hcrypto/libtommath/tommath.tex

150 sci.crypt Usenet news group. I watched him go from a clueless newbie, to the cryptographic equivalent of a reformed smoker, to a real
556 the source code.  For example, one day I may audit the multipliers and the next day the polynomial basis functions.
913 The requested digit count is padded up to next multiple of \textbf{MP\_PREC} plus an additional \textbf{MP\_PREC} (steps two and three).
987 The number of digits $b$ requested is padded (line 24) by first augmenting it to the next multiple of
1478 next four bits from the source are extracted and are added to the mp\_int. The \textbf{used} digit count is
1621 established.  The next logical set of algorithms to develop are addition, subtraction and digit shifting algorithms.  These
1744 for the next loop (line 97 to 99) which set any old upper digits to zero.
2064 obtain what will be the carry for the next iteration.  Step 6.2 calculates the $n$'th digit of the result as single precision shift of $a_n$ plus
2066 forwarding the carry to the next iteration.
2318 variable is used to extract the upper $d$ bits to form the carry for the next iteration.
2337 extract the carry bit(s) to pass into the next iteration of the loop.  The $r$ and $rr$ variables form a
2629 next iteration.
2793 into the next round by dividing $\_ \hat W$ by $\beta$.
2821 a carry for the next pass.  After the outer loop we use the final carry (line 77) as the last digit of the product.
3019 number of digits for the next section of code.
3084 Continued on the next page.\\
3308 results calculated so far.  This involves expensive carry propagation which will be eliminated in the next algorithm.
3627 targeted the DSP56K processor.}  intuition would indicate the next step would be to replace $a/b$ by a multiplication by the reciprocal.  However,
3746 The next optimization arises from this very fact.  Instead of computing $b \cdot \lfloor (q_0 \cdot \mu) / \beta^{m+1} \rfloor$ using a full
4219 for the next iteration of the loop by propagating the carry from $\hat W_{ix}$ to $\hat W_{ix+1}$.
4386 Throughout the next section the term ``restricted modulus'' will refer to a modulus of the form $\beta^p - k$ whereas the term ``unrestricted
4822 of $b$ is shifted left one bit to make the next bit down from the most signficant bit the new most significant bit.  In effect each
4841 computes the same exponentiation.  A group of $k$ bits from the exponent is called a \textit{window}.  That is it is a small window on only a
5081 Continued on next page. \\
5176 At step 12.5 if the $mode$ and currently extracted bit $y$ are both zero the bit is ignored and the next bit is read.  This prevents the
5392 Continued on the next page. \\
5410 \hspace{3mm}13.1  If $i > x.used$ then jump to the next iteration of this loop. \\
5470 Recall from section~\ref{sec:divest} that the estimation is never too low but may be too high.  The next step of the estimation process is
5895 each iteration the quotient $\lfloor a / r \rfloor$ is saved for the next iteration.  As a result a series of trivial $n \times 1$ divisions
6094 factors of two from the difference $u$ to ensure that in the next iteration of the loop both are once again odd.
6532 the multiplicative sub group is $n - 1$.  Any base $a$ must have an order which divides $n - 1$ and as such $a^n$ is equivalent to