ANSI X9.31 : 1998

FOREWORD
1. SCOPE
2. DEFINITIONS, ABBREVIATIONS, AND REFERENCES
   2.1 DEFINITIONS
   2.2 SYMBOLS AND ABBREVIATIONS
   2.3 REFERENCES
3. APPLICATION
   3.1 GENERAL
   3.2 THE USE OF DIGITAL SIGNATURES
4. SIGNATURE ALGORITHM
   4.1 KEY GENERATION
   4.2 SIGNATURE GENERATION
   4.3 SIGNATURE VERIFICATION
APPENDIX A: RANDOM NUMBER GENERATION
   A.1 INTRODUCTION
   A.2 ALGORITHMS
APPENDIX B: GENERATION OF PARAMETERS FOR RDSA
   B.1 INTRODUCTION
   B.2 MILLER-RABIN PROBABILISTIC PRIMALITY TEST
   B.3 LUCAS PROBABILISTIC PRIMALITY TEST
   B.4 GENERATION OF PRIMES
   B.5 GENERATION OF ACTUAL PRIMES - SHAWE-TAYLOR ALGORITHM
APPENDIX C: SECURITY CONSIDERATIONS
   C.1 NON-REPUDIATION
   C.2 FIRST PARTY ATTACKS
   C.3 STRONG PRIMES
   C.4 PRIVATE SIGNATURE EXPONENT
   C.5 CRYPTOGRAPHIC CALCULATION ERRORS
   C.6 ADVERSE EFFECTS ON THE KEY SPACE
   C.7 PARTIAL REVELATION OF THE PRIVATE EXPONENT D
   C.8 PUBLIC KEY VALIDATION
   C.9 STRONG PRIMES AND SAFE PRIMES
   C.10 KEY SIZE GUIDELINES
APPENDIX D: DIGITAL SIGNATURE EXAMPLES
   D.1 ODD E = 3 WITH 1024-BIT N
   D.2 ODD E = 3 WITH 1536-BIT N
   D.3 ODD E = 3 WITH 2048-BIT N
   D.4 ODD E = 3 WITH 4096-BIT N
   D.5 EVEN E = 2 WITH 1024-BIT N
APPENDIX E: IMPLEMENTATION CONSIDERATIONS
   E.1 FAST SIGNATURE ALGORITHM
   E.2 MULTIPLICATIVE INVERSE
   E.3 SIEVING
   E.4 FAST PRIME GENERATION
   E.5 EVEN EXPONENTS
   E.6 TESTING CANDIDATES

Defines a method for digital signature (signature) generation and verification for the protection of financial messages and data using reversible public key cryptography systems without message recovery.