposed Multi-Prime RSA 1. 2. 3. for

Proposed Multi-Prime RSA • The proposed multi-prime RSA

Proposed Two-Prime RSA • Extended CRT-2 protocol 1. 2. 3. for

Proposed Multi-Prime RSA • Comparison of the operational speed where ( , and )

Proposed Multi-Prime RSA • Operational speed improvement has been verified by one example of three-prime RSA • Similar factorization complexity • Still for obtaining any factor from the proposed multi-prime RSA • Predicted to use fewer hardware resources • Will be verified by Implementation results later

FPGA Implementations • Design flow

FPGA Implementations • Structure of modular exponentiation algorithm (to calculate )

FPGA Implementations • Structure of Montgomery modular multiplication algorithm (to calculate )

FPGA Implementations • Hardware structure of Montgomery modular multiplication

FPGA Implementations • Structure of proposed two-prime RSA

FPGA Implementations • Structure of standard CRT-based two-prime RSA

FPGA Implementations • Structure of CRT-2 protocol

FPGA Implementations Implementa-tion results:

FPGA Implementations • Implementation results Conclusion: Not many more resources than the standard CRT-based RSA and much fewer than the systems based on CRT-2 protocol

Conclusions • Conclusions • The immunity of the RSA cryptosystems against the hardware fault attack is greatly increased • The proposed RSA cryptosystems provide more efficient operations than previous work, and they bear similar immunity against the hardware fault attack. • The proposed RSA cryptosystems use fewer resources than previous workin hardware implementations • The standard CRT-based RSA cryptosystems with more factors bears more difficult for the hardware fault attack

Conclusions • Future work • Speed up the basic block: modular exponentiation computation • Implement the RSA cryptosystems with enhanced immunity against other implementation attacks • Download the RSA cryptosystems implemented in Chapter 5 to the FPGA chip

Thesis Examination Thanks ! and Questions ?

Efficient CRT-Based RSA Cryptosystems Immune against the Hardware Fault Attack and