1.1. Typical Data Types for the C Programming Language

1.2. Exercise Scoring System

2.1. Design Flow of the First Few Original LibTomMath Functions

2.2. The mp int Structure

2.3. LibTomMath Error Codes

2.4. Algorithm mp init

2.5. Algorithm mp clear

2.6. Algorithm mp grow

2.7. Algorithm mp init size

2.8. Algorithm mp init multi

2.9. Algorithm mp clamp

3.1. Algorithm mp copy

3.2. Algorithm mp init copy

3.3. Algorithm mp zero

3.4. Algorithm mp abs

3.5. Algorithm mp neg

3.6. Algorithm mp set

3.7. Algorithm mp set int

3.8. Comparison Return Codes

3.9. Algorithm mp cmp mag

3.10. Algorithm mp cmp

4.1. Algorithm s mp add

4.2. Algorithm s mp sub

4.3. Algorithm mp add

4.4. Addition Guide Chart

4.5. Algorithm mp sub

4.6. Subtraction Guide Chart

4.7. Algorithm mp mul 2

4.8. Algorithm mp div 2

4.9. Algorithm mp lshd

4.10. Sliding Window Movement

4.11. Algorithm mp rshd

4.12. Algorithm mp mul 2d

4.13. Algorithm mp div 2d

4.14. Algorithm mp mod 2d

5.1. Algorithm s mp mul digs

5.2. Long-Hand Multiplication Diagram

5.3. Comba Multiplication Diagram

5.4. Algorithm Comba Fixup

5.5. Algorithm fast s mp mul digs

5.6. Algorithm fast mult

5.7. Asymptotic Running Time of Polynomial Basis Multiplication

5.8. Algorithm mp karatsuba mul

5.9. Algorithm mp toom mul

5.10. Algorithm mp mul

5.11. Squaring Optimization Diagram

5.12. Algorithm s mp sqr

5.13. Algorithm fast s mp sqr

5.14. Algorithm mp karatsuba sqr

5.15. Algorithm mp sqr

6.1. Algorithm mp reduce

6.2. Algorithm mp reduce setup

6.3. Algorithm Montgomery Reduction

6.4. Example of Montgomery Reduction (I)

6.5. Algorithm Montgomery Reduction (modified I)

6.6. Example of Montgomery Reduction (II)

6.7. Algorithm Montgomery Reduction (modified II)

6.8. Example of Montgomery Reduction

6.9. Algorithm mp montgomery reduce

6.10. Algorithm fast mp montgomery reduce

6.11. Algorithm mp montgomery setup

6.12. Algorithm Diminished Radix Reduction

6.13. Example Diminished Radix Reduction

6.14. Algorithm mp dr reduce

6.15. Algorithm mp dr setup

6.16. Algorithm mp dr is modulus

6.17. Algorithm mp reduce 2k

6.18. Algorithm mp reduce 2k setup

6.19. Algorithm mp reduce is 2k

7.1. Left to Right Exponentiation

7.2. Example of Left to Right Exponentiation

7.3. Algorithm mp expt d

7.4. k-ary Exponentiation

7.5. Optimal Values of k for k-ary Exponentiation

7.6. Optimal Values of k for Sliding Window Exponentiation

7.7. Sliding Window k-ary Exponentiation

7.8. Algorithm mp exptmod

7.9. Algorithm s mp exptmod

7.10. Sliding Window State Diagram

7.11. Algorithm mp 2expt

8.1. Algorithm Radix-β Integer Division

8.2. Algorithm mp div

8.3. Algorithm mp add d

8.4. Algorithm mp mul d

8.5. Algorithm mp div d

8.6. Algorithm mp n root

8.7. Algorithm mp rand

8.8. Lower ASCII Map

8.9. Algorithm mp read radix

8.10. Algorithm mp toradix

8.11. Example of Algorithm mp toradix.

9.1. Algorithm Greatest Common Divisor (I)

9.2. Algorithm Greatest Common Divisor (II)

9.3. Algorithm Greatest Common Divisor (III)

9.4. Algorithm mp gcd

9.5. Algorithm mp lcm

9.6. Algorithm mp jacobi

9.7. Algorithm mp invmod

9.8. Algorithm mp prime is divisible

9.9. Algorithm mp prime fermat

9.10. Algorithm mp prime miller rabin