BigNum Math Implementing Cryptographic Multiple Precision Arithmetic pdf

BigNum Math Implementing Cryptographic Multiple Precision Arithmetic Wonderful Digest

1.1.3 Benefits of Multiple Precision Arithmetic

The benefit of multiple precision representations over single or fixed precision representations is that no precision is lost while representing the result of an operation that requires excess precision. For example, the product of two n-bit integers requires at least 2n bits of precision to be represented faithfully. A multiple precision algorithm would augment the precision of the destination to accommodate the result, while a single precision system would truncate excess bits to maintain a fixed level of precision.

It is possible to implement algorithms that require large integers with fixed precision algorithms. For example, elliptic curve cryptography (ECC) is often implemented on smartcards by fixing the precision of the integers to the maximum size the system will ever need. Such an approach can lead to vastly simpler algorithms that can accommodate the integers required even if the host platform cannot natively accommodate them 5 . However, as efficient as such an approach may be, the resulting source code is not normally very flexible. It cannot, at run time, accommodate inputs of higher magnitude than the designer anticipated.