US 9,425,961 B2Granted

Method for performing an encryption of an AES type, and corresponding system and computer program product

AssigneeSTMicroelectronics S.r.l.

InventorsRuggero Susella, Silvia Mella

Life of this patent

Estimating the term…

Loading patent…

Abstract

A polynomial representation (bi(x)) in an AES finite field ( Z 2 ⁡ [ x ] ( r ⁡ ( x ) ) ) of input bytes (bi) of a state matrix (B) is obtained. A plurality (1) of irreducible polynomials (fi(y)) and a moving map (ψi) are used to map each polynomial (bi(x)) of the polynomial representation into a respective field of polynomials ( Z 2 ⁡ [ y ] ( f i ⁡ ( y ) ) ) computed with respect to one of the irreducible polynomials (fi(y)), to obtain respective moved polynomials (αi(y)). The moved polynomials (αi(y)) are mapped into a polynomial (a(z)) of a polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) , obtained by applying an isomorphism (ω) between the fields of polynomials ( Z 2 ⁡ [ y ] ( f i ⁡ ( y ) ) ) and the polynomial ring ( Z 2 ⁡ [ z ] ( p ⁡ ( z ) ) ) based upon the Chinese remainder theorem (CRT). AES encryption is applied to the polynomial (a(z)). The polynomial (a(z)) is reconverted into the AES finite field ( Z 2 ⁡ [ x ] ( r ⁡ ( x ) ) ) to obtain an encrypted state matrix (CB).

Claims23

Dependent claims

A method, comprising:

protecting data stored in a hardware data media from attack using Advanced Encryption Standard (AES) cyphering circuitry, the protecting including:
mapping polynomial representations in an AES finite field of bytes of a state matrix into respective fields of polynomials computed with respect to one of a plurality of irreducible polynomials, generating moved polynomials;
applying Chinese-Remainder-Theorem (CRT) based mapping to the generated moved polynomials, generating a polynomial representing the state matrix in a polynomial ring;
applying an AES process to the polynomial representing the state matrix in the polynomial ring, generating an AES-processed polynomial;
and
converting the AES-processed polynomial into the AES finite field, generating an AES-processed state matrix, wherein the method includes:
obtaining the polynomial representation (bi(x)) in the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
of the input bytes (bi) of said state matrix (B);
providing the plurality of irreducible polynomials (fi(y)) and mapping, using a moving map (ψi), each polynomial (bi(x)) of said polynomial representation into the respective field of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
computed with respect to one of said irreducible polynomials (fi(y)), to obtain the respective moved polynomials (αy(y));
mapping said moved polynomials (αi(y)) into a polynomial (a(z)) of the polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
,
obtained by applying an isomorphism (ω) between the direct product of said fields of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
and said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
based upon the Chinese remainder theorem (CRT), said polynomial (a(z)) representing the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
applying the AES process to said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
and
reconverting said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
into the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
to obtain an encrypted state matrix (CB).

156 more elements

A device, comprising:

one or more memories;
and
one or more processing devices including Advanced Encryption Standard (AES) cyphering circuitry, wherein the one or more memories and the AES cyphering circuitry are configured to protect data stored in a hardware data media from attack by:
mapping polynomial representations in an AES finite field of bytes of a state matrix into respective fields of polynomials computed with respect to one of a plurality of irreducible polynomials, generating moved polynomials;
applying Chinese-Remainder-Theorem (CRT) based mapping to the generated moved polynomials, generating a polynomial representing the state matrix in a polynomial ring;
applying an AES process to the polynomial representing the state matrix in the polynomial ring, generating an AES-processed polynomial;
and
converting the AES-processed polynomial into the AES finite field, generating an AES-processed state matrix, wherein the one or more memories and the one or more processing devices are configured to:
obtain the polynomial representation (bi(x)) in the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
of the input bytes (bi) of said state matrix (B);
provide the plurality of irreducible polynomials (fi(y)) and map, using a moving map (ψi), each polynomial (bi(x)) of said polynomial representation into the respective field of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
computed with respect to one of said irreducible polynomials (fi(y)), to obtain the respective moved polynomials (αi(y));
map said moved polynomials (αi(y)) into a polynomial (a(z)) of the polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
,
obtained by applying an isomorphism (ω) between the direct product of said fields of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
and said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
based upon the Chinese remainder theorem (CRT), said polynomial (a(z)) representing the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
apply the AES process to said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
and
reconvert said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
into the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
to obtain an encrypted state matrix (CB).

158 more elements

A system, comprising:

an interface configured to receive and output data;
and
Advanced Encryption Standard (AES) cyphering circuitry coupled to the interface and configured to protect data stored in a hardware data media from attack by:
maping polynomial representations in an AES finite field of bytes of a state matrix into respective fields of polynomials computed with respect to one of a plurality of irreducible polynomials, generating moved polynomials;
applying Chinese-Remainder-Theorem (CRT) based mapping to the generated moved polynomials, generating a polynomial representing the state matrix in a polynomial ring;
applying an AES process to the polynomial representing the state matrix in the polynomial ring, generating an AES-processed polynomial;
and
converting the AES-processed polynomial into the AES finite field, generating an AES-processed state matrix wherein the cyphering circuitry is configured to:
obtain the polynomial representation (b (x)) in the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
of the input bytes (bi) of said state matrix (B);
provide the plurality of irreducible polynomials (fi(y)) and map, using a moving map (ψi), each polynomial (bi(x)) of said polynomial representation into the respective field of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
computed with respect to one of said irreducible polynomials
(fi(y)), to obtain the respective moved polynomials (αi(y));
map said moved polynomials (αi(y)) into a polynomial (a(z)) of the polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
,
obtained by applying an isomorphism (ω) between the direct product of said fields of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
and said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
based upon the Chinese remainder theorem (CRT), said polynomial (a(z)) representing the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
apply the AES process to said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
and
reconvert said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
into the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
to obtain an encrypted state matrix (CB).

159 more elements

A non-transitory computer-readable medium having contents which configure an Advanced Encryption Standard (AES) cyphering circuit to protect data stored in a hardware data media from attack by performing a method, the method comprising:

mapping polynomial representations in an AES finite field of bytes of a state matrix into respective fields of polynomials computed with respect to one of a plurality of irreducible polynomials, generating moved polynomials;
applying Chinese-Remainder-Theorem (CRT) based mapping to the generated moved polynomials, generating a polynomial representing the state matrix in a polynomial ring;
applying an AES process to the polynomial representing the state matrix in the polynomial ring, generating an AES-processed polynomial;
and
converting the AES-processed polynomial into the AES finite field, generating an AES-processed state matrix, wherein the method includes:
obtaining the polynomial representation (bix)) in the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
of the input bytes (bi) of said state matrix (B);
providing the plurality of irreducible polynomials (i((y)) and mapping, using a moving map (ψi) each polynomial (bi(x)) of said polynomial representation into the respective field of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
computed with respect to one of said irreducible polynomials
(fi(y)), to obtain the respective moved polynomials (αi(y));
mapping said moved polynomials (αi(y)) into a polynomial (a(z)) of the polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
,
obtained by applying an isomorphism (ω) between the direct product of said fields of polynomials
(
Z
2
⁡
[
y
]
(
f
i
⁡
(
y
)
)
)
and said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
based upon the Chinese remainder theorem (CRT), said polynomial (a(z)) representing the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
applying the AES process to said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
;
and
reconverting said polynomial (a(z)) that represents the state matrix (B) in said polynomial ring
(
Z
2
⁡
[
z
]
(
p
⁡
(
z
)
)
)
into the AES finite field
(
Z
2
⁡
[
x
]
(
r
⁡
(
x
)
)
)
to obtain an encrypted state matrix (CB).

156 more elements

Dependencies are inferred from the claim text.

Facts

Application: 14/660,569Filed 17 Mar 2015
Priority: IT TO2014A024324 Mar 2014
Published: US 2015/0270967 A124 Sep 2015
Granted: 23 Aug 2016
Term ends: Not estimatedThe source records don’t support an estimate.

Classification7 codes

H04L 9/3093
Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy: involving…
H04L 9/003
Countermeasures against attacks on cryptographic mechanisms: for power analysis, e.g. differential power analysis [DPA] or simple power analysis [SPA]
H04L 9/008
Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols: involving homomorphic…
H04L 9/0631
Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation: substitution permutation…