Method and apparatus for improving digital signatures
View Patent ↗Systems and methods are provided for enchancing pseudo random number generation to thwart various security attacks to a system that relies on digital signature security measures. For example, a random number may be bound to a message that is to be signed using a digital signature. Alternatively, a random number may be bound to a secret seed value, which may be updated subsequent to each signing. Alternatively still, a random number may be bound to both the message to be signed using a digital signature and a secret seed value.
1. A method, comprising:
selecting a random number (rand);
enhancing the rand,
wherein the enhancing of the rand comprises binding the rand with the at least one of the message or document and with a secret seed value (seed),
wherein the binding comprises:
computing a function relative to the at least one of the message or document, the function being represented by the following formula: f(M); and
computing the rand 1 , the rand 1 being represented by the following formula: rand 1 ==g(rand, f(M), seed), wherein g comprises a one-way function, or
reading the seed from a secure memory unit; and
computing the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, seed), wherein g comprises a one-way function; and
deriving a digital signature based at least in part, upon the enhanced random number (rand 1 ), for signing at least one of a message or document transceived by at least one device,
the enhanced random number utilized in setting an r-component of the digital signature such that the r-component of the digital signature is different than each of one or more other r-components of each of one or more other digital signatures.
2. The method of claim 1 , wherein the enhancing of the rand comprises binding the rand with the at least one of the message or document.
3. The method of claim 2 , wherein the binding comprises:
computing a function relative to the at least one of the message or document, the function being represented by the following formula: f(M); and
computing the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, f(M)), wherein g comprises a one-way function.
4. The method of claim 1 , wherein the enhancing of the rand comprises binding the rand with a secret seed value (seed).
5. The method of claim 4 , wherein the binding comprises:
reading the seed from a secure memory unit; and
computing the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, seed), wherein g comprises a one-way function.
6. The method of claim 1 , wherein the enhancing of the rand comprises binding the rand with at least a secret seed value (seed), the seed being updated subsequent to the signing of the at least one of the message or document.
7. The method of claim 6 , further comprising:
adding a counter value into the seed; and
storing a new seed in a memory unit.
8. A non-transitory computer-readable medium including computer executable instructions stored thereon, the computer executable instructions, which when executed by a processor, cause an apparatus to:
select a random number (rand);
enhance the rand,
wherein causing the apparatus to perform the enhancing of the rand further comprises computer executable instructions, which when executed by a processor, cause an apparatus to bind the rand with the at least one of the message or document and with a secret seed value (seed),
wherein causing the apparatus to bind further computer executable instructions, which when executed by a processor, cause an apparatus to:
compute a function relative to the at least one of the message or document, the function being represented by the following formula: f(M); and
compute the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, f(M), seed), wherein g comprises a one-way function, or
read the seed from a secure memory unit; and
compute the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, seed), wherein g comprises a one-way function; and
derive a digital signature based at least in part, upon the enhanced random number (rand 1 ), for signing at least one of a message or document transceived by the apparatus,
the enhanced random number utilized in setting an r-component of the digital signature such that the r-component of the digital signature is different than each of one or more other r-components of each of one or more other digital signatures.
9. An apparatus, comprising:
at least one processor, and
at least one memory including computer program code, the at least one memory and the computer program code configured to, with the at least one processor, cause the apparatus to perform at least the following:
select a random number (rand);
enhance the rand,
wherein causing the apparatus to perform the enhancing of the rand comprises the at least one memory, the computer program code, and the at least one processor to cause the apparatus to bind the rand with the at least one of the message or document and with a secret seed value (seed),
wherein causing the apparatus to bind comprises the at least one memory, the computer program code, and the at least one processor causing the apparatus to:
compute a function relative to the at least one of the message or document, the function being represented by the following formula: f(M); and
compute the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, f(M), seed), wherein g comprises a one-way function, or
read the seed from a secure memory unit; and
compute the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, seed), wherein g comprises a one-way function; and
derive a digital signature based at least in part, upon the enhanced random number (rand 1 ), for signing at least one of a message or document transceived by the apparatus,
the enhanced random number utilized in setting an r-component of the digital signature such that the r-component of the digital signature is different than each of one or more other r-components of each of one or more other digital signatures.
10. The apparatus of claim 9 , wherein causing the apparatus to perform the enhancing of the rand comprises the at least one memory, the computer program code, and the at least one processor causing the apparatus to bind the rand with the at least one of the message or document.
11. The apparatus of claim 10 , wherein causing the apparatus to bind comprises the at least one memory, the computer program code, and the at least one processor causing the apparatus to:
compute a function relative to the at least one of the message or document, the function being represented by the following formula: f(M); and
compute the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, f(M)), wherein g comprises a one-way function.
12. The apparatus of claim 9 , wherein causing the apparatus to perform the enhancing of the rand comprises the at least one memory, the computer program code, and the at least one processor causing the apparatus to bind the rand with a secret seed value (seed).
13. The apparatus of claim 12 , wherein causing the apparatus to bind comprises the at least one memory, the computer program code, and the at least one processor causing the apparatus to:
read the seed from a secure memory unit; and
compute the rand 1 , the rand 1 being represented by the following formula: rand 1 =g(rand, seed), wherein g comprises a one-way function.
14. The apparatus of claim 9 , wherein causing the apparatus to perform the enhancing of the rand comprises the at least one memory, the computer program code, and the at least one processor causing the apparatus to bind the rand with at least a secret seed value (seed), the seed being updated subsequent to the signing of the at least one of the message or document.
15. The apparatus of claim 14 , wherein the at least one memory, the computer program code, and the at least one processor further cause the apparatus to:
add a counter value into the seed; and
store a new seed in a memory unit.
16. The apparatus of claim 9 , wherein the digital signature comprises an elliptic curve digital signature.