A Cryptographic Library for the Motorola DSP56000

A New Modified CMM Modular Exponentiation Algorithm

“…Therefore based on the computational analyses of Montgomery reduction algorithm from [15] for n-bit modulus and k-bit exponent, the following four operations S 1 C 1 mod N, S 1 C 2 mod N, S 1 C 3 mod N and S 1 C 4 mod N require These results are represented graphically in Figure 3. Window width % of improvements Improvement over [2] Improvement over [15] Improvement over [17] Improvement over [16] As it is shown in Table 1 and Figure 3, the proposed modular exponentiation algorithm reduces the multiplication steps considerably.…”

Fast batch modular exponentiation with common-multiplicand multiplication

“…Consider following numbers x, y and m in radix b representation with n digits : Montgomery reduction takes an integer a such that 0  a < Rm and yields aR 1 mod m. To compute the Montgomery reduction of the product of two integers x and y, multi-precision multiplication and Montgomery reduction method can be combined efficiently [18]. Montgomery multiplication MontMult(x, y) yields xyR 1 mod m as described in Algorithm MontMult of …”

Applied cryptography: Protocols, algorithms, and source code in C

“…Certificates play an important role in a number of public-key protocols such as PEM [825] (see Section 24.10) and X. 509 [304] (see Section 24.9).…”

“…Good survey articles are [258,872]. Many different chips perform RSA encryption [1310,252,1101,1317,874,69,737,594,1275,1563,509,1223]. A partial list of currently available RSA chips, from [150,258], is listed in Table 19.3.…”