MA28140 datasheet(16/72 Pages) DYNEX

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MA28140

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THE HASHING FUNCTION

One purpose of the Hashing Function is to compress the

variable amount of data bits constituted by the extended

message x into a pre-signature P of fixed length (60 bits). The

device realising the Hashing Function is a 60-bit linear

feedback shift register (LFSR), as shown in Figure 8. The 60

feedback coefficients C0, C1,......,C59 are part of the

Authentication Key.

The LFSR is initialised to the 60-bit value P’ = 1000....000

(where Bit P0 = 1) before the process of each authenticated

TC Segment begins. P will be the value in the LFSR after the

last bit of the variable-length extended message x has been

shifted in. The extended message x (x = [m,l,z]) consists of the

following data elements, placed one after the other in that

order:

- the received message m, i.e., the TC Segment

(variable from 1 to 240 octets) without the

Authentication Tail;

- the received LAC value l, i.e., 4 octets (2 bits of LAC

ID, plus 30 bits of LAC Count);

- three octets of virtual fill z, consisting of 24 zeros.

The purpose of the 24 bits of virtual fill is to ensure that the

Hashing Function is provided with a minimum of data bits. The

24 bits of virtual fill z are generated by the PTD. Note that since

m (the TC Segment) cannot be equal to zero, the total length of

an authenticated TC Segment (i.e., [m,l,s]) cannot be smaller

than 10 octets (Segment Header (1 octet) + Authentication tail

(9 octets)). Anything smaller than 10 octets is rejected as being

too short.

THE HARD KNAPSACK

The purpose of the Hard Knapsack is to ensure that it is not

possible to deduce the presignature P from the signature S.

The Hard Knapsack is based on the concept of the modular

knapsack. It consists of 60 weights (numbered from W0 to

W59, each weight being 48 bits long) and is defined by the

following transformation:

j=59

S' = (

∑P

jWj) mod 2

j=0

where the bits Pj of the presignature P select the

corresponding weights Wj of the knapsack.

The result is the 48-bit knapsack sum S’. The most

significant bit of the sum is called S’0.

THE DELETION BOX

The Deletion Box deletes the 8 least significant bits of the

48-bit knapsack sum S’, i.e., bits S’40 through S’47. The result

is the 40-bit authentication signature S (numbered from Bit 0 to

Bit 39, as for signature s).

THE SIGNATURE COMPARATOR

The Signature Comparator compares the received 40-bit

signature s with the onboard generated 40-bit signature S.

Figure 7: Functional Diagram of the Authentication Processor

Hashing

Function

Hard

Knapsack

Deletion

Box

Signature

Comparator

Signature Valid

Segment

(m, l, s)

MA28140 Datasheet(PDF) 16 Page - Dynex Semiconductor

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