こんにちは、ヒロキュレです。新しいバランスを紹介します。アンバラストアウェルハウンドミネガーを使用します。コーションドリンクキュアリー・ヨーグイこの職業は安ひくりきます。ユータロー、キヨーグラー、用意した書きです。まず、このリサーチのコントロビューションを紹介します。マジュバレート・パブリックキークリプトシステムキャンディデートのポストコンターンプクリプトシステムユータロー、ヨーグイはマジュバレート・シュニチャーを Genealusでの一つ、新しいバランスを紹介しました。ここで、ユータロー、キュアリンク、ユータロー、キュアリンク、ユータロー、キュアリンク、マジュバレートを紹介します。バランスはCPr بهりゃんとユータロー、キュアリー、キュアリンク、リリースはルーバーワー、キュアリースはクリプトシステム、キュアリー、キュアリンク、プロジェクトは50%-70%のプロジェクトです。これが私のプレゼンテーションのアウトラインです。まず、パブリッキークリプトシステムについてお話しします。ポストコンタムクリプトグラフィーはクリプトシステム、コンタムコンピューターのセキューアグラフィーです。そして、このような数人がいます。このプレゼンテーションについてお話しさせております。これがマルチヴァリア8コロナウイ hito polydomiaのクリプトグラフィーとしてそれらのM-Qプログラムについてお話しします。このプレゼンテーションについてお話しします。マルチヴァリアアルコロティクトシステムについてN パブリッキークリプトシステムでN パブリッキークリプトシステムでN パブリッキークリプトシステムでM イケーションでFX is equal to 0, this program is proven to be NP-complete and S is considered to besecure against quantum attacks, attackers.Next about your V signature scheme.Ambarastor Oil and Vinegar, which is called your V, is one of themarch-valid signature schemes and it has withstood various attacks for about 20 years.Actually, Rainbow, which is one of the variants of your V, was selected as one of the third round finalists of the NIST PQC project.Your V is highly evaluated for its small signature and short execution time, but it has a program that itspublic size is much larger than other candidates of PQC.Here, we briefly explained the key generation step of your V.First, we generate an easily invertible quadratic map F such that each polynomial FK is designed to be this form.At least one variable of each quadratic term is from X1 to XV.Here, our V is said to be equal to N-M.Second, randomly choose an invertible linear map S in order to hide the structure of F.Finally, the quadratic map P is given by composing F and S.And then, the public key is P and the secret key is F and S.In your V, given a message M to be signed, we generate the signature S by computing S inverse F inverse M.And verification is performed by confirming whether M equals PS or not.Here, I explain a way of inverting F.First, we randomly fix the values from X1 to XV.And then, the remaining system becomes a linear system of M equations in M variables due to the structure of the central map F.And we can solve it easily.If there is no solution to this equation, then return to step 1 and choose new random values.This is an example for the central map F of your V.Here, Q equals 3, N equals 4, M equals 2, V equals 2.Actually, these two polynomials F1 and F2 do not involve quadratic terms of X3 and X4.Let me solve this equation Fx equals 01.First, we randomly fix X1 and X2 to 02.Then, the polynomial becomes a linear system and X3 and X4 are easily found to be 12.As a result, a solution of this system is 0212.Next, I introduce the representation matrices for the public and the secret keys of your V.When we assume the order of the finite field is O,the polynomial Fy of the central map F is represented by an n times n symmetric matrix Fy, like this.And then, every lower right sub-matrix of Fy becomes 0 matrix,since this part represents coefficients of quadratic terms in n variables from Xv plus1 to Xn.The linear map S is also represented by an n times n matrix S, like this.And furthermore, the quadratic polynomial Pi of the secret public key P is represented by an n times n symmetric matrix Pi.This Pi is obtained by S transports FyS from the equation P equals Fs.Next, about our proposed quotient ring UV.Here, I introduce polynomial matrices.Let L be a positive integer and F be a polynomial in Fqx with a degree L.Then, for any element G in the quotient ring FqxF,we can uniquely define L times L matrix Pi GF over Fq,satisfying this equation.For example, if Q equals 2, F equals X cubed plus X plus1,and then, for any element G equals AX squared plus BX plusC.Pi GF is determined like this form.Here, this matrix can be represented by only 3 elements A, B, C.And so, if we can apply such a Pi to the representation matrices Pi for the public key of UV,then we will be able to reduce the public key size.From the definition of the polynomial matrices,the map from G to Pi GF is an injective ring form of this, like this.So, if we assume that the secret key of UV are set as block Pi GF matrices,which is block matrices whose every component corresponds to Pi GF.And we then wonder if the public key of Pi are also block Pi GF matrices or not.But to compute the public key Pi, S is transposed like this.So, for that Pi becomes block Pi GF matrices,this Pi GF must be stable under the transpose operation.To solve this problem, we introduced the concept of L times L invertible matrix W such thatfor any G in FQXF,W Pi G is symmetric.Here, we suppose that FI are constructed as block W Pi GF matrices,and S is constructed as block Pi matrix,then through the transformation like this,we obtain that Pi are block W Pi GF matrices.Now I showed that actually there exists such a matrix W.This proposition shows that if F equals X to the power of L minus A,X to the power of I minus 1,and W is L times L matrix like this form.And then for any G in the quotient ring,W Pi GF is symmetric.Actually,if Q equals 2 and F equals X cubed plus X plus 1,then for any element,G equals X squared plus P X plus G.Pi GF is determined like this,and W Pi GF becomes symmetric by using W,determined by this statement.In the case of F equals X to the power of L minus 1,then the matrix Pi GF is a circular matrix like this.Actually,there exists a variant of UV using circular matriceswhich is called by block anti-circulant UV BSUV.BSUV reduces the power key size by applying these circular matrices.But the tag utilizing the property of the circular matrices was proposed in 2020.The tag on BSUV utilizes the property thatsome of the elements of every row and columnis the same as those of other rows and columns.By using this property,we can execute the transformation like this.For any circular matrix,we multiply this symmetric matrixwho's every element of the first row and column is 1and other diagonal elements are minus 1from both sides,and then it becomes this formwho's every element of the first row and columnis 0 except the 1 1 element.About this security problem,in this problem,we show that if X is a reducible polynomialand W is an invertible matrixthat makes W Pi GF symmetricthen there is no L times L matrix Land IJ such thatfor any G in the quotient ringand the IJ element of L transposeW Pi GF L equals 0.This theorem indicates thatif we choose F as anreducible polynomial in a proposed variantthen it will be resistant to the attack on BSUV.On the other hand,if F is reduciblethen there exists such a transformation.Actually,in the case ofSagran matrices, X to the power of L minus 1is reduciblelike thisand thus there exists atransformationshown in the previous page.Now we explain the key generationof our proposed scheme QRUV.First,we choose anreducible polynomial F of the formX to the power of Lminus X to the power of I minus 1and an L times L matrixWsuch that for any element Gin the quotient ringW Pi GF is symmetric.Second,represidential matricesFI for the central mapare designed to bebrokeW Pi GF matricesand AC is designed to bebroke-fine matrix.Then,therepresidential matrices areW Pi GFcomputed by this equationPi equals S transposeFiSandevery Pi becomesbrokeW Pi GF matrixlike this figureevery block ofPi isW Pi matrixandit can be represented byonly L elements.N times N matrixPican be represented byonly N squaredover L elements.As a result,this reduces thepublicity size.In this research,we propose parametersof QRUVconsidering sometransformations overthe OFF QL.In this table,we comparepublicity and signature sizefor our proposedQRUV parametersandwith those ofcompressed rainbowwhich isoptimized variant of rainbowfor security level 1,3and 5for the NISP QC project.As a result,thepublicity size of QRUVcan be reducedby approximatelyfrom 50%to 70%compared with that ofcompressed rainbow,at the cost ofa small increasein the signature size.Please note thatalthough thepublicity size could be furtherreduced bysetting the block size L largerand enlarging the block sizewould likely increasethe signature size andexecution time.About the security of QRUVwe confirm that theproposed parameterssatisfies the requirementsfor each security levellike this.In this table,we considerthe complexity ofexisting attacksand some attacksutilizingthe quotient ring structureof QRUVsuch as this pullbackand lifting attacks.Four more detailsPlease see table 4in the procedure.Finally,we concludethis presentation.In this research,we proposea new variant of your V usingfor nominal matricesand QRUVWe use thepublicity sizefrom 50 to 70%compared with rainbow.Our future bugs wereextending QRUV tomaterial version of theQR rainbow andoptimizingimplementations.That's all.Thank you for listening.