List of Tables

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Chapter 1: Introduction

Table 1.1: Arithmetic and Number Theory in C in Directory flint/src

Table 1.2: Arithmetic and Number Theory in C++ in Directory flint/src

Table 1.3: Arithmetic Module in 80×86 Assembler (see Chapter 18) in Directory flint/src/asm

Table 1.4: Arithmetic Libraries in 80×86 Assembler (see Chapter 18) in Directory flint/lib

Table 1.5: Tests (see Section 12.2 and Chapter 17) in Directory flint/test

Table 1.6: RSA Implementation (see Chapter 16) in Directory flint/rsa

Chapter 3: Interface Semantics

Table 3.1: FLINT/C error codes

Chapter 5: Modular Arithmetic: Calculating with Residue Classes

Table 5.1: Composition table for addition modulo 5

Table 5.2: Composition table for multiplication modulo 5

Chapter 6: Where All Roads Meet: Modular Exponentiation

Table 6.1: Requirements for exponentiation

Table 6.2: Numbers of multiplications for typical sizes of exponents and various bases 2^k

Table 6.3: Values for the factorization of the exponent digits into products of a power of 2 and an odd factor

Table 6.4: Numbers of multiplications for typical sizes of exponents and various bases 2^k

Table 6.5: Exponentiation functions in FLINT/C

Chapter 7: Bitwise and Logical Functions

Table 7.1: Values of a Boolean function

Table 7.2: Values of the CLINT function and_l()

Table 7.3: Values of the CLINT function or_l()

Table 7.4: Values of the CLINT function xor_l()

Chapter 8: Input, Output, Assignment, Conversion

Table 8.1: Diagnostic values of the function vcheck_l()

Chapter 10: Basic Number-Theoretic Functions

Table 10.1: The largest known primes (as of August 2000)

Table 10.2: The number of primes up to various limits x

Chapter 12: Strategies for Testing LINT

Table 12.1: Group law for the integers to help in testing

Table 12.2: FLINT/C test functions

Chapter 13: Let C++ Simplify Your Life

Table 13.1: LINT constructors

Table 13.2: LINT arithmetic operators

Table 13.3: LINT bitwise operators

Table 13.4: LINT logical operators

Table 13.5: LINT assignment operators

Chapter 14: The LINT Public Interface: Members and Friends

Table 14.1: LINT status functions and their effects

Table 14.2: LINT manipulators and their effects

Table 14.3: LINT flags for output formatting and their effects

Chapter 15: Error Handling

Table 15.1: LINT function error codes

Chapter 16: An Application Example: The RSA Cryptosystem

Table 16.1: Recommended key lengths according to Lenstra and Verheul

Chapter 19: Rijndael: A Successor to the Data Encryption Standard

Table 19.1: Elements of

Table 19.2: Powers of g(x) = x + 1

Table 19.3: Logarithms to base g(x) = x + 1 (e.g., log_g(x) 3 = 25, log_g(x) 255 = 7)

Table 19.4: Number of Rijndael rounds as a function of block and key length

Table 19.5: Representation of message blocks

Table 19.6: rc(j) constants (hexadecimal)

Table 19.7: rc(j) constants (binary)

Table 19.8: Representation of the round keys

Table 19.9: The values of the S-box

Table 19.10: The values of the inverted S-box

Table 19.11: ShiftRow for blocks of length 128 bits (L_b = 4)

Table 19.12: ShiftRow for blocks of length 192 bits (L_b = 6)

Table 19.13: ShiftRow for blocks of length 256 bits (L_b = 8)

Table 19.14: Distances of line rotations in ShiftRow

Table 19.15: Interpretation of variables

Table 19.16: Interpretation of fields

Table 19.17: Interpretation of functions

Appendix D: Calculation Times

Table D.1: Calculation times for several C functions (without assembler support)

Table D.2: Calculation times for several C functions (with 80×86 assembler support)

Table D.3: Calculation times for several GMP functions (with 80×86 assembler support)

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