5812-DS01-R datasheet(38/84 Pages) BOARDCOM

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BCM5812

Advance Data Sheet

3/11/03

B roa dcom Co rpo rat ion

Page 30

Cryptographic Operations

Document

5812-DS01-405-R

Generally, the public exponent e can be chosen to be short, but the private exponent is derived and should be nearly as long

as the modulus. The effort to exponentiate is proportional to the logarithm of the exponent; therefore, the private key

operation takes considerably longer than the public key operation. This can be speeded up by taking advantage of the

knowledge of p and q, and doing exponential using residue arithmetic according to the Chinese Remainder Theorem (CRT).

In effect, this breaks d into two components, dp = d mod (p-1) and dq = d mod (q-1), does two, half-sized exponentiations

modulo p and modulo q, and combining the result using an inverse constant (q-1 mod p).

The BCM5812 provides both RSA public key and CRT private key operations. Figure 27 shows the command context for

the RSA public key operation. As with Diffie-Hellman, the modulus and exponent are specified in bits, with parameter sizes

in the command context, input, and output according to Table 10 on page 27. This operation uses MCR2@, and opcode

0x03.

Figure 27: RSA Public Key

The single input buffer length is given in the input fragment length, in bytes, and must be one of the parameter field sizes in

Table 10. The input can be byte aligned, and may require padding with zeros to the parameter field size. The output buffer

must be the same length, but must be 32-bit aligned. The exponent and modulus parameter field sizes must be the same.

The exponent must be smaller than the modulus.

Figure 28 shows the RSA CRT private key operation command context.The five CRT parameters, p, q, dp, dq, and q

-1, are

each half the size of the public key modulus. Table 11 shows the allowed parameter field sizes in 32-bit words and bytes.

LENGTH

Command Context

OPCODE

MODULUS LENGTH

MODULUS

64-256

Bytes

EXPONENT LENGTH

EXPONENT

64-256

Bytes

COMMAND CONTEXT ADDRESS

NEXT INPUT FRAGMENT CHAIN ENTRY

RESERVED

INPUT FRAGMENT LENGTH

INPUT FRAGMENT ADDRESS

RESERVED

NEXT OUTPUT FRAGMENT CHAIN ENTRY

RESERVED

OUTPUT BUFFER LENGTH

OUTPUT FRAGMENT ADDRESS

Input

(Modulus Length)

Output

(Modulus Length)

Packet Descriptor

LENGTH

Command Context

OPCODE

MODULUS LENGTH

MODULUS

64-256

Bytes

EXPONENT LENGTH

EXPONENT

64-256

Bytes

COMMAND CONTEXT ADDRESS

NEXT INPUT FRAGMENT CHAIN ENTRY

RESERVED

INPUT FRAGMENT LENGTH

INPUT FRAGMENT ADDRESS

RESERVED

NEXT OUTPUT FRAGMENT CHAIN ENTRY

RESERVED

OUTPUT BUFFER LENGTH

OUTPUT FRAGMENT ADDRESS

Input

(Modulus Length)

Output

(Modulus Length)

Packet Descriptor

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