{"title":"对最优扩展字段中的算法的体系结构支持","authors":"J. Großschädl, Sandeep S. Kumar, C. Paar","doi":"10.1109/ASAP.2004.10004","DOIUrl":null,"url":null,"abstract":"Public-key cryptosystems generally involve computation-intensive arithmetic operations, making them impractical for software implementation on constrained devices such as smart cards. We investigate the potential of architectural enhancements and instruction set extensions for low-level arithmetic used in public-key cryptography, most notably multiplication in finite fields of large order. The focus of the present work is directed towards a special type of finite fields, the so-called optimal extension fields GF(p/sup m/) where p is a pseudo-Mersenne (PM) prime of the form p = 2/sup n/ - c that fits into a single register. Based on the M/PS32 instruction set architecture, we introduce two custom instructions to accelerate the reduction modulo a PM prime. Moreover, we show that the multiplication in an optimal extension field can take advantage of a multiply/accumulate unit with a wide accumulator so that a certain number of 64-bit products can be summed up without overflow. The proposed extensions support a wide range of PM primes and allow a reduction modulo 2/sup n/ - c to complete in only four clock cycles when n /spl les/ 32.","PeriodicalId":120245,"journal":{"name":"Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"Architectural support for arithmetic in optimal extension fields\",\"authors\":\"J. Großschädl, Sandeep S. Kumar, C. Paar\",\"doi\":\"10.1109/ASAP.2004.10004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Public-key cryptosystems generally involve computation-intensive arithmetic operations, making them impractical for software implementation on constrained devices such as smart cards. We investigate the potential of architectural enhancements and instruction set extensions for low-level arithmetic used in public-key cryptography, most notably multiplication in finite fields of large order. The focus of the present work is directed towards a special type of finite fields, the so-called optimal extension fields GF(p/sup m/) where p is a pseudo-Mersenne (PM) prime of the form p = 2/sup n/ - c that fits into a single register. Based on the M/PS32 instruction set architecture, we introduce two custom instructions to accelerate the reduction modulo a PM prime. Moreover, we show that the multiplication in an optimal extension field can take advantage of a multiply/accumulate unit with a wide accumulator so that a certain number of 64-bit products can be summed up without overflow. The proposed extensions support a wide range of PM primes and allow a reduction modulo 2/sup n/ - c to complete in only four clock cycles when n /spl les/ 32.\",\"PeriodicalId\":120245,\"journal\":{\"name\":\"Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-09-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ASAP.2004.10004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ASAP.2004.10004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Architectural support for arithmetic in optimal extension fields
Public-key cryptosystems generally involve computation-intensive arithmetic operations, making them impractical for software implementation on constrained devices such as smart cards. We investigate the potential of architectural enhancements and instruction set extensions for low-level arithmetic used in public-key cryptography, most notably multiplication in finite fields of large order. The focus of the present work is directed towards a special type of finite fields, the so-called optimal extension fields GF(p/sup m/) where p is a pseudo-Mersenne (PM) prime of the form p = 2/sup n/ - c that fits into a single register. Based on the M/PS32 instruction set architecture, we introduce two custom instructions to accelerate the reduction modulo a PM prime. Moreover, we show that the multiplication in an optimal extension field can take advantage of a multiply/accumulate unit with a wide accumulator so that a certain number of 64-bit products can be summed up without overflow. The proposed extensions support a wide range of PM primes and allow a reduction modulo 2/sup n/ - c to complete in only four clock cycles when n /spl les/ 32.