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ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.1 AN EXAMPLE OF AN ELLIPTIC CURVE GROUP OVER F2M 4.1 An Example of an Elliptic Curve Group over F2m. As a very small example, consider the field F 2 4, defined by using polynomial representation with the irreducible polynomial f (x) = x 4 + x + 1. The element g = (0010) is a generator for the field . The powers of gare:
BLACKBERRY CERTICOM CRYPTOGRAPHY AND KEY MANAGEMENT BlackBerry Certicom’s code signing key server enables Tier 1s and OEMs to sign and secure their device software with traditional or quantum resistant cryptography, protecting signing keys with a hardened key management server. This enables a robustly secured device boot chain. Learn More. 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
BLACKBERRY CERTICOM SECURITY CREDENTIAL MANAGEMENT SYSTEM BlackBerry Certicom’s Security Credential Management System (SCMS) services for securing vehicle-to-vehicle and vehicle-to-infrastructure, or V2X, communication are based on industry technology standards and trust service principles. Our SCMS platform is built to IEEE 1609.2 and CAMP specifications and offers trusted security credentials toABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.1 AN EXAMPLE OF AN ELLIPTIC CURVE GROUP OVER F2M 4.1 An Example of an Elliptic Curve Group over F2m. As a very small example, consider the field F 2 4, defined by using polynomial representation with the irreducible polynomial f (x) = x 4 + x + 1. The element g = (0010) is a generator for the field . The powers of gare:
BLACKBERRY CERTICOM CRYPTOGRAPHY AND KEY MANAGEMENT BlackBerry Certicom’s code signing key server enables Tier 1s and OEMs to sign and secure their device software with traditional or quantum resistant cryptography, protecting signing keys with a hardened key management server. This enables a robustly secured device boot chain. Learn More. 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
BLACKBERRY CERTICOM SECURITY CREDENTIAL MANAGEMENT SYSTEM BlackBerry Certicom’s Security Credential Management System (SCMS) services for securing vehicle-to-vehicle and vehicle-to-infrastructure, or V2X, communication are based on industry technology standards and trust service principles. Our SCMS platform is built to IEEE 1609.2 and CAMP specifications and offers trusted security credentials toCERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sTHE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm CERTICOM SECURITY FOR RFID PRODUCT AUTHENTICATION Proven Security for the Supply Chain and Anti-Counterfeiting Prevention. Certicom Security for RFID Product Authentication addresses critical infrastructure, privacy, security, and efficiency requirements for the pharmaceutical, medical supply, cosmetics, machine peripherals, document management, and collectibles industries.CERTICOM DEVICE CA
Certicom’s certificate-based authentication quickly and efficiently prevents unauthorized devices from accessing restricted services. With the Certicom Device Certificate Service, device manufacturers order certificates in bulk by providing Certicom with a list of MACECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itselfMQV - CERTICOM
MQV Key Agreement. The MQV elliptic curve key agreement method is used to establish a shared secret between parties who already possess trusted copies of each other’s static public keys. Both parties still generate dynamic public and private keys and then exchangepublic keys.
2.4 QUIZ 1 - CERTICOM 1. Does the elliptic curve equation y 2 = x 3 - 7x - 6 over real numbers define a group? 2. What is the additive identity of regular integers? 3. Is (4,7) a point on the elliptic curve y 2 = x 3 - 5x + 5 over real numbers? 4. What are the negatives of the following elliptic curve points over real numbers? BLACKBERRY CERTICOM SECURITY CREDENTIAL MANAGEMENT SYSTEM BlackBerry Certicom’s Security Credential Management System (SCMS) services for securing vehicle-to-vehicle and vehicle-to-infrastructure, or V2X, communication are based on industry technology standards and trust service principles. Our SCMS platform is built to IEEE 1609.2 and CAMP specifications and offers trusted security credentials toCERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this BLACKBERRY CERTICOM CRYPTOGRAPHY AND KEY MANAGEMENT BlackBerry Certicom’s code signing key server enables Tier 1s and OEMs to sign and secure their device software with traditional or quantum resistant cryptography, protecting signing keys with a hardened key management server. This enables a robustly secured device boot chain. Learn More. 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
BLACKBERRY CERTICOM SECURITY CREDENTIAL MANAGEMENT SYSTEM BlackBerry Certicom’s Security Credential Management System (SCMS) services for securing vehicle-to-vehicle and vehicle-to-infrastructure, or V2X, communication are based on industry technology standards and trust service principles. Our SCMS platform is built to IEEE 1609.2 and CAMP specifications and offers trusted security credentials toCERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this BLACKBERRY CERTICOM CRYPTOGRAPHY AND KEY MANAGEMENT BlackBerry Certicom’s code signing key server enables Tier 1s and OEMs to sign and secure their device software with traditional or quantum resistant cryptography, protecting signing keys with a hardened key management server. This enables a robustly secured device boot chain. Learn More. 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
BLACKBERRY CERTICOM SECURITY CREDENTIAL MANAGEMENT SYSTEM BlackBerry Certicom’s Security Credential Management System (SCMS) services for securing vehicle-to-vehicle and vehicle-to-infrastructure, or V2X, communication are based on industry technology standards and trust service principles. Our SCMS platform is built to IEEE 1609.2 and CAMP specifications and offers trusted security credentials toCERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company's CERTICOM SECURITY FOR RFID PRODUCT AUTHENTICATION Proven Security for the Supply Chain and Anti-Counterfeiting Prevention. Certicom Security for RFID Product Authentication addresses critical infrastructure, privacy, security, and efficiency requirements for the pharmaceutical, medical supply, cosmetics, machine peripherals, document management, and collectibles industries.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite BCERTICOM DEVICE CA
Certicom’s certificate-based authentication quickly and efficiently prevents unauthorized devices from accessing restricted services. With the Certicom Device Certificate Service, device manufacturers order certificates in bulk by providing Certicom with a list of MAC CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in thisMQV - CERTICOM
MQV Key Agreement. The MQV elliptic curve key agreement method is used to establish a shared secret between parties who already possess trusted copies of each other’s static public keys. Both parties still generate dynamic public and private keys and then exchangepublic keys.
2.4 QUIZ 1 - CERTICOM 1. Does the elliptic curve equation y 2 = x 3 - 7x - 6 over real numbers define a group? 2. What is the additive identity of regular integers? 3. Is (4,7) a point on the elliptic curve y 2 = x 3 - 5x + 5 over real numbers? 4. What are the negatives of the following elliptic curve points over real numbers? BLACKBERRY CERTICOM SECURITY CREDENTIAL MANAGEMENT SYSTEM BlackBerry Certicom’s Security Credential Management System (SCMS) services for securing vehicle-to-vehicle and vehicle-to-infrastructure, or V2X, communication are based on industry technology standards and trust service principles. Our SCMS platform is built to IEEE 1609.2 and CAMP specifications and offers trusted security credentials toABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
THE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
2.4 QUIZ 1 - CERTICOM 1. Does the elliptic curve equation y 2 = x 3 - 7x - 6 over real numbers define a group? 2. What is the additive identity of regular integers? 3. Is (4,7) a point on the elliptic curve y 2 = x 3 - 5x + 5 over real numbers? 4. What are the negatives of the following elliptic curve points over real numbers? 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
THE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
2.4 QUIZ 1 - CERTICOM 1. Does the elliptic curve equation y 2 = x 3 - 7x - 6 over real numbers define a group? 2. What is the additive identity of regular integers? 3. Is (4,7) a point on the elliptic curve y 2 = x 3 - 5x + 5 over real numbers? 4. What are the negatives of the following elliptic curve points over real numbers? 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sTHE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 2.1 ELLIPTIC CURVE ADDITION: A GEOMETRIC APPROACH 2.1 Elliptic Curve Addition: A Geometric Approach. P + Q = R is the additive property defined geometrically. Elliptic curve groups are additive groups; that is, their basic function is addition. The addition of two points in an elliptic curve is defined geometrically. The negative of a point P = (xP,yP) is its reflection in the x-axis:the
BLACKBERRY CERTICOM CRYPTOGRAPHY AND KEY MANAGEMENT BlackBerry Certicom’s code signing key server enables Tier 1s and OEMs to sign and secure their device software with traditional or quantum resistant cryptography, protecting signing keys with a hardened key management server. This enables a robustly secured device boot chain. Learn More. THE GROWING IMPORTANCE OF ECC IN FIPS 140-2 The Growing Importance of ECC in FIPS 140-2-2. In the US, requirements for government security are regulated by FIPS (Federal Information Processing Standard) publications, which are developed by NIST (National Institute of Standards for Technology) for use government-wide. NIST develops FIPS when there are compelling federalgovernment
CERTICOM ECC CHALLENGE Certicom ECC Challenge Abstract Certicom is pleased to present the Certicom Elliptic Curve Cryptosystem (ECC) Challenge. The first of its kind, the ECC Challenge has been developed to increase the industry’s understanding and ITRON SECURES METERING SYSTEMS WITH CERTICOM AMI SOLUTION The utility market is evolving to become much more interactive by incorporating fine-grained, real-time data collection, and real-time management of customer devices (air conditioning, pool pumps, etc).ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
THE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
2.4 QUIZ 1 - CERTICOM 1. Does the elliptic curve equation y 2 = x 3 - 7x - 6 over real numbers define a group? 2. What is the additive identity of regular integers? 3. Is (4,7) a point on the elliptic curve y 2 = x 3 - 5x + 5 over real numbers? 4. What are the negatives of the following elliptic curve points over real numbers? 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
THE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
2.4 QUIZ 1 - CERTICOM 1. Does the elliptic curve equation y 2 = x 3 - 7x - 6 over real numbers define a group? 2. What is the additive identity of regular integers? 3. Is (4,7) a point on the elliptic curve y 2 = x 3 - 5x + 5 over real numbers? 4. What are the negatives of the following elliptic curve points over real numbers? 5.2 THE ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEM 5.2 The Elliptic Curve Discrete Logarithm Problem. In the multiplicative group Zp*, the discrete logarithm problem is: given elements r and q of the group, and a prime p, find a number k such that r = qk mod p. If the elliptic curve groups is described using multiplicative notation, then the elliptic curve discrete logarithmproblem is: given
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sTHE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 2.1 ELLIPTIC CURVE ADDITION: A GEOMETRIC APPROACH 2.1 Elliptic Curve Addition: A Geometric Approach. P + Q = R is the additive property defined geometrically. Elliptic curve groups are additive groups; that is, their basic function is addition. The addition of two points in an elliptic curve is defined geometrically. The negative of a point P = (xP,yP) is its reflection in the x-axis:the
BLACKBERRY CERTICOM CRYPTOGRAPHY AND KEY MANAGEMENT BlackBerry Certicom’s code signing key server enables Tier 1s and OEMs to sign and secure their device software with traditional or quantum resistant cryptography, protecting signing keys with a hardened key management server. This enables a robustly secured device boot chain. Learn More. THE GROWING IMPORTANCE OF ECC IN FIPS 140-2 The Growing Importance of ECC in FIPS 140-2-2. In the US, requirements for government security are regulated by FIPS (Federal Information Processing Standard) publications, which are developed by NIST (National Institute of Standards for Technology) for use government-wide. NIST develops FIPS when there are compelling federalgovernment
CERTICOM ECC CHALLENGE Certicom ECC Challenge Abstract Certicom is pleased to present the Certicom Elliptic Curve Cryptosystem (ECC) Challenge. The first of its kind, the ECC Challenge has been developed to increase the industry’s understanding and ITRON SECURES METERING SYSTEMS WITH CERTICOM AMI SOLUTION The utility market is evolving to become much more interactive by incorporating fine-grained, real-time data collection, and real-time management of customer devices (air conditioning, pool pumps, etc).CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
4.1 AN EXAMPLE OF AN ELLIPTIC CURVE GROUP OVER F2M 4.1 An Example of an Elliptic Curve Group over F2m. As a very small example, consider the field F 2 4, defined by using polynomial representation with the irreducible polynomial f (x) = x 4 + x + 1. The element g = (0010) is a generator for the field . The powers of gare:
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
4.1 AN EXAMPLE OF AN ELLIPTIC CURVE GROUP OVER F2M 4.1 An Example of an Elliptic Curve Group over F2m. As a very small example, consider the field F 2 4, defined by using polynomial representation with the irreducible polynomial f (x) = x 4 + x + 1. The element g = (0010) is a generator for the field . The powers of gare:
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
CERTICOM PROFESSIONAL SERVICES Our professionals have developed successful security solutions for numerous customers in a wide range of industries, including broadcasting, consumer and industrial device manufacturing , financial services, government and healthcare. Customers use Certicom Professional Services because they want security done right the firsttime.
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company's BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite BTHE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself ADVANCED METERING INFRASTRUCTURE Advanced Metering Infrastructure (AMI), a Secure ROI for the Utility Industry and Energy Consumer. The utility industry is on the move to modernize its meter reading and data collection system with advanced metering infrastructure. Driven by strong environmental, political and economic factors, and encouraged by legislative policies to conserve CERTICOM PLATFORMS AND PRODUCTS Certicom Platforms and Products – End of Sales and End of Life. Certicom may periodically elect to discontinue specific products or platforms. This document describes Certicom’s intended communication and transition plans for any discontinued product and platforms. The policy is intended to provide our customers with the sufficient AN INTRODUCTION TO THE USES OF ECC-BASED CERTIFICATES An Introduction to the Uses of ECC-based Certificates. Increased network use to communicate sensitive data and complete critical transactions has created a need for greater confidence in the identities of the person, computer, or services involved in the communication. Digital certificates and public-key cryptography provide an enhanced levelCERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
4.1 AN EXAMPLE OF AN ELLIPTIC CURVE GROUP OVER F2M 4.1 An Example of an Elliptic Curve Group over F2m. As a very small example, consider the field F 2 4, defined by using polynomial representation with the irreducible polynomial f (x) = x 4 + x + 1. The element g = (0010) is a generator for the field . The powers of gare:
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
ABOUT CERTICOM
About BlackBerry Certicom. Founded in 1985, the same year Elliptic Curve Cryptography (ECC) was invented, Certicom was acquired by BlackBerry in 2009. Now part of the BlackBerry Technology Solutions (BTS) business unit, BlackBerry Certicom has industry leading expertise in Elliptic Curve Cryptography and has established theworld’s largest
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company'sECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive. ZIGBEE SMART ENERGY 1.2 TEST CERTIFICATE GENERATION ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite B 4.0 ELLIPTIC CURVE GROUPS OVER F2M 4.0 Elliptic Curve Groups over F2m. There are finitely many points on a curve over F 2 m . Elements of the field F 2 m are m-bit strings. The rules for arithmetic in F 2 m can be defined by either polynomial representation or by optimal normal basis representation. Since F 2 m operates on bit strings, computers can perform arithmetic in this 2.2 ELLIPTIC CURVE ADDITION: AN ALGEBRAIC APPROACH 2.2 Elliptic Curve Addition: An Algebraic Approach. Although the previous geometric descriptions of elliptic curves provides an excellent method of illustrating elliptic curve arithmetic, it is not a practical way to implement arithmetic computations. Algebraic formulae are constructed to efficiently compute the geometricarithmetic.
4.1 AN EXAMPLE OF AN ELLIPTIC CURVE GROUP OVER F2M 4.1 An Example of an Elliptic Curve Group over F2m. As a very small example, consider the field F 2 4, defined by using polynomial representation with the irreducible polynomial f (x) = x 4 + x + 1. The element g = (0010) is a generator for the field . The powers of gare:
CERTICOM WHITEPAPER SERIES CERTICOM WHITEPAPER SERIES Automotive security and trust management: The case for PKI Jim Alfred, Vice President, BlackBerry TechnologySolutions, Certicom
CERTICOM PRODUCTS
Certicom’s new Asset Management System is a comprehensive infrastructure solution designed to help semiconductor companies manage, secure and control manufacturing processes in a global, outsourced manufacturing environment. Some of these processes include timely, secure and reliable capture and reporting of multi-point yielddata, virtual
CERTICOM PROFESSIONAL SERVICES Our professionals have developed successful security solutions for numerous customers in a wide range of industries, including broadcasting, consumer and industrial device manufacturing , financial services, government and healthcare. Customers use Certicom Professional Services because they want security done right the firsttime.
CERTICOM® KEY MANAGEMENT As a cost-effective factory provisioning system, Certicom KeyInject protects against the growing device cloning threat from third party contract manufacturers. It is a core component of the Certicom Trust Infrastructure and focuses in controlling and reporting on the volume of keyed devices at manufacture time. This helps protect a company's BLACKBERRY CERTICOM OFFICIAL HOME PAGE Industry Solutions. With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions. Automotive.ECC TUTORIAL
ECC cryptography for secure devices & software from Certicom addresses wireless security, anti-cloning, VoIP, DRM, & IPSec, along with government requirements like FIPS 140-2 and Suite BTHE BASICS OF ECC
NIST, ANSI and IEEE have standardized ECC, as detailed below. The National Institute of Standards and Technology (NIST) issues standards that mandate what cryptographic algorithms US Federal Government agencies can use, such as: Federal Information Processing Standards (FIPS) 186-2: The Digital Signature Standard (DSS).This standardizes the Elliptic Curve Digital Signature Algorithm CERTICOM DEVICE CERTIFICATION AUTHORITY FOR ZIGBEE SMART The ZigBee Smart Energy PKI uses Elliptic Curve Qu Vanstone (ECQV) implicit certificates, which serve as an identity certificate for each ZigBee Smart Energy device as it gets enrolled on the network. Each certificate binds a device MAC address and manufacturing identifier to an ECC key pair, allowing the device to uniquely authenticate itself ADVANCED METERING INFRASTRUCTURE Advanced Metering Infrastructure (AMI), a Secure ROI for the Utility Industry and Energy Consumer. The utility industry is on the move to modernize its meter reading and data collection system with advanced metering infrastructure. Driven by strong environmental, political and economic factors, and encouraged by legislative policies to conserve CERTICOM PLATFORMS AND PRODUCTS Certicom Platforms and Products – End of Sales and End of Life. Certicom may periodically elect to discontinue specific products or platforms. This document describes Certicom’s intended communication and transition plans for any discontinued product and platforms. The policy is intended to provide our customers with the sufficient AN INTRODUCTION TO THE USES OF ECC-BASED CERTIFICATES An Introduction to the Uses of ECC-based Certificates. Increased network use to communicate sensitive data and complete critical transactions has created a need for greater confidence in the identities of the person, computer, or services involved in the communication. Digital certificates and public-key cryptography provide an enhanced level* SOLUTIONS
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With over 500 patents covering Elliptic Curve Cryptography (ECC), BlackBerry Certicom provides device security, anti-counterfeiting, and product authentication to deliver end-to-end security with managed public key infrastructure, code signing and other applied cryptography and key management solutions.Automotive
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V2X communication allows for real-time communication between vehicles and infrastructure. The success of V2X technology depends on trusted verification of each and every message exchanged between cars andinfrastructure.
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ASSET MANAGEMENT SYSTEM Deployed in production environments around the world, AMS helps OEMs and device manufacturers to secure their global supply chains through a secure and traceable process. Learn Secure Provisioning SOFTWARE DEVELOPMENT KITS Security Builder SDKs help OEMs and enterprises quickly and easily add security to their embedded devices and applications. Application developers can secure their devices with proven, standards-based crypto implementations without open source vulnerabilities andencumbrances.
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