Public key accelerator (PKA) RM0453
708/1461 RM0453 Rev 1
1. Inward (or outward) conversion into (or from) Montgomery domain
a) Let’s assume A is an integer in the natural domain
Compute r2modn using Montgomery parameter computation
Result AR= A x r2modn mod n is A in the Montgomery domain
b) Let’s assume BR is an integer in the Montgomery domain
Result B = BR x 1 mod n is B in the natural domain
Similarly, above value AR computed in a) can be converted into the natural
domain by computing A = AR x 1 mod n
2. Simple modular multiplication A x B mod n
a) Compute r2modn using Montgomery parameter computation
b) Compute AR = A x r2modn mod n. Output is in the Montgomery domain
c) Compute AB= AR x B mod n. Output is in natural domain
3. Multiple modular multiplication A x B x C mod n
a) Compute r2modn using Montgomery parameter computation
b) Compute AR = A x r2modn mod n. Output is in the Montgomery domain
c) Compute BR = B x r2modn mod n. Output is in the Montgomery domain
d) Compute ABR= AR x BR mod n. Output is in the Montgomery domain
e) Compute CR = C x r2modn mod n. Output is in the Montgomery domain
f) Compute ABCR= ABR x CR mod n. Output is in the Montgomery domain
g) (optional) Repeat the two steps above if more operands need to be multiplied
h) Compute ABC= ABCR x 1 mod n to retrieve the result in natural domain
Operation instructions for Montgomery multiplication are summarized in Table 149.
24.4.6 Modular exponentiation
Modular exponentiation operation is commonly used to perform a single-step RSA
operation. It consists in the computation of A
e
mod n.
Operation instructions for modular exponentiation are summarized in Table 150 (normal
mode) and in Table 151 (fast mode). Fast mode usage is explained in Section 24.3.6.
Table 149. Montgomery multiplication
Parameters with direction Value (Note) Storage Size
IN
MODE 0x10 PKA_CR 6 bits
Operand length (In bits, not null) RAM@0x404 32 bits
Operand A (0 ≤ A < n) RAM@0x8B4
ROS
Operand B (0 ≤ B < n) RAM@0xA44
Modulus value n (Odd integer only, n < 2
3136
)RAM@0xD5C
OUT Result: AxB mod n - RAM@0xBD0
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