Method of preventing power analysis attacks on microelectronic assemblies

In a microelectronic assembly including an integrated circuit (IC) for execution of an embedded modular exponentiation program, wherein in the modular exponentiation program a secret exponent (E) having a plurality of bits characterizes a private key, a method of providing a digital signature to prevent the detection of the secret exponent when monitoring power variations during the IC execution, the method comprising the steps of:

• selecting at least one predetermined bit in the secret exponent, wherein the at least one predetermined bit is a bit other than a least significant bit (LSB) and a most significant bit (MSB);
• using a first algorithm, sequentially selecting bits to the right of the at least one predetermined bit for exponentiation until the LSB is selected;
• and
• using a second algorithm, subsequent to selecting the LSB, sequentially selecting bits to the left of the at least one predetermined bit for exponentiation until the MSB is selected,
• wherein the first algorithm is different from the second algorithm.

In a microelectronic assembly including an integrated circuit (IC) for execution of an embedded elliptic-curve scalar multiplication program, wherein in the elliptic-curve scalar multiplication program a secret scalar having a plurality of bits characterizes a private key, a method of providing a digital signature to prevent the detection of the secret scalar when monitoring power variations during the IC execution, the method comprising the steps of:

• selecting at least one predetermined bit in the secret scalar, wherein the at least one predetermined bit is a bit other than a least significant bit (LSB) and a most significant bit (MSB);
• using a first algorithm, sequentially selecting bits to the left of the at least one predetermined bit for scalar multiplication until the MSB is selected;
• and
• using a second algorithm, subsequent to selecting the MSB, sequentially selecting bits to the right of the at least one predetermined bit for scalar multiplication until the LSB is selected,
• wherein the first algorithm is different from the second algorithm.

In a microelectronic assembly including an integrated circuit (IC) for execution of an embedded elliptic-curve scalar multiplication program, wherein in the elliptic-curve scalar multiplication program a secret scalar having a plurality of bits characterizes a private key, a method of providing a digital signature to prevent the detection of the secret scalar when monitoring power variations during the IC execution, the method comprising the steps of:

• selecting at least one predetermined bit in the secret scalar, wherein the at least one predetermined bit is a bit other than a least significant bit (LSB) and a most significant bit (MSB);
• using a first algorithm, sequentially selecting bits to the right of the at least one predetermined bit for scalar multiplication until the LSB is selected;
• and
• using a second algorithm, subsequent to selecting the LSB, sequentially selecting bits to the left of the at least one predetermined bit for scalar multiplication until the MSB is selected,
• wherein the first algorithm is different from the second algorithm.