Keys for elliptic curve cryptography

Patent metadata

Field	Value
Publication number	US-11831771-B2
Application number	US-202117506377-A
Country	US
Kind code	B2
Filing date	Oct 20, 2021
Priority date	Oct 30, 2020
Publication date	Nov 28, 2023
Grant date	Nov 28, 2023

Abstract

Cryptographic circuitry, in operation, generates N first pairs of elliptic curve cryptography (ECC) keys r(i), R(i), with i varying from 1 to N, using K second pairs of ECC keys p(k), P(k), with k varying from 1 to K, wherein K is smaller than N. Each pair r(i), R(i) of the first pairs of keys is a linear combination of pairs of the second pairs of ECC keys according to:∀i∈[1;N]⁢{r⁡(l)=∑j=1KA⁡(i,j)*p⁡(j)R⁡(i)=∑j=1KA⁡(i,j)*P⁡(j),wherein A(i,j) designates a general term of a matrix A of size N*K, and all the sub-matrices of size K*K are invertible. The cryptographic circuitry, in operation, executes cryptographic operations using one or more pairs of the first pairs of ECC keys.

First claim

The invention claimed is:

1. A method, comprising:
generating, using cryptographic circuitry, N first pairs of elliptic curve cryptography (ECC) keys r(i), R(i), with i varying from 1 to N, using K second pairs of ECC keys p(k), P(k), with k varying from 1 to K, wherein K is smaller than N, and each pair r(i), R(i) of the first pairs of keys is a linear combination of pairs of the second pairs of ECC keys according to:

∀

i
∈

[

1
;
N

]

⁢

{

r
⁡

(
i
)

=

∑

j
=
1

K

⁢

A
⁡

(

i
,
j

)

⋆

p
⁡

(
j
)

R
⁡

(
i
)

=

∑

j
=
1

K

⁢

A
⁡

(

i
,
j

)

⋆

P
⁡

(
j
)

,

wherein A(i,j) designates a general term of a matrix A of size N*K, and all sub-matrices of size K*K are invertible; and
executing, using the cryptographic circuitry, cryptographic operations using one or more pairs of the first pairs of ECC keys.

2. The method according to claim 1 , comprising initialization of the N first pairs of keys before the application of the linear combination.

3. The method according to claim 2 , wherein during the initialization, the N first pairs of ECC keys are set to zero and to the point at infinity, respectively.

4. The method according to claim 2 , wherein during the initialization, the N first pairs of keys are initialized to the value taken by the last generated first pair of keys.

5. The method according to claim 2 , wherein during the initialization, the N first pairs of keys (r(i), R(i)) are initialized to the value taken by one of the last W generated pair of keys (r(i−j), R(i−j)), where j<=W, j<i and j>=1.

6. The method according to claim 1 , wherein matrix A is a Vandermonde matrix.

7. The method according to claim 1 , wherein the first and second pairs of keys are formed of a scalar and of a point on an elliptic curve.

8. The method of claim 1 , wherein the cryptographic operations include:
generating a digital signature;
generating a key agreement; or
combinations thereof.

9. The method of claim 1 , comprising:
generating the K second pairs of ECC keys; and
storing the generated K pairs of ECC keys.

10. A device, comprising:
a memory; and
cryptographic circuitry coupled to the memory, wherein the cryptographic circuitry, in operation:
generates N first pairs of elliptic curve cryptography (ECC) keys r(i), R(i), with i varying from 1 to N, using K second pairs of ECC keys p(k), P(k), with k varying from 1 to K, wherein K is smaller than N, and each pair r(i), R(i) of the first pairs of keys is a linear combination of pairs of the second pairs of ECC keys according to:

∀

i
∈

[

1
;
N

]

⁢

{

r
⁡

(
i
)

Assignees

• St Microelectronics Srl
• Proton World Int Nv

Inventors

• Simon Thierry
• Peeters Michael
• Caserta Francesco

Classifications

• H04L9/3073 Primary

  involving pairings, e.g. identity based encryption [IBE], bilinear mappings or bilinear pairings, e.g. Weil or Tate pairing · CPC title

• H04L9/0838

  Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these (network architectures or network communication protocols for key exchange in a packet data network H04L63/061) · CPC title

• H04L9/3247

  involving digital signatures · CPC title

• H04L2209/12

  Details relating to cryptographic hardware or logic circuitry · CPC title

• H04L9/3066 Primary

  involving algebraic varieties, e.g. elliptic or hyper-elliptic curves · CPC title