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 November-15-18

Outline Introduction Literature Review Proposed Efficient Two-Prime RSA Cryptosystem Proposed Efficient Multi-Prime RSA Cryptosystem FPGA Implementations and Results Conclusions November-15-18

Introduction Network security is needed everywhere: November-15-18

Introduction Wide applications need security Electronic banking and voting Electronic commerce, such as online bidding Email, file exchange/submission Web browsing, etc. November-15-18

Introduction Cryptography Cryptography guarantees the needed security 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 November-15-18

Introduction Secret-Key Cryptography Disadvantages: 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 November-15-18

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. November-15-18

Introduction Public-Key Cryptography Advantages: Disadvantage: Easier key management Key can remain unchanged for longer time Yields efficient digital signature mechanisms Disadvantage: Slower throughputs since keys have larger wordlengths November-15-18

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 November-15-18

Outline Introduction Literature Review Proposed Efficient Two-Prime RSA Cryptosystem Proposed Efficient Multi-Prime RSA Cryptosystem FPGA Implementations and Results Conclusions November-15-18

Literature Review RSA Cryptosystem Public quantities: n, e; secret quantities: d, Encryption/decryption: Encryption: Decryption: Signing/signature verification: Signing: Signature verification: November-15-18

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 November-15-18

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 November-15-18

Outline Introduction Literature Review Proposed Efficient Two-Prime RSA Cryptosystem Proposed Efficient Multi-Prime RSA Cryptosystem FPGA Implementations and Results Conclusions November-15-18

Proposed Two-Prime RSA Standard CRT-based two-prime RSA To calculate: November-15-18

Proposed Two-Prime RSA Standard CRT-based two-prime RSA Vulnerable to the hardware fault attack: When available: and factors the system November-15-18

Proposed Two-Prime RSA CRT-2 protocol proposed by Yen et al. 1. 2. 3. where November-15-18

Proposed Two-Prime RSA 1. 2. 3. where November-15-18

Proposed Two-Prime RSA Block diagram of the proposed two-prime RSA November-15-18

Proposed Two-Prime RSA Comparison of the operational speed Division Modular exponentiation CRT-2 protocol by Yen. et al. The proposed two-prime RSA where ( ) , and November-15-18

Proposed Two-Prime RSA Factorization complexity The complexity of factoring the proposed RSA system: The complexity of factoring CRT-2: Similar November-15-18

Outline Introduction Literature Review Proposed Efficient Two-Prime RSA Cryptosystem Proposed Efficient Multi-Prime RSA Cryptosystem FPGA Implementations and Results Conclusions November-15-18

Proposed Multi-Prime RSA Standard CRT-based multi-prime RSA November-15-18

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 November-15-18

Proposed Multi-Prime RSA 1. 2. 3. for November-15-18

Proposed Multi-Prime RSA The proposed multi-prime RSA November-15-18

Proposed Two-Prime RSA Extended CRT-2 protocol 1. 2. 3. for November-15-18

Proposed Multi-Prime RSA Comparison of the operational speed Division Modular exponentiation Extended CRT-2 protocol The proposed multi-prime RSA where ( , and ) November-15-18

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 November-15-18

Outline Introduction Literature Review Proposed Efficient Two-Prime RSA Cryptosystem Proposed Efficient Multi-Prime RSA Cryptosystem FPGA Implementations and Results Conclusions November-15-18

FPGA Implementations Design flow November-15-18

FPGA Implementations Structure of modular exponentiation algorithm (to calculate ) November-15-18

FPGA Implementations Structure of Montgomery modular multiplication algorithm (to calculate ) November-15-18

FPGA Implementations Hardware structure of Montgomery modular multiplication November-15-18

FPGA Implementations Structure of proposed two-prime RSA November-15-18

FPGA Implementations Structure of standard CRT-based two-prime RSA November-15-18

FPGA Implementations Structure of CRT-2 protocol November-15-18

FPGA Implementations Implementa-tion results: CLB usage LUT Equivalent gates Standard CRT-based two-prime RSA 1,226 4,775 46,324 Proposed two-prime RSA 1,431 5,615 55,913 CRT-2 protocol 1,997 6,577 85,229 Standard three-prime RSA 1,759 6,939 68,144 Proposed three-prime RSA 2,130 8,252 82,233 Extended CRT-2 protocol 2,646 9,121 109,756 November-15-18

FPGA Implementations Implementation results Standard 2-prime Proposed (CRT-2) Resources Usage (%) 82.6 100 152 3-prime Resources usage (%) 82 133 Conclusion: Not many more resources than the standard CRT-based RSA and much fewer than the systems based on CRT-2 protocol November-15-18

Outline Introduction Literature Review Proposed Efficient Two-Prime RSA Cryptosystem Proposed Efficient Multi-Prime RSA Cryptosystem FPGA Implementations and Results Conclusions November-15-18

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 work in hardware implementations The standard CRT-based RSA cryptosystems with more factors bears more difficult for the hardware fault attack November-15-18

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 November-15-18

Thesis Examination Thanks ! and Questions ? November-15-18