BACKGROUND INFORMATION
The present invention relates generally to processors and controllers and standard cells for arithmetic logic units (ALUs) in such processors and controllers.
A standard cell for ALUs in microcontrollers may be implemented using a semi-custom design style. Chip card controllers have to meet high requirements in terms of resistance to invasive probing and/or non-invasive differential power analysis (DPA) of security-critical information. One prior art device uses bitwise XOR masking of all data using time-variant masks, so-called “one-time pad (OTP)” masks.
FIG. 1 shows a so-called “mirror adder”, a conventional full adder cell 10 which implements the equations
co
—
n= a·b+b·ci+ci·a (1)
s_n=a⊕b⊕ci (2).
The mirror adder thus logically combines the two operand bits a and b and the carry-in bit ci in order to obtain the inverted carry-out bit co_n and the inverted sum bit s_n. In a standard-cell implementation of the mirror adder, co_n and s_n are usually additionally inverted by two inverters so that then the outputs of the mirror adder cell are usually the carry bit co and the sum bit s.
When output signals produced by a conventional full adder are supplied with masked input data, the equations
y=a·b+b·c+c·a (3)
z=a⊕b⊕c (4)
are transformed under the “masking operation”, that is, the XOR combination
{circumflex over (x)}=x⊕k (5)
of x=a, b and c with an OTP bit k.
One then obtains â·{circumflex over (b)}+{circumflex over (b)}·ĉ+ĉ·â=(a·b+b·c+c·a)⊕k=y⊕k=ŷ and â⊕{circumflex over (b)}⊕ĉ=a⊕b⊕c⊕k=z⊕k={circumflex over (z)}. The “full adder equations” are form-invariant (covariant) under the “masking operation”: from input data masked with k, the full adder computes output data which is also obtained when output data from unmasked input data is masked with k.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a prior art mirror adder.
The present invention will be described with respect to a preferred embodiment, in which:
FIG. 2 shows a masked mirror adder according to the present invention;
FIG. 3 shows ALU control circuitry for the masked mirror adder of FIG. 2;
FIG. 4 shows the controlled cell and the interaction of the control circuitry of FIG. 3 with the adder of FIG. 2;
FIG. 5 shows a possible implementation for the XNOR3 gate of FIG. 3; and
FIG. 6 shows a table summarizing the logical operations of the ALU cell.
DETAILED DESCRIPTION
Attempts to implement OTP masks using conventional standard cells have led to unacceptable values for the computing speed and energy expenditure. Because of this, commercial implementation of OTP-masked computation has been difficult.
One embodiment of the present invention provides a cell for an arithmetic logic unit comprising:
- a first input;
- a second input;
- a carry bit input;
- a first control input and a second control input;
- a circuit connected to the first input, the second input, the carry bit input, the first control input, and the second control input, the circuit having a first output and a second output;
- the second output having a first value as a function of the first input and the second input when the first control input and the second control input are supplied values equal to a value at the carry bit input, and having a second value as a function of the first input and second input when the values at the first control input and the second control input are independent of the value at the carry-in input.
A further embodiment of the present invention provides control circuitry for an ALU cell comprising:
- a mask bit input;
- a carry bit input;
- and
- a circuit outputting a masked carry bit and having two control outputs.
A further embodiment of the present invention also provides control circuitry for an ALU cell comprising:
- a current mask bit input;
- a previous mask bit input inputting the mask bit from an immediately upstream ALU cell;
- a carry bit input;
- three control bit inputs;
- and
- a circuit outputting a masked carry bit and having two control outputs as a function of the current mask bit input and the previous mask bit input.
In a further embodiment, the present invention provides a masked ALU cell comprising:
- a carry bit input;
- a mask bit input;
- a control circuit receiving the carry bit input and the mask bit input and outputting a masked carry bit, the control circuit having at least three control states; and
- a base circuit logically combining a first input, a second input and the masked carry bit to: (a) logically add the carry bit input, the second input and the masked carry bit when the control circuit is in a first of the three control states, (b) logically XOR or XNOR the first input and second input when the control circuit is in a second state of the three control states; and (c) logically AND, OR, NOR or NAND the first input and second input when the control circuit is in a third state of the three control states.
The present invention also provides a method for logically combining two inputs in a masked ALU cell comprising:
- receiving a carry bit from an adjacent upstream ALU cell;
- masking the carry bit by performing an exclusive-or on the carry bit with a mask bit; and
- controlling an ALU cell to logically add two inputs and the masked carry bit in the ALU cell as well as perform bitwise AND, OR, NAND, NOR, XOR or XNOR on the two inputs.
The present invention provides a mirror adder, control circuitry and methods suited especially well for standard cell implementation. The ALU cell of the present invention not only provides the arithmetic function of (one-bit) addition of two binary numbers (the two operands), but also is programmable by suitable control signals so as to perform logical operations, namely bitwise NAND, NOR or XOR operations, on the two operands. When suitably inverting the operands or the result, it is then possible to implement any possible bitwise logical operations as well as arithmetic operations. Moreover, all these operations are intended to be performed such that all data (operands, carries (carry-ins/carry-outs), and results) are XOR-masked using time-variant OTP masks.
Compared to an OTP implementation using conventional standard cells, this means significantly (several hundred percent) higher computing speeds and significantly lower energy expenditure.
FIG. 2 shows a possible mirror adder implementation 20 in CMOS according to the present invention, with transistors TP1 to TP12 and TN1 to TN12. The transistors TN9 and TP12 are connected to an input control signal xe1; and transistors TN12 and TP9 are connected to input signal xe0.
From this, it follows that the relationship between co*_n and a*, b* and ci* in FIG. 2 is the same as that between co_n and a, b, and ci in FIG. 1:
co*
—
n= a*·b*+b*·ci*+ci*·a* (6)
and, secondly, that the equation for s*_n in FIG. 2 is:
s*_n= a*⊕b*⊕ci* (7)
if it holds that xe1=xe0=ci*,
and, respectively,
s*
—
n=
co*
—
n
=a*·b*+b*™ci*+ci*·a* (8)
for xe1=1, xe0=0
Other values for xe1 and xe0 are not needed in this embodiment.
With the definition
y*=y⊕kp, (9)
(where kp denotes the mask bit for bit position p) for masked data, it follows from the covariance of the full adder equations under the masking operation, first of all, that the circuit specified in FIG. 2 has the properties required for calculating (6) the masked carry-out co*_n from the masked inputs a*, b* and ci*.
As for the inverted sum bit s*_n, i.e., the equations (7) and (8), (7) represents the conventional (covariant) full adder equation for the inverted sum bit if ci* denotes the carry bit masked with kp of bit position p-1.
However, if it is provided that the carry-in bit ci* for bit position p is equal to mask bit kp or to its inverse kp, respectively, it follows that (7) implements the kp-masked XOR and XNOR operations on a* and b*, respectively:
s*_n= a*⊕b*⊕kp (10)
for ci*=kp, and, respectively,
for ci*= kp.
Alternatively to equation (7), or to the ADD, XOR and XNOR operations, as described above, the operations NAND and NOR can be implemented by (8). To this end, in addition to the conditions xe1=1, xe0=0 for the validity of (8), it should again be provided that the carry-in bit ci* for bit position p is equal to mask bit kp or to its inverse kp, respectively. If so, it follows that (8) implements the kp-masked NAND and NOR operations on a* and b*, respectively:
for ci*=kp, and, respectively,
for ci*= kp.
FIG. 3 shows a control circuit 30 by which the value combinations for xe1, xe0 and ci* specified above for the implementation of the various operations can be generated as a function of the mask bits kp (of the bit position p associated with the currently considered ALU cell) and kp-1, (of the bit position p-1 whose carry-out bit cop-1 represents the carry-in bit of bit position p), the carry-in bit ci′= m1·cop-1*_n (see FIG. 4) of bit position p and the control signals m3, m2 and m1.
The table of FIG. 6 summarizes the generation of xe1, xe0 and ci*:
In this regard, it should further be noted that the combinations of control signals m3, m2, m1 (0, 0, 1 and 0, 1, 1 and 1, 1, 1), which are not listed in the above table, are excluded by an external control logic, because otherwise the resulting expressions for the output data of the ALU cell of the present invention would be useless for arithmetic-logic purposes.
FIG. 4 shows the generation of co*p= m1·cop*_n, as well as the interconnection of the subcircuits 20, 30 shown in FIGS. 2 and 3 of the masked mirror ALU cell of the present invention. m1 and the value co*_n are inputted to a NAND gate 40 to generate the carry bit for the next downstream cell, so that co*p becomes ci′ for the next cell. s*_n can pass through an inverter 50 to form s*. The operations listed in the table shown in FIG. 6 reflect s*. The external control logic 32 can prevent concurrent values for m3, m2, m1 of (0, 0, 1) and (0, 1, 1) and (1, 1, 1), for this embodiment.
All circuit elements included FIG. 4 or its subfigures (which may have for example 63-66 transistors, depending on the implementation) can be integrated physically (in the layout) into one unit, in an extension of conventional standard cell libraries. This, together with the minimal number of transistors and the small number and small electrical capacitance of the switching nodes, is the reason for the high computing speed and the low energy expenditure of this cell.
FIG. 5 illustrates an advantageous implementation of the XNOR3 circuit symbolically shown in FIG. 3, using the so-called “transmission gate” design style.
Patent Application
20080126456
