MASON ECE 645 - Hardware Implementations of RSA Using Fast Montgomery Multiplications (34 pages)

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Hardware Implementations of RSA Using Fast Montgomery Multiplications



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Hardware Implementations of RSA Using Fast Montgomery Multiplications

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Pages:
34
School:
George Mason University
Course:
Ece 645 - Computer Arithmetic
Computer Arithmetic Documents

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Hardware Implementations of RSA Using Fast Montgomery Multiplications ECE 645 Prof Gaj Mike Koontz and Ryon Sumner Overview Introduction Functional Specifications Implemented Design and Optimizations Tools Testing Results Conclusions Introduction RSA Encryption Decryption Worldwide use in securing data transmission Public private key based Large 512 bit keys required for protection of data Large keys Slower decryption times Alice M M Public Key Bob Private Key X M Hacker RSA Encryption CypherData CypherData RSA Decryption Introduction Picture taken from Lecture 11 Exponentiation Multi Precision Arithmetic in Software George Mason University Prof Gaj http teal gmu edu courses ECE645 viewgraphs S06 Lecture11 EXP SW 2 pdf pp 2 Functional Specification RSA Encryption Decryption Algorithm z To calculate Y XE mod N S X Y 1 for i 0 to k 1 if Ei 1 Y Y S mod N S S S mod N Functional Specification Picture taken from Lecture 11 Exponentiation Multi Precision Arithmetic in Software George Mason University Prof Gaj http teal gmu edu courses ECE645 viewgraphs S06 Lecture11 EXP SW 2 pdf pp 21 Functional Specification Picture taken from Lecture 11 Exponentiation Multi Precision Arithmetic in Software George Mason University Prof Gaj http teal gmu edu courses ECE645 viewgraphs S06 Lecture11 EXP SW 2 pdf pp 22 Functional Specification Montgomery Multiplication z MP A B N z Algorithm S 0 0 for i in 0 to k 1 loop qi S i 0 Ai B0 mod 2 S i 1 S i Ai B qi N 2 end loop return S k Functional Specification 5 2 Montgomery Multiplication z MP52 A1 A2 B1 B2 N z Algorithm S1 0 0 S2 0 0 for i in 0 to k 1 loop qi S1 i 0 S2 i 0 Ai B10 B20 mod 2 S1 i 1 S2 i 1 CSR S1 i S2 i Ai B1 B2 qi N 2 end loop return S1 k S2 k Functional Specification RSA Encryption Decryption with 5 2 MP z RSA C d N K 22k mod N P1 P2 5to2 MontMult K 0 C 0 N R1 R2 5to2 MontMult K 0 1 0 N for i in 0 to dk loop if d i 1 R1 R2 5to2 MontMult R1 R2 P1 P2 N P1 P2 5to2 MontMult P1 P2 P1 P2 N end loop M1 M2 5to2 MontMult 1 0 R1 R2 N



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