Mathematical Operations Arbitrary Precision Math
4.5.2 Mathematical Operations
With few exceptions, the majority of the remainder of the functions that make up the BN package all perform mathematical operations such as addition and multiplication. Most of the functions require at least two BIGNUM operands and store their result in a third BIGNUM . It is often safe to use one of the operands to store the result, but it isnt always, so you should exercise care in doing so. Consult Table 4-1 , which lists the most common arithmetic functions, if youre not sure. Unless otherwise noted in the table, the BIGNUM that will receive the result of the operation may not be the same as any of the operands. Each of the functions returns nonzero or zero, indicating success or failure, respectively. Many of the functions in Table 4-1 are shown as accepting an argument labeled ctx. This argument is a pointer to a BN_CTX structure. This argument may not be specified as NULL , but instead should be a context structure returned by BN_CTX_new . The purpose of the context structure is to store temporary values used by many of the arithmetic operations. Storing the temporary values in a context increases the performance of the various functions. When a context structure is no longer needed, it should be destroyed using BN_CTX_free . Table 4-1. Arithmetic functions for BIGNUMs Function Comments BN_addr, a, b r = a + b r may be the same as a or b. BN_subr, a, b r = a - b BN_mulr, a, b, ctx r = a x b r may be the same as a or b. BN_sqrr, a, ctx r = powa, 2 r may be the same as a. This function is faster than BN_mulr, a, a. BN_divd, r, a, b, ctx d = a b, r = a b Neither d nor r may be the same as either a or b. Either d or r may be NULL. BN_modr, a, b, ctx r = a b BN_nnmodr, a, b, ctx r = absa b BN_mod_addr, a, b, m, ctx r = absa + b m BN mod subr, a, b, m, r = absa - b m 89 ctx BN_mod_mulr, a, b, m, ctx r = absa x b m r may be the same as a or b. BN_mod_sqrr, a, m, ctx r = abspowa, 2 m BN_expr, a, p, ctx r = powa, p BN_mod_expr, a, p, m, ctx r = powa, 2 m BN_gcdr, a, b, ctx Finds the greatest common divisor of a and b. r may be the same as a or b.4.5.3 Generating Prime Numbers
Parts
» Network Security With OpenSSL 2002
» Goals of Cryptography Cryptography for the Rest of Us
» Symmetric key encryption Cryptographic Algorithms
» Public key encryption Cryptographic Algorithms
» Cryptographic hash functions and Message Authentication Codes
» Overview of SSL Introduction
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» Memory sourcessinks File sourcessinks
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» The Basics Arbitrary Precision Math
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» Using Engines Support Infrastructure
» Background Step 1: SSL Version Selection and Certificate Preparation
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» Incorporating certificate revocation lists
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» Further extension of the examples
» Setting SSL options Step 3: SSL Options and Cipher Suites
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» The final product Step 3: SSL Options and Cipher Suites
» Beyond the example Step 3: SSL Options and Cipher Suites
» Client-side SSL sessions SSL Session Caching
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» An on-disk, session caching framework
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» Block Ciphers and Stream Ciphers
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» Initializing Symmetric Ciphers Encrypting with the EVP API
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» Computing Shared Secrets Diffie-Hellman
» The Basics Digital Signature Algorithm DSA
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» Writing and Reading DER-Encoded Objects
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» Net::SSLeay Variables Net::SSLeay for Perl
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» Net::SSLeay Low-Level Bindings
» M2Crypto.SSL High-Level Classes
» Miscellaneous crypto High-Level Classes
» Extensions to httplib: httpslib
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» General Functions OpenSSL Support in PHP
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» Encryption and Signing Functions
» PKCS7 SMIME Functions OpenSSL Support in PHP
» Object Stacks Advanced Programming Topics
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