Introduction Cryptographic Background QMLE and Cryptography Inhomogeneous QMLE Homogeneous QMLE Conclusion

Charles Bouillaguet

Description

Introduction Cryptographic Background QMLE and Cryptography Inhomogeneous QMLE Homogeneous QMLE Conclusion Quadratic Maps Linear Equivalence Charles Bouillaguet Université de Versailles Saint-Quentin Versailles, France Séminaire des candidats du LIFL 22–23 Mars 2012

• séminaire des candidats du lifl


• ?ij ·


• qmle homogeneous


• matrix equivalence


• introducing quadratic


• invertible matrix


• maps

Sujets

• Versailles
• Matrix equivalence
• Invertible matrix

Informations

• Publié par: pefav
• Publié le: 01 mars 2012
• Nombre de lectures: 12
• Langue: English
• Poids de l'ouvrage: 3 Mo

Extrait

nIrtdocuitnorCpyotrgpaihcaBkcrguondMQELnadrCpyotrgpayhnIohomegenuosMQELoHomegen QuadraticMapsLinearEquivalence CharlesBouillaguet UniversitédeVersaillesSaint-Quentin Versailles,France SéminairedescandidatsduLIFL 22–23Mars2012 uosMQELoCcnulisno

nIt B or a ud c tc k oin ot rCy B p a ot s g i ar c hp s i : caBc M gk a or t u r n i d x Q E M q EL u a i n v d a C l yr e n A (x)= ∑ A i ∙ x i 1 = i tpo n g c arp e yhnIohm A and B areequivalentmatricesiff: A =◦ T invertiblematrix goneoesu B B MQEL Computationalproblem: A , B −→ S , T oHomegenuosMQELoCn n (x)= ∑ B i ∙ x i 1 = i ◦ S invertiblematrix lcsuoin

nIt B or a ud c tc k oin ot rCy B p a ot s g i ar c hp s i : caBc M gk a or t u r n i d x Q E M q EL u a i n v d a C l yr e n A (x)= ∑ A i ∙ x i 1 = i tpo n g c arp e yhnIohm A and B areequivalentmatricesiff: − ◦ 1 T invertiblematrix A = goneoesu B B MQEL Computationalproblem: A , B −→ S , T oHomegenuosMQELoCn n (x)= ∑ B i ∙ x i i1 = ◦ S invertiblematrix lcsuoin

CnoitcudortnI ψ nn (x)= ∑∑ α ij ∙ x i x j i=1j=i I Quadratic case( A n (x)= ∑ A i ∙ x i 1=i I Linear γ + i x ∙ i β 1 = i ∑ n + :)spamcitardauqsuoenegomoh ni :)secirtam(esac spaMcitardauQgnicudortnI noisulcnoCELMQsuoenegomoHELMQsuoenegomohnIyhpargotpyrCdnaELMQdnuorgkcaBcihpargotpyr

:)secirtam(esac ψ nnn (x)= ∑∑ α ij ∙ x i x j + ∑ β i ∙ x i + γ i=1j=ii=1 I Quadratic case(inhomogeneousquadraticmaps): A n (x)= ∑ A i ∙ x i 1=i I Linear spaMcitardauQgnicudortnI noisulcnoCELMQsuoenegomoHELMQsuoenegomohnIyhpargotpyrCdnaELMQdnuorgkcaBcihpargotpyrCnoitcudortnI