# US 2021/0344476 A1 · A Cryptographic System and Method > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2021/0344476 A1 - Document ID: US20210344476A1 - Status: Published application - Kind: A1 - Application number: 16/268,098 - Filed: 2018-12-21 - Published: 2021-11-04 - Earliest claimed: 2018-12-21 - Assignees: Communique Laboratory Inc. - Applicants: Communique Laboratory Inc. - Inventors: Sergey Bezzateev; Sergey Strakhov; Andrew Cheung - Web page: https://patentgrep.com/patent/US20210344476A1 ## CPC - H04L 9/002: {Countermeasures against attacks on cryptographic mechanisms (network architectures or network communication protocols for protection against malicious traffic H04L63/1441)} - G06F 21/602: {Providing cryptographic facilities or services} - H04L 9/3026: {details relating to polynomials generation, e.g. generation of irreducible polynomials} - H04L 9/3247: {involving digital signatures} - H04L 9/50: {using hash chains, e.g. blockchains or hash trees} - H04L 9/0852: {Quantum cryptography (transmission systems employing electromagnetic waves other than radio waves, e.g. light, infrared H04B10/00; wavelength-division multiplex systems H04J14/02; WDM arrangements H04J14/03)} - H04L 9/304: {based on error correction codes, e.g. McEliece} - H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract A system and method for encryption of data. The system and method utilizes a cryptographic function that provides asymmetric encryption/decryption and digital signing capabilities that are hardened against cyber attack from quantum computers. ## Claims ### Claim 1 A cryptographic system, comprising: an input device configured to receive data to be encrypted, decrypted, signed, and verified; and a processor configured to receive the data to be encrypted, decrypted, signed, and verified and to encrypt, decrypted, signed, and verified the data using instructions from a cryptographic engine; wherein the instructions, when executed, cause encryption, decrypted, signed, and verified of the data using a code-based encryption scheme based on binary irreducible Goppa code in which a support set consists of rational functions with a degree of a denominator not greater than a degree of a Goppa polynomial and wherein the encrypted data is protected against an attack from a quantum computer. ### Claim 2 (depends on 1) The cryptographic system of claim 1, wherein the instructions when executed also use the Goppa code in a weighted Hamming metric. ### Claim 3 (depends on 1) The cryptographic system of claim 1, wherein the Goppa polynomial has the degree not less than r, where r is a maximum degree of a denominator of a rational function over F2m[x] in the set of L, where L is a set of rational functions of degree not greater than r where r is greater than to 1, and with coefficients from a finite field GF(2m). ### Claim 4 (depends on 3) The cryptographic system of claim 3, wherein the instructions when executed also uses the Goppa code in a weighted Hamming metric. ### Claim 5 (depends on 4) The cryptographic system of claim 4, wherein the code based encryption scheme is a generalized (L, G) code in which a set of proper rational functions (L) over (F2m[x]) are chosen, wherein the denominators of L are various irreducible polynomials from F2m[x] with degree less than or equal to r where r is greater than 1, and where the numerators are formal derivatives of the denominators. ### Claim 6 (depends on 5) The cryptographic system of claim 5, wherein the instructions when executed further generate a private key satisfying the relationship K={S, P, L, G(x)} wherein: a parity check matrix H is generated for binary generalized Goppa code with Goppa polynomial G(x) of degree equal to t, where G(x) is an irreducible polynomial with coefficients from a Galois field GF(2m) locator polynomials for support set L of binary generalized (L, G) code are generated as irreducible polynomials with coefficients from the field GF(2m) having a degree not greater than r; a vector length set N={n1, n2, . . . , nr} of Goppa code is generated, where ni=I2m(i), i=1, . . . , r, and n=Σi=1r ni, where I2m(i) is a number of irreducible polynomials of degree i with coefficients from the field GF(2m); a vector position weight set W={w1, w2, . . . , wr} is generated, where the first n1 positions have weight w1=1, the second n2 positions have weight w2=2, and the last nr positions have weight wr=r; a random mt×mt non-singular matrix S is selected, where deg G(x)=t; a random n×n permutation matrix P is selected; and a public key H*=S×H×P is computed. ### Claim 7 A cryptographic system, comprising: an input device configured to receive data to be encrypted, decrypted, signed, and verified; and a processor configured to receive the data to be encrypted, decrypted, signed, and verified and to encrypt, decrypted, signed, and verified the data using instructions from a cryptographic engine; wherein the instructions, when executed, cause encryption, decrypted, signed, and verified of the data using a code-based encryption scheme based on binary irreducible Goppa code in which locator polynomials for support set L have degree not greater than r, where r is the maximum degree of the denominator of a rational function over F2m[x] and wherein the encrypted, decrypted, signed, and verified data is protected against attack from a quantum computer. ### Claim 8 (depends on 7) The cryptographic system of claim 7, wherein the instructions when executed also uses the Goppa code in a weighted Hamming metric. ### Claim 9 A method of encrypting, decrypted, signed, and verified data, comprising the steps of: receiving data at an input device; and forwarding the data to a processor for encrypting, decrypted, signed, and verified the data using instructions provided by a cryptographic engine; wherein the instructions, when executed, encrypt, decrypted, signed, and verified the data using a code-based encryption scheme based on binary irreducible Goppa code in which a support set consists of rational functions with a degree of a denominator not greater than the degree of Goppa polynomial and wherein the encrypted, decrypted, signed, and verified data is protected against attack from a quantum computer. ### Claim 10 (depends on 9) The method of claim 9, wherein the instructions when executed also use the Goppa codes in a weighted Hamming metric. ### Claim 11 (depends on 9) The method of claim 9, wherein the polynomials have degree not greater than r, where r is the maximum degree of the denominator of a rational function over F2m[x] in the set of L, where L is a set of rational functions of degree not greater than r where r is greater than 1, and with coefficients from a finite field GF(2m). ### Claim 12 (depends on 11) The method of claim 11, wherein the instructions when executed also use the Goppa codes in a weighted Hamming metric. ### Claim 13 (depends on 12) The method of claim 12, wherein the code based encryption scheme is a generalized (L, G) code in which a set of proper rational functions (L) over (F2m[x]) are chosen, wherein the denominators of L are various irreducible polynomials from F2m[x] with degree less than or equal to r where r is greater than 1, and where the numerators are formal derivatives of the denominators. ### Claim 14 (depends on 13) The method of claim 13, wherein the instructions when executed further generate a private key satisfying the relationship K={S, P, L, G(x)} wherein: a parity check matrix H is generated for binary generalized Goppa code with Goppa polynomial G(x) of degree equal to t, where G(x) is an irreducible polynomial with coefficients from a Galois field GF(2m); locator polynomials for support set L of binary generalized (L, G) code are generated as irreducible polynomials with coefficients from the field GF(2m) having a degree not greater than r; a vector length set N={n1, n2, . . . , nr} of Goppa code is generated, where ni=I2m(i), i=1, . . . , r, and n=Σi=1r ni, where I2m(i) is a number of irreducible polynomials of degree i with coefficients from the field GF(2m); a vector position weight set W={w1, w2, . . . , wr} is generated, where the first n1 positions have weight w1=1, the second n2 positions have weight w2=2, and the last nr positions have weight wr=r; a random mt×mt non-singular matrix S is selected, where deg G(x)=t; a random n×n permutation matrix P is selected; and a public key H*=S×H×P is computed. ### Claim 15 A method of encrypting data, comprising the steps of: receiving data to be encrypted at an input device; and providing the data to be encrypted to a processor for encrypting that data using instructions from a cryptographic engine; wherein the instructions, when executed, cause encryption of the data using a code-based encryption scheme based on binary irreducible Goppa code in which locator polynomials for support set L have degree not greater than r, where r is the maximum degree of the denominator of a rational function over F2m[x] and wherein the encrypted data is protected against attack from a quantum computer. ### Claim 16 (depends on 15) The method of claim 15, wherein the instructions when executed also use the Goppa codes in a weighted Hamming metric. ### Claim 17 (depends on 9) The method of claim 9 wherein the data to be encrypted is a message vector to be securely transmitted from a sender to a receiver. ### Claim 18 (depends on 15) The method of claim 15 wherein the data to be encrypted is a message vector to be securely transmitted from a sender to a receiver. ### Claim 19 (depends on 9) The method of claim 9 wherein the data when encrypted is a digital signature. ### Claim 20 (depends on 15) The method of claim 15 wherein the data when encrypted is a digital signature.