MA28140 Datasheet, PDF (16/72 Pages) Dynex Semiconductor – Packet Telecommand Decoder

MA28140
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_jW_j) mod 2⁴⁸
j=0
where the bits Pj of the presignature P select the
corresponding weights W_j 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.
TC
Segment
(m, l, s)
m
l
x
Hashing
P
Hard
S'
Deletion
S
Function
Knapsack
Box
z
S
Signature
Signature Valid
s
Comparator
Figure 7: Functional Diagram of the Authentication Processor
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