Ashraf Abusharekh Kris Gaj Department of Electrical & Computer Engineering George Mason University
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1 COMPARATIVE ANALYSIS OF SOFTWARE LIBRARIES FOR PUBLIC KEY CRYPTOGRAPHY Ashraf Abusharekh Kris Gaj Department of Electrical & Computer Engineering George Mason University 1
2 OBJECTIVE Evaluation of Multi-precision Arithmetic Libraries for Use in Public Key Cryptography Practical Recommendations Which library is best for a particular application? 2
3 PUBLIC KEY SCHEMES OPERATIONS(1) Signature Scheme RSA DSA ECDSA System Parameters N/A Primality Testing EC Generation Point Counting Key Generation Modular Exponentiation Multiplication GCD xgcd Modular Exponentiation Scalar Multiplication Signature Generation Modular Exponentiation Addition Multiplication Modular Exponentiation xgcd Scalar Multiplication Addition Multiplication xgcd Signature Verification Modular Exponentiation Multiplication Modular Exponentiation xgcd Scalar Multiplication Multiplication xgcd Point Addition3
4 PUBLIC KEY SCHEMES OPERATIONS(2) Large Integers ( ) Addition, Multiplication, Modular Exponentiation, GCD, xgcd, Primality Testing Elliptic Curve Points ( ) Elliptic Curve Point Addition and Scalar Multiplication Problem: Operations are difficult to implement. Solution: Use existing libraries. 4
5 LIBRARIES Many arithmetic and number theoretic libraries, commercial and in the public domain have been developed to perform these multi-precision arithmetic operations efficiently Beecrypt, BIGNUM, Botan, bnlib, CLN, cryptolib, CryptoPP, freelip, GMP, Libgcrypt, LiDIA, linteger, MIRACL, nettle, NTL, OpenSSL, PARI, PIOLOGIE, zen.. Problem: Which one to use? 5
6 EVALUATED LIBRARIES 6
7 PLATFORMS Processor/hardware 2.00 GHz Pentium IV Processor, 512 MB RAM Sun: 2x 400 MHz UltraSPARC-Solaris-II, 4-MB E-cache, 2048 MB RAM Operating System Windows XP Cygwin RedHat Linux 9.0 Solaris 5.8 Compiler GNU C/C GNU C/C GNU C/C
8 EVALUATION CRITERIA PRIMARY Performance of Primitive Operations Support for Public Key Cryptosystems Primitive Operations Public Key Schemes SECONDARY Documentation & Ease of Use Supported Compilers 8
9 Evaluation Criteria Documentation & Ease of Use Sufficient Documentation GMP LiDIA MIRACL NTL CLN PIOLOGIE Best Insufficient Worst CryptoPP OpenSSL Hard Ease of use Easy 9
10 SUN WorkShop C++ Evaluation Criteria Supported Compilers MIPSpro C++ MSVC KAI C++ VisualAge C++ IBM CSet++ IBM C++ HP C++ HP ac++ GNU C/C++ MSVC MSVC Digital C++ Intel C/C++ Microsoft embedded Visual C++ MSVC front end GNU C/C++ GNU C/C++ Intel C/C++ Borland C/C++ Sun WorkShop, Forte C++ DEC C GNU C/C++ Apogee C++ CodeWarrior Pro CodeWarrior Pro Borland C/C++ MSVC Watcom C++ Borland Builder C++ Borland C/C++ ARM C GNU C/C++ GNU C/C++ GNU C/C++ GNU C/C++ PIOLOGIE CryptoPP OpenSSL MIRACL NTL CLN GMP 10 LiDIA
11 OPERATIONS, OPERAND SIZES Large Integers (768/1024/2048) Multiplication, Modular Exponentiation, GCD, xgcd, Primality Testing E(F P ) (162/224/384) Addition, Point Scalar Multiplication E(F 2^n ) (163/233/409) Addition, Scalar Multiplication 11
12 METHODOLOGY(1) Measuring Performance of Operations RDTSC Method: Clock Cycles Pentium IV: RDTSC Instruction Timing Method: Milliseconds UltraSPARC-II, gettimeofday() 100 execution times for each operation 12
13 METHODOLOGY(2) Operands Large Integers: Random I n, J n, K n, n = {768, 1024, 2048} Random Primes P n (j), n = {768, 1024, 2048}, j = [0, 9] E(F 2^n ) SEC 2 recommended 163, 233, 409. Random Points T n, S n, n = {163, 233, 409} E(F P ) Random, 162, 226, 386. Random Points T n, S n, n = {162, 226, 386} 13
14 METHODOLOGY(3) Operation Ranking P4-WinXP/MULTIPLICATION(Clock Cycles) Library result 768 result 1024 result 2048 CLN 8,940 11,763 29,133 CryptoPP 38,432 37,928 78,755 GMP 3,423 5,364 17,605 LiDIA 3,573 6,047 18,722 MIRACL 10,974 18,613 71,512 NTL 3,381 5,426 17,722 OpenSSL 9,055 15,218 48,438 Piologie 29,910 41, ,977 Min n 3,381 5,364 17,605 Library P4-WinXP/MULTIPLICATION Ranking R 768 R 1024 R 2048 CLN CryptoPP GMP LiDIA MIRACL NTL OpenSSL Piologie Rank Operation Rank/Lib/OS= 3 n=768,1024,2048 R n where R n = result n Min n 14
15 METHODOLOGY(4) Library Ranking X 1 X 2 X 3 X 4 X 5 X 6 Library MUL E = 3 E = Large E GCD xgcd P4-WinXP Rank CLN CryptoPP GMP LiDIA MIRACL NTL OpenSSL PIOLOGIE Library Rank/OS= N N k=1 X k 15
16 RESULTS LARGE INTEGERS RESULTS P4-WinXP RESULTS RedHat Rank Rank GMP NTL LiDIA CLN OpenSSL MIRACL CryptoPP Piologie 0.00 GMP NTL LiDIA CLN MIRACL OpenSSL Piologie CryptoPP Library Library RESULTS UltraSPARC-Solaris Rank GMP NTL LiDIA CLN OpenSSL PIOLOGIE MIRACL CryptoPP Library 16
17 Results Operations On Large Integers Fast Medium Slow GMP WinXP/Solaris RH RH/Solaris WinXP NTL 4.9 OpenSSL 4.4 MIRACL PIOLOGIE 7.0 CryptoPP 14.6 LiDIA 5.0 MIRACL 7.3 OpenSSL CryptoPP 35.0 PIOLOGIE15.5 CLN Free 17
18 RESULTS E(F p ) RESULTS P4-WinXP RESULTS RedHat Rank OpenSSL Miracl LiDIA CryptoPP Rank OpenSSL LiDIA Miracl CryptoPP Library Library RESULTS UltraSPARC-Solaris Rank OpenSSL LiDIA Miracl CryptoPP Library 18
19 RESULTS E(F 2^n ) RESULTS P4-WinXP RESULTS RedHat Rank Miracl LiDIA CryptoPP Rank LiDIA Miracl CryptoPP Library Library RESULTS UltraSPARC-Solaris Rank LiDIA Miracl CryptoPP Library 19
20 Results Operations On EC Points EC2 ECP WinXP RH/Solaris WinXP RH/Solaris 1.0 MIRACL 1.0 LiDIA 1.0 OpenSSL OpenSSL LiDIA 1.4 MIRACL MIRACL 1.25 LiDIA 1.3 CryptoPP CryptoPP LiDIA 1.8 MIRACL CryptoPP 3.6 CryptoPP 8.2 Free 20
21 FACTORS AFFECTING PERFORMANCE Low level routines Targeting Pentium 4 and UltraSPARC Algorithms Choice of algorithm and algorithm parameters Different implementations 21
22 Factors Affecting Performance Examples 768bit 1024bit 2048bit P4-WinXP/MULTIPLICATION (Clock Cycles) Piologie Library result 768 result 1024 result 2048 Libraries OpenSSL MIRACL GMP/LiDIA/NTL SPARC GMP/LiDIA/NTL PIV Classic Karatsuba Karatsuba-Comba CLN CryptoPP GMP LiDIA MIRACL NTL 8,940 38,432 3,423 3,573 10,974 3,381 11,763 37,928 5,364 6,047 18,613 5,426 29,133 78,755 17,605 18,722 71,512 17,722 CryptoPP OpenSSL 9,055 15,218 48,438 CLN Piologie Min n 29,910 3,381 41,163 5, ,977 17,605 22
23 SUPPORT FOR PUBLIC KEY CRYPTOSYSTEMS PIOLOGIE OpenSSL NTL MIRACL LiDIA GMP CryptoPP CLN Support for Primitive Large Integers Operations Support for Primitive E(F p ) Operations Support for Primitive E(F 2^n ) Operations EC Generation and Point Counting EC2/ECP 23
24 Which library is best for implementing PK Schemes operating on LARGE INTEGERS? High Performance GMP,NTL, LiDIA CLN PIOLOGIE OpenSSL MIRACL Best Low Worst CryptoPP Low Primitives Schemes High Support 24
25 CONCLUSION(1) Support for operations on large integers, Group A) {GMP(fastest), NTL, LiDIA, CLN}: best performance under all platforms tested. Trade off: amount of time and effort needed for implementation. Group B) {OpenSSL, MIRACL} trail libraries from group A in terms of overall performance. Support implementations of cryptographic schemes => faster development. {CryptoPP} is the best choice for the fast development based on the wide range of cryptographic schemes implemented. Trade off: performance as compared to other libraries. 25
26 Which library is best for implementing PK Schemes operating on LARGE INTEGERS? High Performance : A lot of time devoted for development (low support) Free Use GMP. Medium Performance/Medium Time Devoted For Development : Free Use OpenSSL. High Support/Not Enough Time to Develop Free Use CryptoPP. 26
27 High Performance Which library is best for implementing PK Schemes operating on ECP? OpenSSL LiDIA MIRACL Best Low Worst CryptoPP Low Primitives Schemes High Support 27
28 High Which library is best for implementing PK Schemes operating on EC2? Best Performance LiDIA MIRACL Low Worst CryptoPP Low Primitives Schemes High Support 28
29 CONCLUSION(2) Support for E(F 2^n ), LiDIA has the best performance under Pentium IV- RedHat 9.0 and UltraSPARC-Solaris. Under Pentium IV, Windows XP, MIRACL has the best performance. CryptoPP is the slowest under all platforms. Support for E(F p ), OpenSSL has the best performance under all platforms, LiDIA performance is better than MIRACL on Pentium IVRedHat 9.0 and UltraSPARC-Solaris, while under Pentium IV-Windows XP, MIRACL is better than LiDIA. CryptoPP is the slowest. 29
30 Which library is best for implementing PK Schemes operating on ECP? High Performance : A lot of time devoted for development (low support) Free Use OpenSSL. Medium Performance/Good Support Not Free Use MIRACL. High Support/Not Enough Time to Develop Free Use CryptoPP. 30
31 Which library is best for implementing PK Schemes operating on EC2? High Performance : A lot of time devoted for development (low support) Not Free Use LiDIA. Medium Performance/Good Support Not Free Use MIRACL. High Support/Not Enough Time to Develop Free Use CryptoPP. 31
32 Thank You 32
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