By Michael Welschenbach
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Extra info for Cryptography in C and C++, Second Edition - (May 25, 2005)
Stlm]) the following appears: #define UCHAR_MAX 0xffU #define USHRT_MAX 0xffffU #define UINT_MAX 0xffffffffU #define ULONG_MAX 0xffffffffUL One should note that with respect to the number of binary places there are actually only three sizes that are distinguished. The type USHRT (respectively USHORT in our notation) can be represented in a 16-bit register; the type ULONG ﬁlls the word length of a CPU with 32-bit registers. The type ULONG_MAX determines the value of the largest unsigned whole numbers representable by scalar types (cf.
It is necessary to plan carefully, since decisions made at this point will be difﬁcult to revise at a later time. ” It is necessary to determine the order of magnitude of the numbers to be processed and the data type to be used for coding these numerical values. The basic function of all routines in the FLINT/C library is the processing of natural numbers of several hundred digits, which far exceeds the capacity of standard data types. We thus require a logical ordering of a computer’s memory units by means of which large numbers can be expressed and operated on.
Set t ← ai + bi + c, si ← t mod B , and c ← t/B . 3. Set i ← i + 1; if i ≤ n − 1, go to step 2. 4. Set t ← ai + c, si ← t mod B , and c ← t/B . 5. Set i ← i + 1; if i ≤ m − 1, go to step 4. 6. Set sm ← c. 7. Output s = (sm sm−1 . . s0 )B . The digits of the summands, together with the carry, are added in step 2, with the less-signiﬁcant part stored as a digit of the sum, while the more-signiﬁcant part is carried to the next digit. If the most-signiﬁcant digit of one of the summands is reached, then in step 4 any remaining digits of the other summand are added to any remaining carries one after the other.
Cryptography in C and C++, Second Edition - (May 25, 2005) by Michael Welschenbach